2022-2023 Department of Mathematics Events

July, 2023

PhD Dissertation Defense (Hybrid)

Speaker:  Bishal Dhakal, Ph.D. Candidate, Florida Atlantic University

Title:   Solving V.I. Arnold's Problem about Asymptotic Enumeration of Morse Functions on the 2-Sphere: A Combinatorial and Analytic Approach with Computer Assisted Proofs

Co-Advisors:  Dr. Jason Mireles-James and Dr. Erik Lundberg

Abstract: The goal of this dissertation is to estimate the precise asymptotics for the number of geometric equivalence classes of Morse functions on the 2-sphere. Our approach involves utilizing the Lagrange inversion formula, Cauchy's coefficient formula, and the saddle point method for the asymptotic analysis of contour integrals to analyze the generating function derived by L. Nicolaescu, expressed as the inverse of an elliptic integral. We utilize complex analysis, nonlinear functional analysis in infinite sequence spaces, and interval arithmetic to write all the necessary MATLAB programs that validate our results. This work answers questions posed by Arnold and Nicolaescu, furthering our understanding of the topological properties of Morse functions on two-dimensional manifolds. It also demonstrates the effectiveness of a computer assisted approach for asymptotic analysis.

Zoom Meeting information:

Topic: Bishal Dhakal's Ph.D. Dissertation Defense!

Time: Jul 5, 2023, 01:45 PM Eastern Time (US and Canada)

Join Zoom Meeting

https://fau-edu.zoom.us/j/8047682050?pwd=cEh0dFFxb2lqSVdJMzJjalJuQndRUT09

Meeting ID: 804 768 2050

Passcode: F39wbA

Please contact Dr. Hongwei Long <hlong@fau.edu>  for an electronic copy of the dissertation. A hardcopy of the dissertation is not displayed in the departmental office in order to avoid multiple people touching the same hardcopy at this pandemic time.

All are cordially invited.

PhD Dissertation Defense

Speaker: Harsha Nawarathna, Ph.D. Candidate, Florida Atlantic University

Title:  Integral Input-to-Output Stability Analysis for Nonlinear Systems with Time Delays

Advisor: Dr. Yuan Wang

Abstract

Please contact Dr. Hongwei Long <hlong@fau.edu>  for an electronic copy of the dissertation. A hardcopy of the dissertation is not displayed in the departmental office in order to avoid multiple people touching the same hardcopy at this pandemic time.

All are cordially invited.

Young CryptograpHers

Shaping the Future of Cybersecurity

Young CryptograpHERS is a Cybersecurity summer camp specially designed for high school girls. Participants will be introduced to the fundamental principles of cybersecurity and learn how to apply conceptual knowledge to real-world situations. The camp will focus on Post-Quantum Cryptography, the area of math that is in charge of protecting our information in the era of quantum technology. The program includes lectures and activities by FAU faculty, alumni and speakers from industry and government. Our goal is to motivate and inspire talented students who are interested in a cybersecurity career. 

The camp is generously sponsored by a grant from NSA. This means participation is free, as the funding covers all costs for the students, including registration, catering, and camp gear! Attendance is limited and subject to availability, so apply now to take advantage of this opportunity.

Regsiter Here!

Association for Women in Mathematics (FAU Student Chapter) Teatime

Guest Speaker:  Dr. Angela Robinson, National Institute of Standards and Technology

Grab your favorite mugs and come enjoy a wonderful time with us!

The event is open to everyone!

PhD Dissertation Defense 

Speaker :  David Urizar, Ph.D. Candidate

Advisor : Dr. Zvi Rosen 

Title :  Angular Rigidity Theory in Planar Frameworks 

Abstract :    For this talk, we will briefly mention some recent relevant papers that motivated the further development of analyzing rigid frameworks using angular constraints.  We will discuss classical rigidity (using length constraints) and bearing rigidity (using directional constraints).  The object of study is called a framework, that is, mapping vertices of a graph into the real or complex plane satisfying some given set of constraints.  We will discuss a new type of angular rigidity matrix using chromatic graphs. These chromatic graphs are derived from the angle graph of a given constrained framework. We give some preliminary results as well as some characterizations on graphs with four vertices.  We also discuss a conjecture involving the rigidity matroid of an angle constrained graph.  Finally, we will give some computational results for the realization space of small graphs. 

Please contact Dr. Hongwei Long    <hlong@fau.edu>     for an electronic copy of the dissertation. A hardcopy of the dissertation is not displayed in the departmental office in order to avoid multiple people touching the same hardcopy at this pandemic time. 

Zoom Meeting information: 

https://fau-edu.zoom.us/j/5601533003?pwd=SG9PTm1FTGV6WjNhZm1oY3I3ZENDUT09 

Meeting ID: 560 153 3003 

Passcode: Hello1 

All are welcome to attend

June, 2023

MS Thesis Defense

Speaker:   Austin Lazar, Master's Candidate, Florida Atlantic University

Title: Spatial Analysis of North Atlantic Storm Trajectories 

Advisor: Dr. Yang Li 

Abstract:       Storms in the North Atlantic Ocean are observed on a continual basis yearly. Storm trajectories exhibit random behavior and are very costly to society. Data from the National Oceanic and Atmospheric Administration (NOAA) contains every storm’s track from 1851 to 2022. Data points of each storm’s track can help aid in decision making regarding their behavior. In this article, data analysis is performed on historical storm tracks during the years, 1966 to 2022, where access to satellite data is available. Analysis on this data will be used to determine if the storm’s trajectory is statistically dependent on other storms’ trajectories at varying distances in space. The proposed model is a spatial statistical model that is "fitted" on an in-sample data set to determine the spatial relationship for storm trajectories at all pair-wise directions or orientations. The model is tested on an out-of-sample data set and obtained a performance of a 58.4 root mean squared error and a 42.56 mean absolute error. 

Please contact Dr. Hongwei Long    <hlong@fau.edu>     for an electronic copy of the thesis. A hardcopy of the thesis is not displayed in the departmental office in order to avoid multiple people touching the same hardcopy at this pandemic time. 

All are cordially invited.

May, 2023

Information Session on MST in Teaching Mathematics

Topics to include course information, admission information and GeoGebra topics.

JOIN ON ZOOM

Crypto Cafe

Speaker:  Rick Hensbergen, Esther.ai, Founder

Title:   Performance of penetration testing to secure cloud-based solutions 

Abstract:   TBA

Florida's Summer Institute in Biostatistics and Data Science Program

April 2023

FAU Math Day (for high school students)

For more information and to register: https://www.math.fau.edu/mathday/index.php
REGISTRATION IS NOW OPEN!

Invariant Theory Reading Seminar 

Textbook:   Classical Invariant Theory , by Peter J. Olver, Cambridge University Press (1999).  

Refreshments will be served.

FAU MATH CLUB

Meets weekly on Wednesdays at 4:00 pm.  Starting today, FAU Math Club will meet bi-weekly in SE-43, Room 271 (Computer Lab). 
On alternating Wednesday afternoons, FAU Math Club Study Sessions will be held on SE-43, Room 215.  

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact  Adam Zaidan

Spring, 2023  FAU MATH CLUB FLYER

Analysis & Applications

Speaker:   Papiya Bhattacharjee, Ph.D.; Florida Atlantic University

Title:   Pointfree Topology and Spaces of Primes

Abstract:  A pointfree topology, also called a "frame", is a complete lattice which satisfies the frame law.  The category of frames with frame homomorphisms arise from other categories, such as topologies, commutative rings with identity, and lattice-ordered groups. In this talk the speaker will focus on the study of M-frames and its prime elements. We can start with an M-frame L, and consider the different types of prime elements, such as Min(L), Max(dL), and Max(L). We can topologize these spaces with the well-known Zariski topology (also known as hull-kernel topology) and study various topological properties such as compactness, Hausdorffness, normality, etc. This talk will focus on the topological properties of the prime spaces and the corresponding internal properties of the frame.

Crypto Cafe

Speaker:  Cariel Cohen, Chief Technology Officer, Securily

Bio:  With over 20 years of experience in the cybersecurity industry, our speaker is a co-founder and passionate coder with a love for cryptography, authentication and patents. He has extensive experience working with major public corporations, including Aqua Security, Sony Pictures, and 5B Technologies. Throughout his career, he has been dedicated to ethical hacking and compliance, ensuring that businesses remain secure and compliant in the face of emerging cybersecurity threats.

Title:  Securing Cloud Business Applications: A Practical Approach to Cybersecurity and Compliance with Cariel Cohen

Abstract:  This topic explores practical approaches to securing business applications and addressing cybersecurity and compliance challenges faced by businesses in today's dynamic digital landscape. Cariel will share insights on best practices for securing cloud workloads, data, and applications, including implementing access controls, training employees on cybersecurity awareness, and protecting data against a variety of risks. Attendees will gain valuable knowledge and practical solutions that are used in helping businesses thrive in the face of emerging cybersecurity threats and ever-changing compliance requirements.      FLYER

https://securily.com/blog/internet-security-cybersecurity-basics

To Join on Zoom : https://fau-edu.zoom.us/j/83768244916?pwd=cWNoOTlVVThGbnB1M3NzQ28vclpUdz09

MS Exam

Speaker:  Dylan Alexander, Florida Atlantic University

Title:  A Survey of Braid Groups and their Application to Cryptography 

Abstract:  In this presentation we introduce braid groups, a structure studied in algebraic topology. We discuss the conjugacy problems, a pair of computationally hard problems within the theory of braid groups thought to be hard enough to allow cryptographic primitives to be built on them. Finally, we discuss some applications of braid groups to cryptography and give examples of braid group-based cryptographic primitives. 

All are invited to attend.

FAU MATH CLUB

Meets weekly on Wednesdays at 4:00 pm.  Starting today, FAU Math Club will meet bi-weekly in SE-43, Room 271 (Computer Lab). 
On alternating Wednesday afternoons, FAU Math Club Study Sessions will be held on SE-43, Room 215.  

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact  Adam Zaidan

Spring, 2023  FAU MATH CLUB FLYER

Algebra Seminar

Speaker:  Warren McGovern, Ph.D., Florida Atlantic University Honors College

Title:  Examples of Frames, Lattice-ordered groups.

Abstract:  Over the past seminar we have seen several talks on frames. I would like to start from the beginning and talk about the main source of these examples and how algebra plays a role in them besides a lattice being a type of universal algebra.

Algebra Seminar

Speaker:  Warren McGovern, Ph.D., Florida Atlantic University Honors College

Title:  Examples of Frames, Lattice-ordered groups.

Abstract:  Over the past seminar we have seen several talks on frames. I would like to start from the beginning and talk about the main source of these examples and how algebra plays a role in them besides a lattice being a type of universal algebra.

