2023-24 Department of Mathematics Events                                                      



 

January 2024

Mon.-Wed.
Jan. 8-10
8:00 am
Bahia Mar,
Ft. Lauderdale

The International Symposium on Artificial Intelligence and Mathematics (ISAIM, 2024) & International Workshop on Combinatorial Image Analysis (IWCIA'24)

Register Here!

Saturday
Jan. 20
9:00 am

American Mathematics Competition - Middle School Students

The AMC8-Middle School Math Day will be held at FAU
For More Information and to REGISTER, CLICK HERE!

Tuesday
Jan. 22
10:00 am
SE 215
ZOOM

Crypto Cafe

Speaker:  Dr. Veronika Kuchta, Florida Atlantic University

Title:  Post-Quantum Signatures from Secure Multiparty Computation  (Dr. Kuchta will present Chapter 3 of Feneuil’s thesis).

Abstract:  The ongoing effort to build a quantum computer urges the cryptography community to develop new secure cryptosystems based on quantum-hard cryptographic problems. In this thesis, we focus on the design of signature schemes built from zero-knowledge proofs of knowledge. More precisely, we focus on the MPC-in-the-Head paradigm which provides a generic way to build zero-knowledge proofs using techniques from secure multiparty computation.
We propose several new signature schemes using the MPC-in-the-Head framework. Most of these schemes are competitive with the existing schemes in the post-quantum literature.  They have signature sizes between 5 KB and 20 KB for 128-bit security, and have very small public keys (less than 200 B). Their security relies on a large scope of hard problems. Some of them rely on code-based assumptions, such as the hardness of solving the syndrome decoding problem for random linear codes. Others rely on the multivariate quadratic problem, the subset sum problem, and the MinRank problem.  We also develop two new MPC-in-the-Head techniques. The first one aims to efficiently address a context of small secret values over large modulus. The second one consists of a new way of transforming an MPC protocol into a zero-knowledge proof. This new transformation provides new trade-offs in terms of communication costs vs running times. In particular, it enables us to achieve small verification times.  Several submissions in the NIST call for additional post-quantum signatures rely (sometimes partially) on ideas developed in this thesis. 

Keywords: zero-knowledge proofs, post-quantum signatures, MPC-in-the-Head.

+Zoom (click here)

Saturday
Jan. 27
2:30-4 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!      Register Here for Fall, 2024 Math Circles

Tuesday
Jan. 29
10:00 am
SE 215
ZOOM

Crypto Cafe   

Speaker:    Dr. Vincenzo Pallozzi Lavorante, Postdoctoral fellow, University of South Florida 

Title: Locality and complexity distribution in coding theory, an approach based on Galois theory

Abstract: The storage of information and the necessity to ease the heaviness of big data computations are two key aspects to consider when investigating new problems in coding theory.  The concept of locality is closely linked to the reliability of distributed storage systems, while matrix multiplication is often the first operation required for secure distribution. This presentation will provide an overview of the latest developments and explore how Galois theory can offer valuable tools for addressing and contributing to these areas.

Bio: Dr. Pallozzi Lavorante received a Ph.D. in Mathematics in 2022 from the University of Modena and Reggio Emilia in Italy. Since August 2022 he has been a Postdoctoral fellow at the University of South Florida. His research interest focuses on Galois Theory and polynomials over finite fields with applications to coding theory, code-based cryptography, and finite geometry.

+Zoom (click here)

 

December, 2023

Friday
Dec. 1
4:00 pm
SE 215

Analysis and Applications Seminar

Speaker:  Taylor Brysiewicz, University of Western Ontario

Title: Algebraic Matroids, Monodromy, and the Heron Variety

Abstract: Heron's formula gives the area of a triangle in terms of the lengths of its sides. More generally, the volume of any simplex is determined by its edge-lengths via a Cayley-Menger determinant.
In work-in-progress with Seth Asante and Michelle Hatzel, we ask *Which other sets of volumes of faces of an n-simplex, when known, determine the remaining unknown face-volumes?*.
An answer to this question is encoded in the algebraic matroid of the Heron variety. Moreover, we ask *When are these unknown volumes recoverable via formulae in the known volumes?*
We answer these questions for n<5 by combining techniques in computational group theory, computer algebra, field theory, and numerical algebraic geometry. Of particular focus is the problem of recovering the 10 edge lengths of a 4-simplex from its 10 triangular face areas, a problem motivated by applications in theoretical physics.

