2022 Department of Mathematics Events

 

 

November 2022

Thursday
Nov., 3
SE 215
11:00 am

Analysis and Applications Seminar

Thursday
Nov. 3
SE 215
5:00 pm

FAU's Math Club

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

Friday
Nov. 4
SE 215
11:00 am

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.

Sat.
Nov. 5
PS 109
2:30-4:00 pm

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:  http://www.math.fau.edu/math-circle/

Thursday
Nov., 10
SE 215
11:00 am

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

Thursday
Nov. 10

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

Wednesday
Nov. 16  

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

Wednesday
Nov. 16
SE 215
3:00 pm

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. 

Wednesday
Nov. 16
SE 215
4:00 pm

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!

Thursday
Nov. 17
SE 215
11:00 am

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

Thursday
Nov. 17
SE 215
5:00 pm

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.

Friday
Nov. 18
SE 215
4:00 pm

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)). 

Saturday
Nov. 19
PS 109
2:30-4:00 pm

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:  http://www.math.fau.edu/math-circle/

Monday
Nov. 21
SE 215
4:00 pm

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

Thursday
Oct. 6
SE 215
5:00 pm

FAU's Math Club

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

Saturday
Oct. 8

PS 109
2:30-4:00 pm

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:   http://www.math.fau.edu/math-circle/

Thursday
Oct., 17
SE 215
11:00 am

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.

Tuesday
October 18
SE 215
4:00 pm

Crypto Café

Speaker:   Dr. Shi Bai, Florida Atlantic University

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

Thursday
Oct. 20
SE 215
5:00 pm

FAU's Math Club

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

Friday
Oct. 21
SE 215
4:00 pm

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.   

Saturday
Oct. 22
PS 109
2:30-4:00 pm

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:   http://www.math.fau.edu/math-circle/

Thursday
Oct., 27
SE 215
11:00 am

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.

Thursday
Oct. 27
SE 215
5:00 pm

FAU's Math Club

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

Friday
Oct., 28
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.

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.

                   Date/Time/Location              

September 2022

Thurs., Sept. 8
SE 215
11:00 am     

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!

Wed., Sept. 14
SE 215
4:00 pm

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

Thurs., Sept. 15
SE 215
11:00 am

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.

Thurs., Sept. 15
SE 215
5-7 pm

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.

Thurs. Sept. 22
SE 215
11:00 am

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.

 

Thurs., Sept. 22
SE 215
5:00 pm

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.

Sat., Sept. 24
PS 109
2:30-4:00

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:  http://www.math.fau.edu/math-circle/

Tues., Sept. 27
SE 215
4:00 pm

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 http://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.

Fri., Sept. 30
SE 215
4:00 pm

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   

 

MS Exam:  Pitambar Acharya

Title: Bayesian Model Averaging: An Overview 

Abstract: In probability theory and statistics, the notion of  Bayes' theorem  (Thomas Bayes: circa 1701 – 7 April 1761), describes the probability of an event, based on prior knowledge of conditions that might be related to the event. In this presentation, we will give an overview of Bayesian Model Averaging (BMA).  It is a well known fact that standard statistical practice ignores model uncertainty. So, statisticians/data scientists typically select a model from a given class of models and then proceed as if the model generated the data. This consequently leads to over-confident inferences. BMA is an intuitively attractive solution to the problem of accounting for model uncertainty. Nowadays, the use of BMA is implemented rigorously in a number of fields and we will explore some applications. 

All are cordially invited. 

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

 Aug., 31
SE 215
5:00 pm

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

Jul., 25-29
8:30 am-5:00 pm

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

Thurs., May 19
SE 215
2:00 pm

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. 

Fri., May 6
SE 215
ZOOM option
11:00 am

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 of a connected graph 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_1, v_2, ..., v_n} and edge set = {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 := 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. 

Fri., May 13
10:00 am
ZOOM

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. 

 

April 11
1:00 p.m.
SE 271

Master of Science Exam (Presentation)

Speaker:  Raya Shimshi (in person) 

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

April 14
10:00 am
SE 215

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.

 

April 19
4:00 pm
ZOOM

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.

Thurs., April, 21
Sandbox (Library)
3-6 pm

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 21st 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 21st at Sandbox!

Thurs., April 21
ZOOM
6:30 p.m.

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

Thurs, March 3
10 am
SE 215

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 http://www.math.fau.edu/crypto_cafe.php

Mon.-Fri., Mar 7-11
8:00 am-6:00 pm.

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

Thurs., Mar 17
10:00 am
SE 215

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 http://www.math.fau.edu/crypto_cafe.php

Fri., March 18
2:00 p.m.
SE 215

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!

Fri., Mar 25
1:00 pm
SE 215

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

Thurs., March 31
10:00 am
SE 215

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:

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

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

 

February 2022

Thurs., Feb 3
6 pm
The Sandbox

FAU's Math Club presents "Latex Workshop"

Mon, Feb 7
12:00 pm
SE 271

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

Sat., Feb 19
8:00 am-6:00 pm.

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

Mon-Wed., Jan 3-5
8-5 pm

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.  

Mon.-Wed., Jan 10-13
9-6:00 p.m.

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

Sat., Jan. 22
9-2 pm
AMC8 Middle School Math Day 2022
Register Here
Fri., Jan 28
4:00 pm
SE 215

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.

MuAlphaTheta Math Competition - An event with 13 contests for individuals, teams and school.
Florida Atlantic University, Davie campus