MS Exam

Speaker:  Ali Ittayem, MS Candidate

Title: Geometric Lorentz Attractor 

Abstract: In 1963, Edward Lorentz studied a system of differential equations in connection with problems in hydrodynamics with certain parameter values. In the geometric description of the flow, there is a “strange” attractor which is not topologically structurally stable in a persistent way based on results from Guckenheimer. We will give a geometric description of the flow based upon an examination of a return map and attempt to study the geometry of this strange attractor using symbolic dynamics and the inverse limit construction of Williams. 

All are cordially invited. 

Algebra Seminar

Speaker:  Warren McGovern, Ph.D.,  Florida Atlantic University

Title:  Lattice-ordered groups

Abstract:  A history of lattice-ordered groups and its relation to M-frames.

Math Club

Speaker:  Evelyn Sander, George Mason University

Title: 3D printing chaotic attractors and other dynamical structures

Abstract:  The field of dynamical systems relies crucially on visualization. In his seminal essay that is viewed as the foundation of dynamical systems theory, Poincaré commented "one will be struck by the complexity. . ., which I am not even attempting to draw.” Indeed, without the use of computational visualization techniques, large numbers of discoveries in the field would be impossible. The technology of 3D printing allows us to go beyond the screen to create computational visualizations which we can hold in our hand and observe from all angles. In this talk, I will discuss how to use 3D printing to visualize dynamical systems, including periodic orbits,  chaotic attractors, and unstable manifolds. The talk will be accessible to undergraduates and in particular does not require prior knowledge of dynamical systems. 

Analysis and Applications Seminar

Speaker:  Evelyn Sander, George Mason University

Title:  Cyclic Symmetry Induced Pitchfork Bifurcations in the Diblock Copolymer Model

Abstract:  The Ohta-Kawasaki model for diblock copolymers exhibits a rich equilibrium bifurcation structure. Even on one-dimensional base domains the bifurcation set is characterized by high levels of multi-stability and numerous secondary bifurcation points. Many of these bifurcations are of pitchfork type, and in previous work we showed that pitchfork bifurcations are induced by a simple even or odd symmetry-breaking and can be validated using computer assisted proof. However, this is not the complete picture: many other pitchfork bifurcations do not exhibit even or odd symmetry breaking. In the current work,  we show that in these more involved cases, a cyclic group action is responsible for their existence, based on cyclic groups of even order. We present theoretical results establishing such bifurcation points and show that they can be characterized as nondegenerate solutions of a suitable extended nonlinear system, and show how these results can be validated using computer assisted proofs. 

Mathematical Sciences Colloquium

Speaker:  Batsile Tlhareskgosi, University of South Aftrica

Title:  On ideals of rings of continuous integer-valued functions on a frame

Abstract:  CLICK HERE

Crypto Cafe

Speaker:  Ryan Keegan, University of California, San Diego

Bio: Ryan Keegan is a 4th year PhD student advised by Prof. Nadia Heninger at the University of California, San Diego. His research interests include practical cryptanalysis of real-world systems, particularly problems involving lattice reduction.

Title:  Fast Practical Lattice Reduction through Iterated Compression

Abstract: We introduce a new lattice basis reduction algorithm with approximation guarantees analogous to the LLL algorithm and practical performance that far exceeds the current state of the art. We achieve these results by iteratively applying precision management techniques within a recursive algorithm structure and show the stability of this approach. We analyze the asymptotic behavior of our algorithm, and show that the heuristic running time is $O(n^{\omega}(C+n)^{1+\varepsilon})$ for lattices of dimension $n$, $\omega\in (2,3]$ bounding the cost of size reduction, matrix multiplication, and QR factorization, and $C$ bounding the log of the condition number of the input basis $B$. This yields a running time of $O\left(n^\omega (p + n)^{1 + \varepsilon}\right)$ for precision $p = O(\log \|B\|_{max})$ in common applications. Our algorithm is fully practical, and we have published our implementation. We experimentally validate our heuristic, give extensive benchmarks against numerous classes of cryptographic lattices, and show that our algorithm significantly outperforms existing implementations.

To Join on Zoom : https://fau-edu.zoom.us/j/83768244916?pwd=cWNoOTlVVThGbnB1M3NzQ28vclpUdz09

Analysis and Application Seminar

Speaker:  Wai-Ting, NSF post doctorate

Title:  Dynamics near oblate gravitating bodies 

Abstract:: This talk is devoted to several aspects of the gravitational n-body problem. We study the central configurations of three oblate bodies and the Hill approximation to the restricted four-body problem with a hierarchy between the bodies: two larger bodies, a smaller one and a fourth infinitesimal body. In this problem, we consider the shape of the three massive bodies via oblateness. The resulted limiting Hamiltonian describes the dynamics of the infinitesimal body in a neighborhood of the smaller oblate body. As a motivating example, we apply the theoretical results to a planetary system.

March 2023

FAU MATH CLUB

Meets weekly on Wednesdays at 4:00 pm.  Starting today, FAU Math Club will meet bi-weekly in SE-43, Room 271 (Computer Lab). 
On alternating Wednesday afternoons, FAU Math Club Study Sessions will be held on SE-43, Room 215.  

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact  Adam Zaidan

Spring, 2023  FAU MATH CLUB FLYER

Analysis and Applications

Speaker:  Yang Li, Florida Atlantic University

Title:   Modeling spatial and spatio-temporal processes on spheres using convolution

Abstract:   The wide use of satellite-based instruments provides measurements in climatology on a global scale, which often have nonstationary spatial and spatial-temporal covariance structure. In the first part of this talk, I will address the issue of modeling a spatial random field on spheres which is stationary across longitudes by using a kernel convolution. The observed random field is generated by convolving a latent uncorrelated random field with a class of Matérn type kernel functions. By allowing the parameters in the kernel functions to vary with locations, it is possible to generate a flexible class of covariance functions and capture the nonstationary properties. Since the corresponding covariance functions generally do not have a closed form, numerical evaluations are necessary, and a pre-computation table is used to speed up the computation. The second half of the talk is modeling spatio-temporal processes on spheres which are observed over a substantial fraction of the surface of the Earth over a long period of time. A latent dynamic process is defined on a grid covering the globe. The data vector is first projected onto the low-dimensional space spanned by those grids at each available time point. The resulting time series are fitted with seasonal ARIMA models. Forecasting is made by convolving the latent dynamic processes at all grid points using von Mises-Fisher kernel function. The procedure is illustrated by the total ozone data collected by Total Ozone Mapping Spectrometer during a 12-year period.

54th Southeastern International Conference on Combinatorics, Graph Theory and Computing

(Registration here!)

Invariant Theory Reading Seminar 

Textbook:   Classical Invariant Theory , by Peter J. Olver, Cambridge University Press (1999).  

Refreshments will be served.

FAU MATH CLUB

Meets weekly on Wednesdays at 4:00 pm.  Starting today, FAU Math Club will meet bi-weekly in SE-43, Room 271 (Computer Lab). 
On alternating Wednesday afternoons, FAU Math Club Study Sessions will be held on SE-43, Room 215.  

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact  Adam Zaidan

Spring, 2023  FAU MATH CLUB FLYER

Crypto Cafe

Speaker:  Corentin Jeudy  (IRISA, Rennes Cedex, France)

Title: On the Secret Distributions in Module Learning With Errors

Abstract:   The Module Learning With Errors (M-LWE) problem is a core assumption of lattice-based cryptography, and it underlies the security of the future post-quantum cryptography standards Kyber and Dilithium selected by NIST. The problem is parameterized by a secret distribution as well as an error distribution. There is a gap between the choices of those distributions for theoretical hardness results (uniform secret modulo q) and practical schemes (small bounded secret). In this talk, we narrow this gap by presenting three results focused on the secret distribution. We show that both search and decision M-LWE remain hard when the secret distribution is uniform over small bounded secret, provided that the rank is larger by a log(q) factor. We then show the hardness of search M-LWE for more general secret distributions carrying sufficient entropy.

This talk is based on the published papers "On the Hardness of Module Learning With Errors with Short Distributions" (Journal of Cryptology 2023) and "Entropic Hardness of Module-LWE from Module-NTRU" (Indocrypt 2022) which are joint works with Katharina Boudgoust, Adeline Roux-Langlois and Weiqiang Wen.

+Zoom:  (click here)

Algebra Seminar

Speaker:  Batsile Tlharesakgosi, Unisa

Title:  A lattice-theoretic view of some special ideals of subrings of commutative rings

Abstract

FAU MATH CLUB

Meets weekly on Wednesdays at 4:00 pm.  Starting today, FAU Math Club will meet bi-weekly in SE-43, Room 271 (Computer Lab). 
On alternating Wednesday afternoons, FAU Math Club Study Sessions will be held on SE-43, Room 215.  

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact  Adam Zaidan

Spring, 2023  FAU MATH CLUB FLYER

Analysis and its Applications

Speaker: Sean Perry, Postdoc, University of South Florida

Title:  On the Valence of pq*- Recent work on Hengartner's Problem

Abstract:  Where p and q are complex polynomials, let P = pq*, that is p times the conjugate of q. Given a complex constant w, one may ask about the set of preimages of w under P. Under a certain nondegeneracy assumption, this set is finite. Hengartner asked, in this case, what is its maximum cardinality in terms of n and m, the degree of p and q respectively. Here, we present recent progress on the problem. Namely, we give an upper bound of 3n-1 in the case m=1 using complex dynamics, and an improvement on the Bezout bound from (n+m)^2 to n^2+m^2 in the general case using Sylvester resultants. We also comment on when this bound improves the Bezout bound in the more general context of polyanalytic polynomials.

MS Exam

Speaker:  Ian Morgan

Title: NTRU Public Key Cryptosystem 

Abstract: In this presentation, we describe NTRU, a new public key cryptosystem. NTRU encryption and decryption uses a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory. The security of the NTRU cryptosystem comes from the interaction of the polynomial mixing system with the independence of reduction modulo two relatively prime integers p and q.    

Join Zoom Meeting
https://fau-edu.zoom.us/j/84126685850?pwd=cmhYTEJSTVRQc3lkWmdybXppMmcxdz09

Meeting ID: 841 2668 5850
Passcode: XhRk4K

FAU's Association for Women in Mathematics (AWM) to host Florida Women in Math Day

For more information: https://www.math.fau.edu/awm/index.php

Register here!

Invariant Theory Reading Seminar 

Textbook:   Classical Invariant Theory , by Peter J. Olver, Cambridge University Press (1999).  

Refreshments will be served.