Saturday
Dec. 2
2:30-4 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!    Register Here for Fall, 2023 Math Circles

Monday
Dec. 4
5:30 pm
SE 215

FAU Math Club

Join your friends and other math enthusiasts at FAU's Math Club events!  The purpose of our Club is to improve academic ability, spread awareness of mathematics’ importance, and share a passion for all fields of mathematics!

The club is open to all majors and all math backgrounds. Activities at the club will include:

  • Discussion of mathematics’ applications and importance.
  • Study sessions for mathematical concepts.
  • Group problem solving of math problems from a variety of fields, including set theory, algebra, geometry, topology, and more.
  • Presentation of exciting mathematical research and concepts.
  • Discussions on graduate school and employment

Snacks are always available!  See you there!

Tuesday
Dec. 5
10:00 am
SE 215
Zoom

Crypto Café

Speaker:  Dominic Gold, Florida Atlantic University

Title: TDA-Preprocessing Yields Quantifiable Efficiency Gains in Privacy-Preserving ML Models 

Abstract: Computational tools grounded in algebraic topology, known collectively as topological data analysis (TDA), have been used for dimensionality-reduction to preserve salient and discriminating features in data. TDA's flagship method, persistent homology (PH), extracts distinguishing shape characteristics from the data directly and provide inherent noise-tolerance and compact, interpretable representations of high-dimensional data that are amenable to well-established statistical methods and machine learning (ML) models; this faithful but compressed representation of data motivates TDA's use to address the complexity, depth, and inefficiency issues present in privacy-preserving, homomorphic encryption (HE)-based ML models through ciphertext packing---the process of packing multiple encrypted observations into a single ciphertext for Single Instruction, Multiple Data (SIMD) operations.

By investigating several TDA featurization techniques on the MNIST digits dataset using a logistic regression (LR) classifier, we demonstrated that the TDA methods chosen improves encrypted model evaluation with a 10-25 fold reduction in amortized time while improving model accuracy up to 1.4% compared to naive reductions that used downscaling/resizing. The developed technique also has implications for multiclass classification by sending multiple model classifications in a single packed ciphertext to reduce the communication overhead between the Client and Server, potentially avoiding restriction to a binary classification (as done in past HE-ML literature for secure classification of MNIST digits).

Biography: Dominic Gold is a 6th-year graduate teaching assistant at Florida Atlantic University who studies both cryptography and data science, with his main interest in secure/privacy-preserving machine learning on encrypted data. The intersectionality of his research in homomorphic encryption and topological data analysis shows promising implications for research in both fields, with his work in cryptography recognized by venues such as USENIX and ACM CCS. The ultimate goal of his work is to enable real-time predictions on encrypted biomedical data to improve both the reliability, security, and equitability of healthcare systems.

Zoom (click here)

Meeting ID: 878 9825 0483       Passcode: gHJF6g

All are cordially invited.

Saturday
Dec. 16
2:30-4 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!    Register Here for Fall, 2023 Math Circles

 

November, 2023

Wednesday
Nov. 1
1:00 pm
SE 271

Algebra Seminar

Speaker:   Dr. Robert Lubarsky, Florida Atlantic University

Title:  On the Location of Winning Strategies for F$_\sigma$ Games

Abstract:  Suppose A is a set of infinite sequences of natural numbers. This induces a game G(A): players I and II alternate turns picking a natural number, thereby producing an infinite sequence; I wins if this sequence is in A, II wins if it is not. Does either player have a winning strategy? If A is simply definable, then yes, with the complexity of producing such a winning strategy growing rapidly as the complexity of A increases. I will introduce this topic and discuss some of the issues that come up, aiming at some of the open questions that remain when A is an F$_\sigma$ set, meaning a countable union of closed sets.