Algebra Seminar

Speaker:  Robert Lubarsky, Ph.D., Florida Atlantic University

Title: Heyting Algebras and Constructive Mathematics

Abstract: In the seminar so far there has been a lot of talk of frames. A slight extension of the concept of a frame is a Heyting algebra. Heyting algebras can be used to model constructive, as opposed to classical, mathematics, which is mathematics without the use of Excluded Middle, the assertion that every statement is either true or false. I will discuss the use of some Heyting algebras to model some constructive, non-classical principles, and also show that the failure of some classical principles requires in some sense certain Heyting algebras.

Analysis and its Applications

Speaker: Alex Dowling, Rutgers University (Ph.D. candidate)

Title:  Continuation Sheaves in Dynamics: Sheaf Cohomology & Bifurcation

Abstract:  : Algebraic structures such as the lattices of attractors, repellers, and Morse representations provide a computable description of global dynamics. In recent work that will be presented in this talk, a sheaf-theoretic approach to their continuation is developed. The algebraic structures are cast into a categorical framework to study their continuation systematically and simultaneously. Sheaves are built from this abstract formulation, which track the algebraic data as systems vary. Sheaf cohomology is computed for several classical bifurcations, demonstrating its ability to detect and classify bifurcations. 

AMS/AWM/SIAM Student Chapters invite you to our Pizza Time! 

Register: https://forms.gle/vjvqno3uoxJ8pMuk9a

This time, we are featuring a special guest Dominic Gold. He will discuss with us in a 15-minute talk on 'How to give a good talk'.
We have pizza for everyone.

Meet and Greet New Prospective graduate Students! 

10:30-11:30am Meet with Graduate Students and Faculty in SE 212 

4:00-5:00pm Pizza Party with Graduate Students and Faculty in SE 215 

Please feel free to meet them and join some events (especially the Pizza party).

We look forward to seeing you there!!

Crypto Cafe

Speaker: David J. Wu, The University of Texas at Austin

Title:  Succinct Vector, Polynomial, and Functional Commitments from Lattices

Abstract: 

 In a functional commitment scheme, a user can commit to an input x and later on, open it to an arbitrary function evaluation f(x). We require that both the commitment and the opening be short. Important special cases of functional commitments include vector commitments and polynomial commitments. In this talk, I will introduce a new lattice-based framework for constructing functional commitments that supports functions computable by arbitrary (bounded-depth) Boolean circuits. Our constructions rely on a new falsifiable "basis-augmented SIS" assumption that we introduce, which can be viewed as a new "q-type" variant of the standard SIS assumption.  

(Joint work with Hoeteck Wee)

To Join on Zoom : https://fau-edu.zoom.us/j/83768244916?pwd=cWNoOTlVVThGbnB1M3NzQ28vclpUdz09

Algebra Seminar

Speaker:  Zvi Rosen, Ph.D., Florida Atlantic University

Title:  Neural Codes and Oriented Matroids

Abstract:  In the 1970's, neuroscientists discovered that the hippocampus of a rat contains a virtual map of its environment. When the rat is in region 1, neuron 1 fires an electric impulse, when it moves to region 2, neuron 2 fires, and in the intersection, both neurons fire. In the decades since, algebraists have begun to model this situation abstractly as follows: Fix n convex subsets of Euclidean space, representing stimuli; then, record all possible subsets of [n] whose intersection is nonempty and not covered by other sets. This combinatorial object is called a "convex neural code." 

In this talk, we relate the emerging theory of convex neural codes to the established theory of oriented matroids, which generalize systems of signed linear relations. By way of this connection, we prove that all convex codes are related to some representable oriented matroid, and we show that deciding whether a neural code is convex is NP-hard.

FAU MATH CLUB

Meets weekly on Wednesdays at 4:00 pm.  Starting today, FAU Math Club will meet bi-weekly in SE-43, Room 271 (Computer Lab). 
On alternating Wednesday afternoons, FAU Math Club Study Sessions will be held on SE-43, Room 215.  

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact  Adam Zaidan

Spring, 2023  FAU MATH CLUB FLYER

Analysis and Allications Seminar

Speaker:  Shu Kanazawa, postdoctoral researcher visiting from Ohio State

Title:  Large deviation principle for persistence diagrams of random cubical filtrations

Abstract:   The objective of this work is to investigate the asymptotic behavior of the persistence diagrams of a random cubical filtration as the window size tends to infinity. Here, a random cubical filtration is an increasing family of random cubical sets, which are the union of randomly generated higher dimensional unit cubes with integer coordinates in a Euclidean space. We first prove the strong law of large numbers for the persistence diagrams, inspired by the work of Hiraoka, Shirai, and Trinh. In this talk, we are mainly interested in the decay rate of the probability that the persistence diagram is far from the limiting measure. This is the first result on the large deviation behavior of persistence diagrams themselves. This talk is based on joint work with Yasuaki Hiraoka, Jun Miyanaga, and Kenkichi Tsunoda.

February, 2023

Algebra Seminar

Speaker:   Dr. Papiya Bhattacharjee, Florida Atlantic University

Title:   Inverse Topology on Min(L), for an M-Frame L.

Abstract:  We start with an algebraic frame L with FIP (M-Frame) and look at the minimal prime elements of L, denoted by Min(L). We can endow Min(L) with the hull-kernel topology and the inverse topology, and then investigate various topological properties of the spaces. In this talk the speaker will introduce the concepts of a frame and its elements, describe the topologies on Min(L), and state the known results on the topological properties of Min(L). There are some open questions about the inverse topology on Min(L) that are being investigated by the speaker. The speaker will present the current findings on the inverse topology and prove results related to them.

Invariant Theory Reading Seminar

Textbook:       Classical Invariant Theory  , by Peter J. Olver, Cambridge University Press (1999).  

Refreshments will be served.

Algebra Seminar

Speaker:   Dr. Papiya Bhattacharjee, Florida Atlantic University

Abstract:   We start with an algebraic frame L with FIP (M-Frame) and look at the minimal prime elements of L, denoted by Min(L). We can endow Min(L) with the hull-kernel topology and the inverse topology, and then investigate various topological properties of the spaces. In this talk the speaker will introduce the concepts of a frame and its elements, describe the topologies on Min(L), and state the known results on the topological properties of Min(L). There are some open questions about the inverse topology on Min(L) that are being investigated by the speaker. The speaker will present the current findings on the inverse topology and prove results related to them.

FAU MATH CLUB

Meets weekly on Wednesdays at 4:00 pm.  Starting today, Math Club will meet bi-weekly in SE-43, Room 271 (Computer Lab).  On alternating Wednesday afternoons, FAU Math Club Study Sessions will be held on SE-43, Room 215.

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact    Adam Zaidan

Spring, 2023    FAU MATH CLUB FLYER

Analysis and Applications

Speaker:  Dr. Jason Mireles-James, Florida Atlantic University

Title:  Divergent series in dynamical systems theory: an illustrative example

Abstract:  This talk will focus on a differential equation whose solution leads naturally to ​approximation by divergent series.  The question of what exactly this means can be addressed using tools from Laplace/Borel transform theory.  This will be a basic introductory talk, where I will try to introduce some useful ideas in the context of the concrete example.  I'm primarily interested in bounding the errors associated with truncating the divergent series.  Another important question is to understand the regularity properties of the function being approximated by the divergent series.  Borel resummation and the Resurgence theory of Ecalle provide a powerful framework for studying these kinds of questions, and this talk is meant as a leasurly dip into that pool.  While these idas are important for a number of problems in my research, this will not be a research talk as such.  

Crypto Cafe

Speaker:   Dr. Bill Brumley, Tampere University, Finland

Title:   Side Channel Analysis and Lattice Attacks

Abstract:   Lattice attacks are a typical endgame for side channel attacks targeting digital signature schemes. During the procurement phase, the attacker queries digital signatures, messages, and corresponding side channel traces, then tries to extract secret information from these traces and  apply lattice methods to recover the private key. But in practice, these traces are often incomplete and/or noisy, complicating theoretical models for applying lattices. In this talk, I discuss some of the lattice attack techniques developed over the years, and outline a few interesting open problems that highlight the gap between theory and practice for applied side channel attacks powered by lattice methods.

To Join on Zoom:      https://fau-edu.zoom.us/j/83768244916?pwd=cWNoOTlVVThGbnB1M3NzQ28vclpUdz09

Algebra Seminar

Title : Topologizing the Space of Minimal Primes of an M-Frame

Speaker : Albert Madinya

Abstract  : An M-frame is an algebraic frame possessing a unit and satisfying the Finite Intersection Property. Given an M-frame, call it L, we can topologize the set of minimal prime elements of L, which we will denote by Min(L). One such way we could topologize Min(L) is with the Zariski topology as is done with the prime ideals of a commutative ring. The other is the inverse topology which has a similar construction to that of the Zariski topology. Our aim in this talk is to study these topological spaces and the interplay that exists between the topological properties of Min(L) and the frame-theoretic properties of L.

FAU MATH CLUB

Speaker :  Dr. Evelyn Sander, George Mason University

Title   :  Stable floating configurations for 3D printed objects

Abstract   :   This talk concentrates on the study of stability of floating objects through mathematical modeling and experimentation. The models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes’ Principle. There will be some discussion of a variety of floating shapes with two-dimensional cross sections for which it is possible to analytically and/or computationally a potential energy landscape in order to identify stable and unstable floating orientations, as well as how to adapt the theory to fluids other than water.  I will give a hands on demonstration of code we have developed for testing the floating configurations for new shape and an overview of the methods involved in 3D printing the objects.

This research is joint work over three semesters with  Dan Anderson (GMU),  nine undergraduate students, and two graduate students, all of  whom were part of a student research program at the  GMU Math MakerLab and  MEGL.

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact    Adam Zaidan

Spring, 2023    FAU MATH CLUB FLYER

Analsis and Applications

Speaker  :  Dr.  Evelyn Sander, George Mason University

Title  :   Cyclic Symmetry Induced Pitchfork Bifurcations in the Diblock Copolymer Model

Abstract  :   The Ohta-Kawasaki model for diblock copolymers exhibits a rich equilibrium bifurcation structure. Even on one-dimensional base domains the bifurcation set is characterized by high levels of multi-stability and numerous secondary bifurcation points. Many of these bifurcations are of pitchfork type, and in previous work we showed that pitchfork bifurcations are induced by a simple even or odd symmetry-breaking and can be validated using computer assisted proof. However, this is not the complete picture: many other pitchfork bifurcations do not exhibit even or odd symmetry breaking. In the current work,  we show that in these more involved cases, a cyclic group action is responsible for their existence, based on cyclic groups of even order. We present theoretical results establishing such bifurcation points and show that they can be characterized as nondegenerate solutions of a suitable extended nonlinear system, and show how these results can be validated using computer assisted proofs.

Data Science Faculty Candidate

Speaker:   Marcio Gameiro, FAU faculty candidate

Title:   Computing Dynamics of Data

Abstract: We present combinatorial topological methods to compute the dynamics of data. A discretization of the state space of the systems is used to construct a combinatorial description from which recurrent versus non-recurrent dynamics is extracted. Algebraic topology is then used to validate and characterize the dynamics of the system. We will discuss the combinatorial description and the algebraic topological computations in the context of data derived continuous and discrete models and will present applications to dynamics of gene regulatory networks and control systems in robotics.

Association for Women In Mathematics

A Tea Time with Dr. Monica Hurdal, Florida State University

Grab your favorite mug!  We have donuts and "pi" for your sweet tooth!

Florida GeoGebra, 2023

Data Science Faculty Candidate

Speaker:   Jiahui Chen, FAU faculty candidate

Title:   Mathematics - AI for bioscience

Abstract:   Artificial intelligence (AI) has emerged as a new paradigm for scientific discovery. However, AI modeling of biological data remains a challenge due to their intricate structural complexity, excessively high dimensionality, severe nonlinearity, and intrinsic multiscale. We devise differential geometry and algebraic topology to address these challenges. Specifically, we utilize persistent homology, a main workhorse in topological data analysis (TDA), to simplify biomolecular structure complexity and reduce their dimensionality. Since persistent homology is insensitive to homotopic shape evolution, we developed persistent Laplacians to capture non-topological shape changes in data by their non-harmonic spectra. For volumetric data, like molecular electron density of proteins, we proposed an evolutionary de Rham-Hodge method to extend the traditional Hodge Laplacian to a multiscale formulation. We introduced boundary-induced graph Laplacians to further reduced computational complexity. These new mathematical tools are paired with advanced machine learning algorithms, such as ensemble learning, manifold learning, graph neural networks, and transformers, to reveal the mechanisms of SARS-CoV-2 transmission and evolutions via infectivity strengthening and antibody resistance. We had successfully predicted the incoming dominance of Omicron BA.2 and BA.4/BA.5 variants.

Cryptography Faculty Interview

Dr. Dung Hoang Duong, Faculty candidate

ZOOM: https://fau-edu.zoom.us/j/84652979364?pwd=dHVQN0VjYktXZU5WUUtkVFpOVTY0QT09

Meeting ID: 846 5297 9364 
Passcode: 6dtZaA

Invariant Theory Reading Seminar 

Textbook:       Classical Invariant Theory  , by Peter J. Olver, Cambridge University Press (1999).  

Refreshments will be served.

FAU MATH CLUB

Meets weekly on Wednesdays at 4:00 pm.  Starting today, FAU Math Club will meet bi-weekly in SE-43, Room 271 (Computer Lab). 
On alternating Wednesday afternoons, FAU Math Club Study Sessions will be held on SE-43, Room 215.  

FAU MATH CLUB is Open to all majors at all levels!

For more info, contact    Adam Zaidan

Spring, 2023    FAU MATH CLUB FLYER

Algebra Seminar

Speaker:  Connor Watson, Florida Atlantic University

Title:  Ax-Grothendieck and the Interplay Between Model Theory and Algebra:   Abstract

Join Zoom Meeting:     https://fau-edu.zoom.us/j/86074562272?pwd=Y2tuTXNBdEtjOUZTMTlpVUptdG5SQT09

Meeting ID: 860 7456 2272

Passcode: 8Cg33X

All Are welcome!

Cryptography Faculty Interview

Dr. Qingju Wang, faculty candidate

ZOOM:    https://fau-edu.zoom.us/j/81404366239?pwd=aUdNZW1ncEtpTk5aeG5JL1U5UEtadz09 

Meeting ID: 814 0436 6239 
Passcode: Kr56x4

Crypto Cafe

Speaker:   Mila Anastasova, Florida Atlantic University

Title:   Time-Efficient Finite Field Microarchitecture Design for Curve448 and Ed448 on Cortex-M4.

Abstract:   The elliptic curve family of schemes has the lowest computational latency, memory use, energy consumption, and bandwidth requirements, making it the most preferred public key method for adoption into network protocols. Being suitable for embedded devices and applicable for key exchange and authentication, ECC is assuming a prominent position in the field of IoT cryptography. The attractive properties of the relatively new curve Curve448 contribute to its inclusion in the TLS1.3 protocol and pique the interest of academics and engineers aiming at studying and optimizing the schemes. When addressing low-end IoT devices, however, the literature indicates little work on these curves. In this presentation, we present an efficient design for both protocols based on Montgomery curve Curve448 and its birationally equivalent Edwards curve Ed448 used for key agreement and digital signature algorithm, specifically the X448 function and the Ed448 DSA, relying on efficient low-level arithmetic operations targeting the ARM-based Cortex-M4 platform. Our design performs point multiplication, the base of the Elliptic Curve Diffie Hellman (ECDH), in 3,2KCCs, resulting in more than 48% improvement compared to the best previous work based on Curve448, and performs sign and verify, the main operations of the Edwards curves Digital Signature Algorithm (EdDSA), in 6,038KCCs and 7,404KCCs, showing a speedup of around 11% compared to the counterparts. We present our novel modular multiplication and squaring architectures reaching ∼ 25% and ∼ 35% faster runtime than the previous best-reported results, respectively, based on Curve448 key exchange counterparts, and ∼ 13% and ∼ 25% better latency results than the Ed448-based digital signature counterparts targeting Cortex-M4 platform.

I am going to present our latest work targeting Curve448, however, I will try to integrate our previous work on finite field arithmetic as well during the presentation.

To Join on Zoom:      https://fau-edu.zoom.us/j/83768244916?pwd=cWNoOTlVVThGbnB1M3NzQ28vclpUdz09

January, 2022

MS Exam - Alexander Pepper

Title: A Survey of Modern Tools for Quantum Cryptanalysis, With Application to AES and SHA-3 

Abstract:  This presentation gives an overview of modern tools for analyzing quantum circuits, and gives examples of how these tools may be used to perform cryptanalysis on two modern encryption algorithms. Quantum computing leverages quantum phenomena to perform its fundamental operations. These unique fundamental operations allow us to write more efficient code for encryption and decryption. We will start by providing the language of discourse for quantum computing. With our terminology in order, we will give definitions for the resource requirements of a quantum algorithm. We will show how the quantum resource requirements of symmetrical encryption may be reduced with Grover's algorithm, and we will discuss quantum-resource saving methods for AES and SHA-3. We will then use ProjectQ and Cirq to evaluate the resource requirements of these algorithms, and conclude with a discussion of the ramification of these resource requirements. 

Join Zoom Meeting
https://us04web.zoom.us/j/73083612004?pwd=D5j5x8UHb3DjYyfaSHyNyJ60wYBlz8.1

Meeting ID: 730 8361 2004
Passcode: cfL7et 

Analysis and Applications Seminar

Speaker:  Dr. Necibe Tuncer, Florida Atlantic University

Title:  Structural and practical identifiability analysis of a multiscale immuno-epidemiological model

Abstract:  We perform the identifiability analysis of a multiscale model of seasonal influenza with multiscale data. We show that the well studied target cell limited within-host model is not structurally identifiable. So, we reformulate the model and work with a scaled within-host model which is structurally identifiable. We find that the scaled within-host model is practically identifiable with respect to two distinct viremia data sets while fitting with weighted or unweighted least squares. We introduce a methodology on how to study the structural identifiability of multiscale epidemic models specifically nested immuno-epidemiological models. All parameters of the multiscale model are practically identifiable. Furthermore,  we find that the practical identifiability of the multiscale model is significantly better when fitted to viremia and incidence data as opposed to when fitted to viremia and cumulative incidence data. Comparing first and second order numerical methods for solving the partial differential equations suggests that using a higher order numerical method does not affect the identifiability of the parameters. Further simulations suggest that the choice of the linking functions has some impact on identifiability when viremia and incidences are fitted but no impact when viremia and cumulative incidences are fitted.

FAU AMC8 Middle School Math Day

For more information:  https://www.math.fau.edu/amc-contests/amc8.php

Invariant Theory Reading Seminar 

Textbook:   Classical Invariant Theory , by Peter J. Olver, Cambridge University Press (1999).  

Modus operandi: We will discuss approximately one book chapter,   each time,  under the rotating leadership of an attendee.

The first meeting will start with a motivation for the seminar and Chapter 1 (historical remarks). 

Refreshments will be served.

Crypto Cafe

Speaker: Dr. Veronika Kuchta, Florida Atlantic University

Title:  Proof Systems and ZK-SNARKs

Abstract:    Zero-knowledge proof (ZKP) systems allow a prover holding some secret witness w for a statement x satisfying some NP relation R, to prove knowledge of w to a verifier (the soundness property), without revealing any information on w to the verifier (the zero-knowledge property) beyond that revealed by the NP statement x known to the verifier.  

ZKPs have a myriad of applications in privacy-preserving cryptographic protocols. For statements with large witnesses w, the main limitation of classical ZKPs is that their proof size is proportional to the witness size. To support such applications like verifiable computation and privacy-preserving cryptocurrencies it is desirable to have succinct ZKPs in which the proof (or argument) size is only polylogarithmic in the witness size. This requirement induced constructions of Zero-Knowledge Succinct Non-interactive ARgument of Knowledge (ZK-SNARK).  

In this presentation we will look at different approaches to designing efficient ZK-SNARKs from information-theoretical proof system especially focusing on lattice-based and hash-based ZK-SNARK constructions.

December, 2022

Analysis and Applications Seminar

Thursday
Dec., 1
Se 215
5:00 pm

FAU Math Club

Study Session/Finals Edition

Math Circle for Middle School

Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022.  Math Circle for Middle School Flyer

For more information:  https://www.math.fau.edu/math-circle/

Math Club and Study Sessions

Speaker:  Dr. Necibe Tuncer

Title:   Structural and practical identifiability analysis of a multiscale immuno-epidemiological model

Abstract:  We perform the identifiability analysis of a multiscale model of seasonal influenza with multiscale data. We show that the well studied target cell limited within-host model is not structurally identifiable. So, we reformulate the model and work with a scaled within-host model which is structurally identifiable. We find that the scaled within-host model is practically identifiable with respect to two distinct viremia data sets while fitting with weighted or unweighted least squares. We introduce a methodology on how to study the structural identifiability of multiscale epidemic models specifically nested immuno-epidemiological models. All parameters of the multiscale model are practically identifiable. Furthermore, we find that the practical identifiability of the multiscale model is significantly better when fitted to viremia and incidence data as opposed to when fitted to viremia and cumulative incidence data. Comparing first and second order numerical methods for solving the partial differential equations suggests that using a higher order numerical method does not affect the identifiability of the parameters. Further simulations suggest that the choice of the linking functions has some impact on identifiability when viremia and incidences are fitted but no impact when viremia and cumulative incidences are fitted.