All are cordially invited

Thursday
Nov. 2
11:00 am
SE 215

Analysis and Applications Seminar

Speaker:   Dr. Zvi Rosen, Florida Atlantic University

Title:  Angles in Planar Frameworks

Abstract: What subsets of distances among n points in the plane are enough to determine all pairwise distances? This question was answered with a theorem by Hilda Pollaczek-Geiringer in 1927, re-proved by Gerard Laman in 1970. Interestingly, Whiteley proved in 1987 that the edge directions (or bearings) of a planar framework have the very same combinatorics.

In this talk we will discuss some new results about a more complicated question still: What subsets of angles among n points in the plane are enough to determine all angles?  We will also develop some angle analogs of rigidity-theoretic concepts like Laman numbers, circuits, and the pure condition. This is based on joint work with Sean Dewar, Georg Grasseger, Anthony Nixon, William Sims, Meera Sitharam, and David Urizar.

All are cordially invited

Thursday Nov. 2
4:00 pm
SE 212

Association for Women in Mathematics (AWM) FAU's Student Chapter

FAU's Student Chapter of the AWM presents  "An Afternoon Tea Time!"   (flyer)

Please join us for a cup of tea, cookies and conversation about mathematics.

All are cordially invited!

Saturday
Nov. 4
2:30-4 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!      Register Here for Fall, 2023 Math Circles

Monday
Nov. 6
5:30 pm
SE 215

FAU Math Club

Join your friends and other math enthusiasts at FAU's Math Club events!  The purpose of our Club is to improve academic ability, spread awareness of mathematics’ importance, and share a passion for all fields of mathematics!

The club is open to all majors and all math backgrounds. Activities at the club will include:

  • Discussion of mathematics’ applications and importance.
  • Study sessions for mathematical concepts.
  • Group problem solving of math problems from a variety of fields, including set theory, algebra, geometry, topology, and more.
  • Presentation of exciting mathematical research and concepts.
  • Discussions on graduate school and employment

Snacks are always available!  See you there!

Tuesday
Nov. 7
10:00 am
SE-215
Zoom

Crypto Café

Speaker: Zhenisbek Assylbekov, Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, IN

Title: Intractability of Learning AES with Gradient-based Methods

Abstract: We show  the approximate pairwise orthogonality of a class of functions formed by a single AES output bit  under the assumption that all of its round keys except the initial one are independent. This result implies  the hardness of learning AES encryption (and decryption) with gradient-based methods. The proof relies on the Boas-Bellman type of inequality in inner-product spaces.

Keywords: Advanced Encryption Standard, Block Ciphers, Gradient-based Learning

Bio: Zhenisbek has a PhD in Mathematical Statistics from Hiroshima University. After the PhD and some period of work in industry, he got a job at Nazarbayev University, where he was working as a Teaching Assistant, Instructor, and Assistant Professor in the Department of Mathematics during 2011-2023. Currently, he is an Assistant Professor of Data Science at Purdue University Fort Wayne.  His research interests are in machine learning with applications to natural language processing (NLP). He is interested in both the theoretical analysis of machine learning algorithms and the practical implementation and experimental evaluation of such algorithms on text data. He is also interested in hardness of learning which is closely related to cryptography because cryptographic primitives are exactly what is hard for machine learning.