MS Presentation

Speaker:  Aaron Hangstrom

Crypto Cafe

Speaker:  Jianfeng Xie,  Department of Electrical and Computer Engineering, Villanova University

Title: Hardware Acceleration for Post-Quantum Cryptography: Algorithmic Derivation, and Architectural Innovation

Join Zoom Meeting
https://fau-edu.zoom.us/j/88571801006?pwd=ZDlvdEhrUy84cERSM3Uyb083R1VYZz09

Meeting ID: 885 7180 1006
Passcode: LDJ44q

Math Circle for Middle School

Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022.  Math Circle for Middle School Flyer

For more information:  https://www.math.fau.edu/math-circle/

November 2022

Analysis and Applications Seminar

FAU's Math Club

All are invited to attend and join the Math Club.  We look forward to seeing you there.

MS Exam (Presentation)

Speaker:  Jean-Sebastien Roger

Title:  A Generalizable Brain-Computer Interface (BCI) Using Machine Learning for Feature Discovery

Abstract: This presentation discusses the process and techniques used in a work analyzing the efficacy of generalized neural signal classification for brain-computer interface (BCI). The experiment was aimed at producing and testing a classification framework for BCI which can be generalized to many motor movements and many features of input from electroencephalography (EEG) data. Some current approaches to classification are dependent on identifying key action potentials in EEG data, a generalized approach as the one offered in this article relies on a stochastic search on a sample of neural networks trained on all features in the data. This results in less requirement for extensive domain knowledge and a-priori information specific to the desired outcome. Overall, the results of the proposed method are comparable to some of the top methods proposed on credentialed datasets.   

All are cordially invited.

Math Circle for Middle School

Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022.  Math Circle for Middle School Flyer

For more information:  https://www.math.fau.edu/math-circle/

Analysis and Applications Seminar      ***CANCELLED DUE TO HURRICANE NICOLE

American Mathematics Competitions (AMC 10/12A)     ***CANCELLED DUE TO HURRICANE NICOLE

FAU's Department of Mathematical Sciences will host the AMC 10/12A on the Boca Raton Campus.

Please regsiter your student for the AMC 10/12A.  

REGISTRATION INFO

American Mathematics Competitions (AMC 10/12B)

FAU's Department of Mathematical Sciences will host the AMC 10/12B on the Boca Raton Campus.

Please regsiter your student for the AMC 10/12B. 

REGISTRATION INFO

MS Exam (Presentation)

Master's Degree Canidate:  Collin Bakken 

Title: Discovering Governing Equations from Data: Sparse Identification of Nonlinear Dynamical Systems 

Abstract: A quantitative comprehension of dynamic balances and constraints has led to rapid growth in many areas, including aircrafts, combustion engines, and many more.  Through this work, we will tie together machine learning algorithms with sparsity techniques in order to discover equations based on previously measured data. An essential assumption must be made for this to work: we must assert that only a few important terms govern the dynamics, which means that these equations are sparse.   The main goal is to use sparse regression, which minimizes the number of governing equations needed to represent the data accurately.  The outcomes are models that are often balancing complexity of data with accurate descriptions of data, while not being overwhelming.  Here, we take a deeper look into a range of problems, including the Lorenz system, to further our understanding of sparse identification. 

Florida Atlantic University's Student Chapter of the Association for Women in Mathematics (AWM) will host Department of Mathematical Sciences Chess Tournament

Sign Up Here!

PhD Dissertation Defense 

Ph. D. Candidate:  Floyd Johnson 

Title:  Selected Topics in Quantum and Post-Quantum Cryptography 

Co-Advisors: Dr. Shi Bai and Dr. Rainer Steinwandt 

Abstract:  In 1994 when Peter Shor released his namesake algorithm for factoring and solving the discrete logarithm problem he changed cryptography forever.  Many of the state-of-the-art cryptosystems for internet and other computerized communications will become obsolete with the advent of quantum computers.  Two distinct approaches have grown to avoid the downfall of secure communication: quantum cryptography which is based in physics and information theory, and post-quantum cryptography which uses mathematical foundations believed not to be weak against even quantum assisted adversaries.  In this defense we will be covering a variety of recent advances in topics including cryptanalysis of quantum signature schemes, cryptanalysis of weak instances of the NTRU problem, and two constructions based on lattice-based primitives. 

Join Zoom Meeting
https://fau-edu.zoom.us/j/81898711577?pwd=RHpxUXdJa1p6cExGSUFjQklJajlOdz09

Meeting ID: 818 9871 1577
Passcode: BbAuV9

Math Club

Speaker:  Dr. Robert Lubarsky, FAU

Title:  Logic -- What is It?

Abstract:  One can go merrily along doing mathematics without thinking about the meaning behind it, as mathematicians had for millenia. With a bit of self-reflection though, you can ask what it is that you're ultimately doing. Such questions grew out of actual mathematical practice in the late 19th century, and led to a whirlpool of unclarities and paradoxes. This talk will focus on the issues that came up in this context, and their culmination in arguably the first major theorem in mathematical logic, Godel's Incompleteness Theorems.

FAU Department of Mathematical Sciences Colloquium

Speaker:  Dr. Shi Bai

Title:  Recent developments of practical lattice reduction algorithms

Abstract:    Lattice reduction algorithms have received much attention in recent years due to their relevance in cryptography. We will discuss some of the recent developments on enumeration-based lattice reduction algorithms which are used in practice. We will start with the classic Finke-Post and Kannan enumeration algorithm and then introduce some modern variants. In particular, we will discuss a lattice reduction algorithm that achieves root Hermite factor k^(1/(2k)) in time k^(k/8 + o(k)) and polynomial memory. This improves the previously best-known enumeration-based algorithms which achieve the same quality, but in time k^(k/(2e) +o(k)). 

Math Circle for Middle School

Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022.  Math Circle for Middle School Flyer

For more information:  https://www.math.fau.edu/math-circle/

MS Exam Presentation

Speaker:  Hansraj Jangir

Title: Worst-case to Average-case Reduction for SIS

Abstract:  We will give an introduction to computationally hard problems based on lattices and some basic theorems on LWE (learning with errors) and SIS (shortest integer solution). We will then use Gaussian measures on lattices and high dimensional Fourier transform for smoothing as a tool to come up with worst-case to average-case reductions for SIS. In a nutshell, the worst-case to average-case reductions show how to transform any algorithm that solves SIS on the average into an algorithm that solves “approximate short vector problems” on worst-case lattices.

Hansraj Jangir's MS presentation will also be accessible remotely via Zoom.

Join Zoom Meeting
https://fau-edu.zoom.us/j/7263276757?pwd=YnhwSXUwVXN2TFhrVXpTZDhuamczdz09

Meeting ID: 726 327 6757

Passcode: Fall2021

October 2022

FAU's Math Club

All are invited to attend and join the Math Club.  We look forward to seeing you there.

Math Circle for Middle School

Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022.   Math Circle for Middle School Flyer

For more information:   https://www.math.fau.edu/math-circle/

Analysis and Applications Seminar

Speaker:   Dr. Vincent Naudot, Florida Atlantic Univeristy

Abstract/Title: Bogdanov Takens bifurcations

Abstract: In this talk, we study the bifurcations that arise in the unfolding of a (non-degenerate) Bogdanov-Takens equilibrium. We present an overview of the techniques used to prove the results.  We generalize the bifurcation 
diagram to the case of map, i.e., in the unfolding of a Bogdanov-Takens fixed point.

Crypto Café

Speaker:   Dr. Shi Bai, Florida Atlantic University

For title and abstract, please visit the Crypto Café website:  https://www.math.fau.edu/crypto_cafe.php.

FAU's Math Club

All are invited to attend and join the Math Club.  We look forward to seeing you there.

Department of Mathematical Sciences Colloquium

Speaker:  Ashkaan Fahimipour

Title:  When to quit of you're being exploited

Abstract:     This presentation discusses the process and techniques used in a work analyzing the efficacy of generalized neural signal classification for brain-computer interface (BCI). The experiment was aimed at producing and testing a classification framework for BCI which can be generalized to many motor movements and many features of input from electroencephalography (EEG) data. Some current approaches to classification are dependent on identifying key action potentials in EEG data, a generalized approach as the one offered in this article relies on a stochastic search on a sample of neural networks trained on all features in the data. This results in less requirement for extensive domain knowledge and a-priori information specific to the desired outcome. Overall, the results of the proposed method are comparable to some of the top methods proposed on credentialed datasets.   

Math Circle for Middle School

Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022.   Math Circle for Middle School Flyer

For more information:   https://www.math.fau.edu/math-circle/

Analysis and Applications Seminar

Speaker:   Dominic Gold, Florida Atlantic University

Title:   Applications of Homomorphic Encryption to Data Analysis 

Abstract: Data analysis is the umbrella term for mathematical techniques used to describe, classify, and illustrate data. However, certain types of data are privacy-protected by law (medical records, MRI scans, etc.). Homomorphic encryption allows us to circumvent this hurdle by encrypting the original data (also known as the plaintext) into ciphertext, and then performing operations on this ciphertext that are analogous to the usual operations performed on the plaintext. This tool allows for the extension of many popular data analysis techniques, such as regression, clustering, and even neural networks into the ciphertext domain. Furthermore, this technique permits the user to rely on a computationally superior semi-honest third-party (e.g. a cloud server) to perform the data analysis without a breach of user privacy. 

We will first discuss homomorphic encryption as a black-box technique, then transforming an existing (plaintext) algorithm into its homomorphic encryption counterpart on ciphertext, and finally some applications of homomorphic encryption in the data science field. These examples include, but are not limited to, secure matrix multiplication, secure Euclidean distance for k-Means classification and k-Centroids clustering, and finally the topic of my dissertation which is the adaptation of persistence homology, the main driver behind topological data analysis (TDA), into the ciphertext domain. We conclude by explaining the significance of this research to privacy-protected medical data.

FAU's Math Club

All are invited to attend and join the Math Club.  We look forward to seeing you there.

FAU Department of Mathematical Sciences Colloquium

Speaker:   Dr. Francesco Sica, Florida Atlantic University

Title  : Elliptic Curve Cryptography: past, present and future.

Abstract  : I will survey some of my work in the area of elliptic curve cryptography, both in its implementation 

and its security. I will then propose some problems that could be of interest to graduate students.

Friday
Oct 31
SE 215
4:00 pm

FAU Department of Mathematical Sciences Colloquium

Speaker:   Dr. Francesco Sica, Florida Atlantic University

Title  : Elliptic Curve Cryptography: past, present and future.

Abstract  : I will survey some of my work in the area of elliptic curve cryptography, both in its implementation 

and its security. I will then propose some problems that could be of interest to graduate students.