Video Recording

Wednesday
Nov. 8
1:00 pm
SE 271

Algebra Seminar

Speaker:  Christian Corbett, Florida Atlantic University

Title: Properties of d-elements in algebraic frames with FIP

Abstract:  Given an algebraic frame with the finite intersection property (FIP), we say an element x is a d-element if can be represented as the supremum of double polars of compact elements that lie below x. The collection of all d-elements is denoted as dL. By Zorn’s lemma, there exist maximal d-elements, and so we may equip the maximal elements of with the hull-kernel topology, and we call this topology Max(dL). In this presentation, we will discuss some properties of d-elements, dL, and some of the topological properties of Max(dL).

Wednesday
Nov. 8
3:00 pm

American Mathematics Competition - High School Students

The AMC-10/12A Contest will be held at FAU
For More Information and to REGISTER, CLICK HERE!   

Tuesday
Nov. 14
8:00 am

American Mathematics Competition - High School Students

The AMC-10/12B Contest will be held at FAU
For More Information and to REGISTER, CLICK HERE! 

Thursday
Nov. 16
10:00 am
Zoom

FAU Recruitment Seminar

Speaker:   Francesco Sica, Florida Atlantic University

Presentation:  FAU Math PhD recruitment talk to Nazarbayev University, Kazakhstan 

FAU Ph.D. sudent are welcome to join the Zoom meeting to share your experience as PhD students with the audience from Nazarbayev University in Kazakhstan.

Join Zoom Meeting:   https://fau-edu.zoom.us/j/82700380173?pwd=eEV0aEl1SGZ2S3pnVVg2ZFR2U1hIQT09

Meeting ID: 827 0038 0173           Passcode: hKQh6F

 

Analysis and Applications Seminar

Speaker:  Dr. Francis Motta, Florida Atlantic University

Title:  Mathematical methods for the study of  Plasmodium  intraerythrocytic cycle dynamics

Abstract:   Malaria infections totaled nearly 250 million cases worldwide in 2021, with the estimated number of malaria deaths nearing 620,000. Despite its significant global impact, much remains unknown about the fundamental biology of  Plasmodium, the parasite which causes malaria infection. In this talk we will highlight recent modelling and statistical data analysis approaches tailored to answer important biological questions about the host-parasite dynamics during one of the prominent stages of the  Plasmodium  life cycle, the intraerythrocytic development cycle. The dynamics of the intraerythrocytic development cycle is characterized by population-synchronized periodic cellular development, parasite replication, egress from and reinvasion of red blood cells. Motivated by this dynamic process, we will also discuss ongoing efforts to rigorously define a quantified measure of population (a)synchrony, establish its desirable properties, and develop and apply the appropriate mathematical modelling framework to study the dynamics of synchronization for a population of individuals progressing through a common state space. This will lead us to consider well-trodden mathematical theory of discrete-time, multi-type, Markov branching processes. We will also discuss the potential usefulness of such models to motivate new biological experiments involving  Plasmodium  and speculate on potential biological discoveries that could motivate the need for new mathematical theories and analyses. 

Thursday
Nov. 16
4:00 pm
SE 215
ZOOM

MS Exam

Speaker:  Julie Kent, MS Candidate, Florida Atlantic University

Title:  Three-Gap Theorem 

Abstract:  The Three-Gap Theorem states that there are at most three unique distances between n points on a circle placed at angles a, 2a, 3a, and so on. In this talk, I will work through this proof as well as the more general result. Additionally, I will prove an additional condition which results in only two unique distances.

Join Zoom Meeting:         https://fau-edu.zoom.us/j/2703788960 

Meeting ID: 270 378 8960

Thursday
Nov. 16
4:00 pm
Rm#: TBA
Jupiter Campus

Algebra Seminar (Jupiter Campus)

Speaker: Dr. Yiqiang Zhou, Newfoundland and Labrador's University

Title:  Fine rings and generalizations

Abstract: A ring (associative with identity) is called a fine ring if every nonzero element in it is the sum of a unit and a nilpotent element.  G. Cǎlugǎreanu and T.Y. Lam initiated the study of fine rings in "Fine rings: A new class of simple rings."  J. Algebra Appl. (2016).  In this talk, we review known results and discuss new developments of this study.