September 2022

Analysis and Applications Seminar*

* The Analysis and Applications Seminar will take place every Thursday in SE 215 at 11:00 a.m. (Fall, 2022)

Speaker:  Erick Lundberg

Title: What is the expected number of limit cycles that bifurcate from a randomly perturbed center?

Abstract: We consider the average number of limit cycles bifurcating from a perturbed linear center where the perturbation consists of random (bivariate) polynomials with independent coefficients. This problem reduces, by way of classical perturbation theory of the Poincaré first return map, to a problem on the real zeros of a random univariate polynomial.  Even though real zeros of random univariate polynomials have been studied in great depth, the particular model arising in this problem falls right at the edge of the well-studied cases.  We present the solution to this problem and discuss other interesting questions related to limit cycles of planar systems with random coefficients.

All are invited!

Crypto Cafe

Speaker : Sulani Thakshila, Florida Atlantic University

Title : MNTRU Signatures

Abstract:  The NTRU cryptosystem is a computational problem introduced in 1996 based  on lattices. Module-NTRU lattices generalize NTRU lattices and possess more benefits on the flexibility of ring dimension. In this talk, I will present Fiat-Shamir signatures based on the inhomogeneous variant of Module-NTRU problem. I will present two signature schemes. The first scheme is a lossy identification scheme secure in the QROM. The second scheme is a BLISS-like signature secure in the classic ROM.

Zoom:  https://fau-edu.zoom.us/j/81002845566?pwd=SUVyWktMTHRSd1FiMVM3dy9UUFM0QT09

Video Recording

Analysis and Applications Seminar 

Speaker:  Dr. Jason Mireles-James

Title: A trefoil knot in the Lorenz equations

Abstract: A two parameter family of three-dimensional vector fields is said to have a T-point if there is a value of the parameters so that the one dimensional stable and unstable manifolds attached to the equilibrium solutions intersect so that they form a trefoil knot.  This requires us to move two parameters, as the intersection of one-dimensional curves in three-dimensional space is very degenerate.  The existence of T-points has important dynamical implications, which I will review very briefly. It has been conjectured (based on numerical evidence) that the Lorenz equations (with one parameter fixed and two free) admit T points.  

I'll develop a functional equation which, if it has a solution, establishes the existence of a T-point.  Using power series representations we can project the functional equation into finite dimensions, and then solve it using Newton's method.  Once a good enough numerical approximation has been found, one can try to establish the existence of a true solution nearby by verifying the hypotheses of a Newton-Kantorovich theorem.  This provides a recipe for a computer assisted proof of the existence for T points in explicit two parameter families like the Lorenz system.  This is joint work with Sheldon Newhouse.

FAU's Math Club

First meeting of FAU's Math Club for the 2022-2023 Academic Year!

All are invited to attend and join the Math Club.  We look forward to seeing you there.

Speaker:  Dr. Jason Mireles-James

Title: A trefoil knot in the Lorenz equations

Abstract: A two parameter family of three-dimensional vector fields is said to have a T-point if there is a value of the parameters so that the one dimensional stable and unstable manifolds attached to the equilibrium solutions intersect so that they form a trefoil knot.  This requires us to move two parameters, as the intersection of one-dimensional curves in three-dimensional space is very degenerate.  The existence of T-points has important dynamical implications, which I will review very briefly. It has been conjectured (based on numerical evidence) that the Lorenz equations (with one parameter fixed and two free) admit T points.  

I'll develop a functional equation which, if it has a solution, establishes the existence of a T-point.  Using power series representations we can project the functional equation into finite dimensions, and then solve it using Newton's method.  Once a good enough numerical approximation has been found, one can try to establish the existence of a true solution nearby by verifying the hypotheses of a Newton-Kantorovich theorem.  This provides a recipe for a computer assisted proof of the existence for T points in explicit two parameter families like the Lorenz system.  This is joint work with Sheldon Newhouse.

FAU's Math Club

First meeting of FAU's Math Club for the 2022-2023 Academic Year!

All are invited to attend and join the Math Club.  We look forward to seeing you there.

Math Circle for Middle School

Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022.  Math Circle for Middle School Flyer

For more information:  https://www.math.fau.edu/math-circle/

Crypto Café 

Speaker: Dr. Edoardo Persichetti

Topic(s):  On-going work on post-quantum cryptographic group actions, in various contexts (type of groups, etc).

All are invited to attend! For the list of past talks, please see https://www.math.fau.edu/crypto_cafe.php

A new mail list crypto_math@lists.fau.edu is created for crypto related annoucements.
Please feel free to join if they are interested in keeping in touch with more targeted activities in crypto.
Please send an email to Francesco or Maria if you want to join.

Tea-Time , hosted by FAU's Student Chapter of the Association for Women in Mathematics (AWM). 

Special Guest: Amish Mishra

Topic(s): Summer internship experience, Summer, 2022

Join us for some pizza and enjoy listening to Amish's story.

All are invited.  Please register here: https://forms.gle/1QMmPqzHgeJtygbT8 and forward this invitation to anyone who may be interested. 

August 2022

Fri., Aug 5
SE 215
2:00 pm   

Aug., 11
SE 215
1:00 pm

PhD Dissertation Defense (Thursday, August 11, 1:00 pm) in SE 215 (in-person with remote access): 

Speaker: Bikram Bhusal, PhD Candidate

Title: Stability Analysis and Parameter Estimation of a Stochastic Logistic Growth Model with Multiplicative Alpha-Stable Lévy Noise. 

Advisor: Dr. Hongwei Long 

Abstract: 

Since the population growth systems may suffer impulsive environmental disturbances such as earthquakes, epidemics, tsunamis, hurricanes, and so on, stochastic differential equations (SDEs) that are driven not only by Brownian motion but also by alpha-stable Lévy noises are more appropriate to model such statistical behavior of non-Gaussian processes with heavy-tailed distribution, having infinite variance and in some cases infinite first moment. In this dissertation, we study stochastic processes defined as solutions to stochastic logistic differential equations driven by multiplicative alpha-stable Lévy noise. We mainly focus on one-dimensional stochastic logistic jump-diffusion processes driven by Brownian motion and alpha-stable Lévy motion. First, we present the stability analysis of the solution of a stochastic logistic growth model with multiplicative alpha-stable Lévy noise. We establish the existence of a unique global positive solution of this model under certain conditions. Then, we find the sufficient conditions for the almost sure exponential stability of the trivial solution of the model.  Next, we provide parameter estimation for the proposed model.  In parameter estimation, we use the least square method to get optimal and applicable estimators of the drift parameters.  We also investigate the consistency and asymptotics of the proposed estimators.  We assess the validity of the estimators with a simulation study.  

Meeting information: 

Topic: Ph.D. Dissertation Defense for Bikram Bhusal 

Time: Aug 11, 2022 01:00 PM Eastern Time (US and Canada) 

Join Zoom Meeting 

https://fau-edu.zoom.us/j/81740421843?pwd=ekN5dTNpd2d2V01CQ2g5Y2lwRzFldz09 

Aug., 17
SE 215
2:00 pm

PhD Dissertation Defense (in-person with remote access). 

Speaker: Duval Zephirin (Ph.D. candidate)

Title: Optimal Portfolio for the Informed Investor in Mispriced Lévy Market with Stochastic Volatility and Power Utility  

Advisor: Dr. Hongwei Long 

Abstract: We consider a portfolio optimization problem in stochastic volatility jump-diffusion model. The model is a mispriced Levy market that contains informed and uninformed investors. Contrarily to the uninformed investor, the informed investor knows that a mispricing exists in the market. The stock price follows a jump-diffusion process, in which the mispricing and volatility are modelled by Ornstein-Uhlenbeck (O-U) process and Cox-Ingersoll-Ross (CIR) process, respectively. We only present results for the informed investor whose goal is to maximize utility from terminal wealth over a finite investment horizon under the power utility function. We employ methods of stochastic calculus namely Hamilton-Jacobi-Bellman equation, instantaneous centralized moments of returns and three-level Crank-Nicolson method. We solve numerically the partial differential equation associated with the optimal portfolio. Under the power utility function, analogous results to those in the jump-diffusion model under logarithmic utility function and deterministic volatility are obtained. 

Meeting information: 

Topic: Ph.D. Dissertation Defense for Duval Zephirin 

Time: Aug 17, 2022 02:00 PM Eastern Time (US and Canada) 

Join Zoom Meeting 

https://fau-edu.zoom.us/j/89312497707?pwd=K3lQQWxNOTc1TlFmaUZ6OUxOTG5OUT09 

Aug 14-21
Wyndham
Deerfield Beach Resort

2022 Combinatorics, Computing, Group Theory and Applications in South Florida

Early Registration: June 1, 2022

Crypto Cafe is back on Wednesdays, every other week this fall, 2022!

Join us for Crypto Cafe on Wednesday, August 31th.    

The Crypto Cafe Schedule and recording will appear the the Crypto Cafe Website

Speaker   : Francesco Sica, Florida Atlantic University

Title   : A Note on Torsion Point Attacks

Abstract   :  A technical lemma is being used in attacks on the supersingular isogeny problem with torsion points (SSI-T) à la Petit, which propagates an error. In this talk, I will explain how Lemma 6 in Petit’s Asiacrypt 2017 paper is incorrect and how this can be fixed to make his attack work in theory as well as in practice.

July 2022

Young CryptograpHers Summer Camp (In the Sandbox)

Register here!

Jul., 19
10:00 a.m.

MS Exam:  Keegan Lee (on ZOOM)

Title: A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem 

Abstract: We examine the Hidden Subgroup Problem of finding a subgroup H of group G using an oracle function which maps an element of G into set S based only on the coset of H containing G. We present a subexponential complexity algorithm for the special case where G is dihedral of order 2^n, and we discuss expansion of the algorithm for application to dihedral groups of unspecified order. 

Join Zoom Meeting:
https://fau-edu.zoom.us/j/85422768020?pwd=bXJXOWNldWIzMGZZeHdSS21Ddm9tdz09

Meeting ID: 854 2276 8020

Jul., 18
3:00 p.m.

MS Exam: Dominic Blanco (on ZOOM)

Title: The Sitnikov Problem, Low Energy Transfers, and The Economic Feasibility of Asteroid Mining 

Abstract: Asteroid mining can be profitable; however, it is currently not economically feasible. Space companies have reduced the cost of missions by using low energy transfer. Low energy transfer uses connecting orbits requiring much less energy to move a spacecraft. To demonstrate low energy transfer, I investigate the Sitnikov Problem with eccentricity of  and . The Sitnikov Problem is a form of the gravitational three-body problem with two heavy bodies orbiting in a plane while a light third body moves perpendicular to the plane. I compute the Poincaré map and find connecting orbits. I then compare past missions that used low energy transfer to similar missions which did not. In all cases, using low energy transfer lowered the cost. This shows that we should investigate the use of low energy transfer in asteroid mining missions to reduce cost. 

Join Zoom Meeting 
https://fau-edu.zoom.us/j/84304914882?pwd=cNV5vpX8WDi0Pw-O5TudBHQq_SV64y.1 

Meeting ID: 843 0491 4882 

June, 2022

Fri., June 10
2:00 pm
SE-215

PhD Dissertation Defense

Speaker: Binod Rimal (Ph.D. Candidate)

Title: Financial Time-series Analysis with Deep Neural Networks 

Advisor: Dr. William Hahn, Florida Atlantic University, 2016

Abstract: Financial time-series data are noisy, volatile, and nonlinear. The classic statistical linear models may not capture those underlying structures of the data. The rapid advancement in artificial intelligence and machine learning techniques, availability of large-scale data, and increased computational capabilities of a machine opens the door to developing sophisticated deep learning models to capture the nonlinearity and hidden information in the data. Creating a robust model by unlocking the power of a deep neural network and using real-time data is essential in this tech era. This study constructs a new computational framework to uncover the information in the financial time-series data and better inform the related parties. It carries out the comparative analysis of the performance of the deep learning models on stock price prediction with a well-balanced set of factors from fundamental data, macroeconomic data, and technical indicators responsible for stock price movement. We further build a novel computational framework through a merger of recurrent neural networks and random compression for the time-series analysis. The performance of the model is tested on a benchmark anomaly time-series dataset. This new computational framework in a compressed paradigm leads to improved computational efficiency and data privacy. Finally, this study develops a custom trading simulator and an agent-based hybrid model by combining gradient and gradient-free optimization methods. In particular, we explore the use of simulated annealing with stochastic gradient descent. The model trains a population of agents to predict appropriate trading behaviors such as buy, hold, or sell by optimizing the portfolio returns. Experimental results on S\&P 500 index show that the proposed model outperforms the baseline models. 

Please contact Dr. Hongwei Long <hlong@fau.edu>  for an electronic copy of the dissertation. A hardcopy of the dissertation is not displayed in the departmental office in order to avoid multiple people touching the same hardcopy at this pandemic time. 

May, 2022

Ph.D. Dissertation Defense: Archana Timsina 

Title: Identifiability Analysis and Optimal Control of Infectious Diseases Epidemics and Parameterization Method for (Un)Stable Manifolds of Implicitly Defined Dynamical Systems 

Co-Advisors: Dr. Necibe Tuncer and Dr. Jason Mireles-James 

Abstract: This dissertation is a study about applied dynamical systems on two concentrations. Frist, based on the growing association between opioid addiction and HIV infection, a compartmental model is developed to study dynamics and optimal control of two epidemics: opioid addiction and HIV infection. We show that the disease-free-equilibrium is locally asymptotically stable when the basic reproduction number R_0= max (R_0^{u}, R_0^{v})< 1,  here R_0^{v} is the reproduction number of the HIV infection, and R_0^{u} is the reproduction number of the opioid addiction. The addiction-only boundary equilibrium exists when R_0^{u}  > 1 and it is locally asymptotically stable when the invasion number of the opioid addiction is R_{inv}^{u}< 1. Similarly, HIV-only boundary equilibrium exists when R_0^{v}> 1 and it is locally asymptotically stable when the invasion number of the HIV infection is R_{inv}^{v}< 1. We study structural identifiability of the parameters, estimate parameters employing yearly reported data from Central for Disease Control and Prevention (CDC), and study practical identifiability of estimated parameters. We observe the basic reproduction number ¬¬¬¬ R_0 using the parameters. Next, we introduce four distinct controls in the model for the sake of control approach, including treatment for addictions, health care education about not sharing syringes, highly active anti-retroviral therapy (HAART), and rehab treatment for opiate addicts who are HIV infected. US population using CDC data, first applying a single control in the model, and observing the results, we better understand the influence of individual control. After completing each of the four applications, we apply them together at the same time in the model and compare the outcomes using different control bounds and state variable weights. We conclude the results by presenting several graphs. Similarly, we fit a SARS-CoV-2 model to US data of COVID-19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with two-week delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes. 
 
Next, a multiple shooting parameterization method is developed for studying stable/unstable manifolds attached to periodic orbits of systems whose dynamics is determined by an implicit rule. We represent the local invariant manifold using high order polynomials and show that the method leads to efficient numerical calculations. We implement the method for several example systems in dimension two and three. The resulting manifolds provide useful information about the orbit structure of the implicit system even in the case that the implicit relation is neither invertible nor single-valued. 
 
Please contact Dr. Hongwei Long (hlong@fau.edu) for an electronic copy of the dissertation. A hardcopy of the dissertation is not displayed in the departmental office in order to avoid multiple people touching the same hardcopy at this pandemic time. 
  
All are cordially invited. 

Speaker:  Theresa Buscemi (in person presentation): 

Title: Enumeration of Spanning Trees in a Graph by the Matrix Tree Theorem 

Abstract: In Graph Theory, a graph is called a tree if it is connected, undirected, and acyclic, i.e. any two vertices in the graph are connected by exactly one path. A subgraph H of a connected graph G is called a spanning tree if H is a tree which includes all the vertices of G. Now, let G be a connected graph with vertex set V = {v_1, v_2, ..., v_n} and edge set E = {e_1, e_2, ..., e_m}. After arbitrarily assigning orientations to the edges of G, we can define the incidence matrix M of G, whose (i, j)th entry is equal to 1 if e_j leaves v_i, -1 if e_j enters v_i, and 0 if e_j is not incident with v_i. The Matrix Tree Theorem states that the number of spanning trees of G is given by (the absolute value of) the determinant of any (n-1) x (n-1) submatrix of the augmented adjacency matrix D := MM^T. We provide a proof of the Matrix Tree Theorem and demonstrate how the theorem can be applied to count the number of spanning trees in example graphs. 

Virtual Option (ZOOM)

Zoom link:   

https://fau-edu.zoom.us/my/tbuscemi2020?pwd=cHJOZE9QTDZmcXFacTVoNGJGbVludz09 

All are cordially invited. 

Prelim Exam: Sulani Thakshila

Summary:  

One of the most promising fields in the security based problems in Cryptography are utilized lattices due to its hardness and efficiency. The digital signature schemes(DSSs) in lattice-based cryptographic primitives are now very practical in compared with traditional cryptosystems like RSA or DSA which are based on factoring problem or discrete logarithm problem. Unlike the NTRUSign and Hash-and-Sign, Fiat-Shamir(FS) transforma-tion in DSSs first build an identification scheme in a certain form and then convert it into a DSS. In particular, identification scheme that has challenge as a polynomial is transformed into a DDS by improving length of the signature and making collisions resistant hash function family. While security in the identification scheme is based on approximate short vector in the standard model and Random Oracle Model(ROM), security of the DDS is depend on the finding collisions in the family of hash functions. The hardness assumptions here are used in ring-SIS(Short Integer Solution) problem and now it has been adapted to ring-LWE(Learning With Erros) which decreases the size of the signature and keys thereby improving the efficiency. I will explain FS-transformation schemes and how it is related to signature schemes. 

In particular, Abdalla et al. in [1] introduced the idea of lossy identification scheme and give tight reductions in Quantum Random Oracle Model(QROM). The lossy identification scheme comes with an additional lossy key which is the output of the key generation algorithm and computationally indistinguishable from honestly generated ones. The security of the lossy identification scheme is a notion of impersonation of the lossy keys with respect to an adversary has access to lossy public keys and simulated transcript of the model. The NIST submissions TESLA and Dilithium are practical examples of lattice instantiation of [1]. For non-lossy lattice-based identification schemes has underlying signatures in Ducas et al. in [2]. The security of such schemes is non-tight and use the Forking Lemma. For example BLISS signature scheme Ducas et al. in [2] improved the rejection sampling by bimodal Gaussian instead of shifted Gaussian distributions. I will explain the lossy signature scheme and BLISS signature scheme in more detail in the notions of FS- transform in lattices. 

The module lattices is the most appealing aspects of the lattice-based protocols because of strong security proof based on hardness assumptions in worst case problems. I will explain the importance and advantages of modules lattices. The cyclotomic ring Zq[x]/(xn + 1) where n is a power of two plays a big role in constructing lattice-based protocols and the small polynomials invertibile under special congruence conditions, q ≡ 5 (mod 8). Nguyen in [3] showed how to omit this congruence condition instead analysing zeroes in CRR(Chinese Remainder Representation) of small polynomials. Concretely, without the prime condition, Nguyen in [3] provide a upper bound in terms of probability for the non-existence of a short vector in a random module lattice. I will explain non-existence of prime condition improve the tight security in QROM, however with a less speed. 

Join Zoom Meeting
https://fau-edu.zoom.us/j/7290087861?pwd=SHlXYUwxK29mU1ZzRGh6NXJpdzJqZz09

<b>Meeting ID: 729 008 7861
Passcode: UetKL0nL

April, 2022

April 7
4:00 p.m.
SE 215

Speaker: Thomas Benitez (in person) 

Title: A New Zero-Knowledge Protocol for the Syndrome Decoding Problem and Code-Based Signature 

Abstract: Zero-knowledge proofs are an important tool for many cryptographic protocols and applications. The threat of a coming quantum computer motivates the research for new zero-knowledge proof techniques for (or based on) post-quantum cryptographic problems. One of the few directions is code-based cryptography for which the strongest problem is the syndrome decoding of random linear codes.  In this presentation, we introduce a new zero-knowledge proof for the syndrome decoding problem on random linear codes. This protocol achieves a soundness error of 1/n for an arbitrary n.  We provide an optimized version of this zero-knowledge protocol which achieves arbitrary soundness through parallel repetitions and merged cut-and-choose phase. While turning this protocol into a signature scheme, we achieve a signature size of 17 KB for a 128-bit security. This represents a significant improvement over previous constructions based on the syndrome decoding problem for random linear codes. 

All are cordially invited. 

April 8
1:00 pm

SE 216

MS Exam Presentation

Speaker:  Lariza Ramsammy (in person presentation)

Title: Variations on Valuation Domains 

Abstract: It is common knowledge, in Commutative Algebra, that valuation domains are GCD domains with linearly ordered prime ideals. In his 1995 paper in Communications in Algebra, Ayman Badawi gave other characterizations of integral domains with linearly ordered prime ideals, thus providing an alternative proof of this equivalence. In this presentation, we will explore one of these characterizations as well as its implication for local integral domains with related properties, including pseudo-valuation domains and divided domains. Finally, we will discover how these equivalent characterizations lead to a chain of implications among the properties considered.  

All are cordially invited. 