Saturday
Nov. 18
2:30-4 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!      Register Here for Fall, 2023 Math Circles

Monday
Nov. 20
5:30 pm
SE 215

FAU Math Club

Join your friends and other math enthusiasts at FAU's Math Club!  The purpose of our Club is to improve academic ability, spread awareness of mathematics’ importance, and share a passion for all fields of mathematics.

The club is open to all majors and all math backgrounds. Activities at the club will include:

  • Discussion of mathematics’ applications and importance.
  • Study sessions for mathematical concepts.
  • Group problem solving of math problems from a variety of fields, including set theory, algebra, geometry, topology, and more.
  • Presentation of exciting mathematical research and concepts.
  • Discussions on graduate school and employment

Snacks are always available!  See you there!

Tuesday
Nov. 21
10:00 am
SE 215
ZOOM

Crypto Café

Speaker:  Paolo Santini, Universita Polotecnica Delle Marche, Italy

Title: A New Formulation of the Linear Equivalence Problem and Shorter LESS Signatures

Abstract: The problem of determining whether two linear codes are equivalent is called Code Equivalence Problem. When codes are endowed with the Hamming metric (which is the most studied case), the equivalence is mainly considered with respect to monomial transformations (permutations with scaling factors) and the problem is known as the Linear Equivalence Problem (LEP). Code equivalence can be described as a transitive, non-commutative group action and, as such, finds a natural application in cryptography: for example, it is possible to design zero-knowledge proofs, and hence signature schemes. In recent works, it has been shown that LEP can be reformulated using notions such as information sets (arguably, ubiquitous objects in coding theory) and canonical forms. This unlocks some new features, such as the possibility of communicating the equivalence map in a very compact way (which leads to much shorter signatures), as well as opening new attack avenues. In this talk, we recall the basics of code equivalence and then focus on these recent results, aiming to describe how they can be applied to boost the performance of cryptographic schemes.

Zoom (click here)

Meeting ID: 878 9825 0483           Passcode: gHJF6g

All are cordially invited.

Tuesday
Nov. 21
4:00 am
SE 215

Association for Women in Mathematics, (FAU Student Chapter)

Tea Time!

The Student Chapter of the AWM invites you to our traditional  Tea Time on Thursday, November 21, at 4 p.m.,  SE 215. Please come and enjoy fellowship, and discussion about mathematics before the Thanksgiving break. We have cookies and tea for everyone.

AWM future activities will be discussed.

We will also introduce you and all students to the Mentoring program.

Wednesday
Nov. 29
1:00 pm
SE 215

Algebra Seminar

Speaker:   Papiya Bhattacharjee, Florida Atlantic University

Title:  Max(dL)  vs. Min(L), for  M-Frames  L

Abstract     The space of maximal d-ideals of  C(X)  is homeomorphic to the  Z♯-ultrafilters, and this space is the minimal quasi-F cover of a compact Tychonoff space  X. In this talk the notions of maximal d-ideals and  Z♯-
ultrafilters will be generalized for algebraic frames with the FIP. The speaker will also describe the relation between Max(dL) and the minimal primes element spaces of an algebraic frame  L, Min(L) and Min(L)−1.

Thursday
Dec. 30
11:00 am
SE 215

Analysis and Applications

Speaker:   Subhosit Ray, Florida Atlantic University Sandbox

Title:   A Peek into Equivariant Deep Learning

Abstract:   Current research in AI has focused chiefly on increased parameterization and data augmentation techniques to generalize their performance on out-of-distribution signals. Despite these improvements, performance may still fail under some symmetric transformations of the signals. Equivariant deep learning is a relatively niche but growing field that aims to tackle the problems by directly incorporating symmetries in neural architecture. In this presentation, I review a few works on equivariant deep learning and how it combines the world of abstract algebra, such as group theory, into deep learning. 

 

October 2023

Wednesday
Oct. 4
SE 271
1:00 pm

Algebra Seminar

Speaker: Albert Madinya, Florida Atlantic University

Title: Topologizing the Space of Minimal Primes of an Algebraic Frame

Abstract: An algebraic frame L is a partially ordered set in which every subset of L has a supremum and infimum and satisfies the strong distributive law.  Given an algebraic frame 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 Hull-Kernel 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 Hull-Kernel topology. Our aim in this talk to 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.

Thursday
Oct. 5
SE 215
11:00 am

Analysis and Application Seminar

Speaker: Jason Mireles-James, Florida Atlantic University

Title: Divergent Series in Dynamical Systems Theory: Numerical Analytic Continuation for Nonlinear Problems

Abstract: Last semester I gave a short talk about using the Borel transform to study problems in differential equations whose formal power series solutions diverge.  In this case, it would be nice to have rigorous error bounds describing how well the truncated divergent series approximates the true solution of the differential equation.  In last semester's talk we worked out a satisfactory solutions to a simple linear example problem due to Euler.

In this talk I will review some basic ideas about the Borel transform, and also recall very quickly the result from the previous talk.  Then I'll discuss how nonlinearities complicate the picture, leading to some non-local convolution operators.  I'll sketch numerical procedures for managing these complications, at least in a simple example problem, and will indicate how bounds on the numerical errors could be obtained using fixed point methods.  This is all very much work in progress, but I think it is also very interesting stuff and hope you will enjoy. 

Tuesday
Oct. 10
10:00 am
SE215
Zoom

Crypto Café

Speaker: Ngo, Tran, Florida Atlantic University

Title:  Analysis for lattice enumeration

Abstract: Lattice reduction algorithms such as BKZ (Block-Korkine-Zolotarev) play a central role in estimating the security of lattice-based cryptography. The subroutine in BKZ which needs to find the shortest vector in a projected sublattice can be instantiated with enumeration algorithms. The enumeration procedure can be seen as a depth-first search on some `"enumeration tree" whose nodes denote a partial assignment of the coefficients, corresponding to lattice points as a linear combination of the lattice basis with the coefficients. This work provides a concrete analysis for the cost of quantum lattice enumeration based on the quantum tree backtracking algorithm of Montanaro (ToC, '18). More precisely, we give a concrete implementation of Montanaro's algorithm for lattice enumeration based on the quantum circuit model. We also show how to optimize the circuit depth by parallelizing the components. Based on the circuit designed, we discuss the concrete quantum resource estimates required for lattice enumeration. This is a joint work with Shi Bai, Maya-Iggy van Hoof, Floyd B. Johnson, and Tanja Lange.

Video Recording

Zoom (click here)

Meeting ID: 878 9825 0483; Passcode: gHJF6g

All are cordially invited.

Thursday
Oct. 12
11:00 am
SE 215

Analysis and Application Seminar

Speaker:  Dr. Francesco Sica, Florida Atlantic University

Title: In pursuit of the Erymanthian boar: Towards a deterministic subexponential factoring algorithm.

Abstract: I will describe a connection between the computation of the prime factors p,q of pq (an RSA modulus), and the analytic theory of the Riemann zeta function. The problem will be thus reduced to the evaluation of some oscillating series, where I will present some new partial results.

Saturday
Oct. 14
2:30-4:00 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!    Register Here for Fall, 2023 Math Circles

Monday
Oct. 16
5:30 pm
SE 215

FAU SIAM (Society for Industry and Applied Mathematics) Student Chapter

The FAU SIAM (Society for Industry and Applied Mathematics) Student Chapter is delighted to announce that we are hosting a reading group this semester. The group’s mission is to advance undergraduate and graduate student interdisciplinary collaborations across the STEM fields. The first reading group will focus on topics at the intersection of Biology, Mathematics, and Computer Science. We hope to not just discuss open problems in bio-math, but also collaborate to tackle them using topological data analysis, and other state-of-the-art machine learning/data mining techniques. If you are interested in bio-math, machine learning, and/or data mining, please join us for our first meeting on October 16 at 5:30 pm. We plan to meet twice a month and, most importantly, at this first meeting we will have FREE PIZZAS!!! If you are interested in joining, please RSVP by replying to this email to let us know you intend to come. If you have any questions let us know, or you can reach out to the SIAM faculty advisor, Dr. Francis Motta  fmotta@fau.edu . 