Master of Science Exam (Presentation)

Speaker:  Raya Shimshi (in person) 

Title: Super Convergence of Ergodic Averages for Quasiperiodic Orbits (Quantitative Quasiperiodicity) 

Crypto Café

Zoom: https://fau-edu.zoom.us/j/88045709062?pwd=NjN2NGRnVDhkdExwcUxlOHBPUjErUT09

Speaker : Emrah Karagoz, Florida Atlantic University

Title : Correlation Power Analysis on AES

Abstract : The main goal of side channel attacks is to gain physical information (such as timing information, power consumption, electromagnetic leaks etc.) from a cryptographic algorithm implemented on a computer device, and to obtain the cryptographic keys by using this information. Power analysis is a type of side channel attack in which the attacker aims to extract the cryptographic keys by studying the power consumption of the device. On the other hand, AES (Advanced Encryption Standard) is a symmetric algorithm standardized by NIST in 2001, and it has been deployed mostly everywhere to encrypt the sensitive data because of its strong cryptographic security. In this presentation, we will explain how correlation power analysis works on AES so that an attacker can extract the AES key very easily, and therefore we will point out that the implementation of a cryptographic algorithm is as important as its cryptographic security.

Society for Industiral and Applied Mathematics (SIAM) student chapter presents:

Speaker:  Dr. Dan Wilburne, MITRE Corporation. A flyer for the event can be downloaded from the link below:

https://drive.google.com/file/d/1hb184hSqxRpsr2GmjoVrY11RNX-0uQZ-/view?usp=sharing

Title:  My journey as an Applied Mathematician

Zoom:

https://fau-edu.zoom.us/j/89219435411?pwd=UWFUaFliS25lcUJ1NGFBaWxweXBXUT09                                                                                                            

Meeting ID: 892 1943 5411

Passcode: Siam2022

Also, please feel free to visit (or subscribe to) our Youtube channel: https://www.youtube.com/channel/UCLLIwl8E06aAfks2dNKve0g for previous talks and follow our Twitter page (@FAU_SIAMstudent): https://twitter.com/FAU_SIAMstudent for upcoming announcements.

DATA and AI RESEARCH EXHIBITIONS

This event is presented by the FAU Data-Driven Science and AI Conference which will be held in the Student Union on Saturday, May 21, 2022, 8:00 am-5:00 pm. Both the conference and the exhibition are open to to all students. If you attend the event on April 21st, 2022 for DATA and AI RESEARCH EXHIBITIONS at the Sandbox, you will receive the free registration to the May 21^st Data-Driven Science and AI Conference!

There is also an opportunity to present your research in the poster session at the Data-Driven Science and AI Conference. Any poster presenters will also have registration reimbursement for the Conference.  If you are willing to participate in the poster session in the conference, please contact Dr. Wazir Muhammad. The email: wmuhammad@fau.edu, and visit the following link to submit your poster information.

https://forms.gle/WK7RNHTxd1ZoWDGG8

Please submit if you haven’t already.

Thank you for your interest in Data-Driven Science and AI Conference. If you have any questions or need additional information about DATA and AI RESEARCH EXHIBITIONS, please feel free to contact Dr. Maria Provost (mprovost@fau.edu) or visit the website: Data-Driven Science and AI Conference

See you all there on April 21^st at Sandbox!

Math Club - History of AI (Final Math Club event of the semester)

FAU's Math Club and the Society of Women Engineers will host, for its final event of the semester, a talk entitled, Hisotry of AI.
This event will be held in-person in the Engineering East building.  You may also attend virtually via Zoom. 

All are invited.  We hope tp see you there!

Zoom link: https://fau-edu.zoom.us/j/84967758783?pwd=alhOOUg1dGtUcDVLUGNRYW43ODhPdz09

Tues., April 26
SE 215
9:00 am

Prelim Exam:  This event is open to all graduate faculty.  

Speaker: David Urizar, Ph.D. Candidate

Summary:   The proposed preliminary exam would present the fundamentals of rigidity theory.  The student will define key terms: Graph realizations, Laman condition, Laman number,  infinitesimal motion, and pure condition.  Furthermore, he will develop some further theory in the case of 2-dimensional rigidity, considering angle constraints in addition to length constraints for bar-and-joint frameworks. He will explain how algebraic relations of higher degree translate into linear relations on the columns of the rigidity matrix.  He will provide combinatorial characterizations for the number of unique realizations of a rigid body modulo its rigid motions. The student will reformulate the problem of determining rigidity in terms of the algebraic geometry of the configuration space, and present numerous examples to illustrate these ideas.  The student will be prepared to answer questions relating to structural rigidity and its applications. 

March 2022

The Crypto Café is back!

Join us for the first talk of the 2022 edition of our bi-weekly cryptography seminar, starting this Thursday, March 3, at 10:00 a.m. 

Topics will include mathematics and computer science that relate to codes, cryptography, and information security. 

Join us either in-person or virtaully this Thursday, March the 3rd, 2022.

Speaker : Edoardo Persichetti, Florida Atlantic University

Title : Code-based Signatures: New Approaches and Research Directions

Abstract : Code-based cryptography is one of the main areas of research within the context of quantum-secure communication. Yet, designing an efficient and secure code-based signature scheme has been a challenging problem for the last few decades. In this talk, I will summarize some of the long history of code-based signatures, and then illustrate current work and future research directions for this important topic.

Everyone welcome and there will be coffee, and donuts!

Attend virtually on Zoom:

Zoom: https://fau-edu.zoom.us/j/88045709062?pwd=NjN2NGRnVDhkdExwcUxlOHBPUjErUT09

For future/past sessions, also see https://www.math.fau.edu/crypto_cafe.php

53rd Southeastern International Conference on Combinatorics, Graph Theory and Computing, March 7-11, 2022
Regsiter Here 

Crypto Café presents:

Speaker : Abhraneel Dutta, Florida Atlantic University

Title : Two Constant Time Polynomial Inversion Algorithms for Post-Quantum Cryptosystems

Abstract : A very common primitive in code-based cryptography is computing the inverse of a binary polynomial over a binary polynomial ring and making such algorithms constant time helps achieve the prevention against timing side channel attacks. This presentation will focus on a brief introduction to two recent time polynomial inversion algorithms which are capable to run in constant time: Bernstein-Yang's "SafeGCD" polynomial inversion, based on the Extended GCD algorithm and constant time Itoh-Tsuji Inversion (ITI) derived from Fermat's Little Theorem.

To join virtually on Zoom: 

Zoom: https://fau-edu.zoom.us/j/88045709062?pwd=NjN2NGRnVDhkdExwcUxlOHBPUjErUT09

For future/past sessions (growing list), also see https://www.math.fau.edu/crypto_cafe.php

An informal meeting to discuss...

Reflection and  Celebration of Diversity, Equity and Inclusion. 

Everyone is welcome to be a part of this important conversation!  Join us!

PhD Dissertation Defense:  Sean Perry (Doctoral candidate)

Dissertation Title: On the Image Counting Problem from Gravitational Lensing 

Advisor: Dr. Erik Lundberg 

This Doctoral Defense is also being presented on ZOOM.

Join Zoom Meeting
https://fau-edu.zoom.us/j/88203111079?pwd=K0dxcE5WRktNZFZML1JyWHdYSkNuUT09

Meeting ID: 882 0311 1079
Passcode: DzLV5P

Crypto Café 

Time/Room: March 31, 2022, SE-43, Room 215; 10:00 a.m.

Speaker : Tovohery Randrianarisoa, Florida Atlantic University

Title : On Linear Complexity of Finite Sequences: Coding Theory and Applications to Cryptography

Abstract : We define two metrics on vector spaces over a finite field using the linear complexity of finite sequences. We then develop coding theory notions for these metrics and study their properties.  We show how to reduce the problem of finding codewords with given Hamming weight into a problem of finding a vector of a given linear complexity. This implies that our new metric can be used for cryptography in a similar way to what is currently done in the code-based setting with Hamming metric. Recently, Feneuil et al. presented a signature scheme with codes with Hamming metric using a multiparty computation approach. We show that by transforming their work into a setting with linear complexity as metric, we can improve the speed of signing by eliminating all the interpolations steps in the process.

It will also be held on Zoom:

Zoom: https://fau-edu.zoom.us/j/88045709062?pwd=NjN2NGRnVDhkdExwcUxlOHBPUjErUT09

For future/past sessions (growing list), also see https://www.math.fau.edu/crypto_cafe.php

February 2022

FAU's Math Club presents "Latex Workshop"

Cryptography Presentation
Speaker: Francesco Sica, faculty canditate

Title: Factoring with (Less) Hints

Tues, Feb 8
11:00 am
SE 215

Cryptography Presentation
Speaker: Veronika Kuchta, faculty canditate

Title: Post-Quantum Zero-Knowledge Proofs

Thurs, Feb 10
2:00 pm
ZOOM (virtual)

Cryptography Presentation (virtual)
Speaker: Jason LeGrow, faculty candidate

Title:  Some Problems in Isogeny-Based Cryptography

Join Zoom Meeting: https://fau-edu.zoom.us/j/3373397013?pwd=dzhlc2RaS0FJdUl0VzB0M2g2ZzlHQT09

Meeting ID: 337 339 7013
Passcode: 2q1d0Z

Fre, Feb 11
4:00 pm
Zoom (virtual)

The student chapter of SIAM presents:
Speaker: Mr. Alex D. Zharichenko, Aurora Innovation and the University of Pittsburgh.

CLICK HERE FOR THE OFFICIAL FLYER

Title: What got you here won’t get you there: Landing a position in Data Science, Data Engineering and Machine Learning

Join via Zoom:  https://fau-edu.zoom.us/j/87951200366?pwd=alN6NXFZRXRUbm91b3AwSTRhaTJldz09

Meeting ID: 879 5120 0366
Passcode: Industry22

Florida GeoGebra Conference 2022
Register Here!

Sat., Feb 19
9:00 am
SE-43, rm. 215

The FAU Student Chapter of the Association for Women in Mathematics (AWM) presents:
Florida Women in Math Day ( regsitration: SE-43, rm. 215)

Guest Speakers:  Dr. William Hahn (FAU) and Dr. Katherine Stange (University of Colorado).

All information about the event, along with the registration information and event schedule, can be found on the event website.
Register for this free event here.
For questions, please contact us at awmfau@gmail.com.

January 2022

International Symposium on Artificial Intelligence and Mathematics (ISAIM 2022).  this meeting is being held virtually.  Regsitration is free.  The link will be distributed to those who regsiter for the ISAIM 2022 Conference at the ISAIM 2022 website.  

Logical Foundations of Computer Science (LFCS, 2022) Wyndham Deerfield Beach Resort.  

An Afternoon Tea Time
Hosted by the FAU Student Chapter of the Association for Women in Mathematics (AWM)

Sat., Jan 29
8-5 p.m.