On behalf of FAU SIAM Student Chapter,

Matthew Trang
President, SAIM Student Chapter   ttrang2019@fau.edu

Wednesday
Oct. 18
1:00 pm
SE 271

Algebra Seminar

Speaker:  Dr. Parker Edwards, Florida Atlantic University

Title:  An applied topologist's overview of numerical algebraic geometry

Abstract:   Suppose that someone hands you a list of polynomial equations and you want to know information about their set of solutions. The first questions you likely want answered are: 

  • If the set of solutions is finite (0-dimensional), list off high-precision approximations of each solution. 
  • If the set of solutions is positive-dimensional and irreducible, what is the dimension and degree of the variety? 
  • More generally: If the set of solutions is reducible, what are the dimensions and degrees of the individual irreducible components? 

Numerical algebraic geometry (NAG) algorithms answer these questions via numerical solving methods: Think Newton-Raphson style solving, but more sophisticated. In this talk, I will discuss some basics of NAG methods with a few examples and try to give a scope both for the theoretical and practical considerations that go into using NAG software to solve problems.

Thursday
Oct. 19
11:00 am
SE 215

Analysis and Applications Seminar

Speaker:  Noah Corbett, Florida Atlantic University

Title:  Predicting State Switches in Chaotic Dynamical Systems

Abstract:  Making long-term predictions in chaotic dynamical systems is a difficult task, especially when one cannot measure all the variables influencing the system. In this work, we propose a general methodology to predict certain macroscopic features of chaotic dynamical systems, such as state switches, that does not require perfect measurements of all the phase variables. We will then apply the method to the Lorenz System and Chua’s Circuit and analyze the performance of the method for both short- and long-term predictions. 

Tuesday
Oct. 24
10:00 am
SE 215
ZOOM

Crypto Café

Speaker:  William Youmans, Florida Atlantic University

Title: An algorithm for solving the principal ideal problem with subfields

Abstract:  The principal ideal problem (PIP) is the problem of deciding whether a given ideal of a number field is principal and, if it is, of finding a generator. Solving the PIP applies to solving major computational tasks in number theory. It is also connected to the search for approximate short vectors in so-called ideal lattices, which is a crucial problem in cryptography. We present a novel application of norm relations to utilize information from subfields to solve the PIP in fields of degree up to 1800.

Bio:  Dr. William Youmans received a BA in pure mathematics in 2017 and a PhD in mathematics in 2023 from the University of South Florida. Since May 2023 he has been a postdoctoral research fellow at Florida Atlantic University. His research interests include lattice-based cryptography, computational number theory, and quantum algorithms.

Zoom (click here)

Meeting ID: 878 9825 0483    Passcode: gHJF6g

All are cordially invited.

Wednesday
Oct. 25
1:00  pm
Wednesday
SE 271

Algebra Seminar

Speaker:   Daniela Nikolova, Florida Atlantic University

Title:  On the Covering Numbers of Small Symmetric and Alternating Groups, and Some Sporadic Groups

Abstract:  Click HERE

All are cordially invited.

Thursday
Oct. 26
SE 215
11:00 am

Analyisis and Applications

Speaker:  Maxime Murray, Florida Atlantic University

Title:    An overview of the dynamics near the Lagrange points in the circular restricted four-body problem

Abstract:   The circular restricted four-body problem considers the motion of a massless object under the gravitational effect of three bodies, called the primaries, whose motion is restricted to the equilateral triangle configuration of Lagrange. This system admits up to 10 equilibrium points,  and a vertical family of Lyapunov periodic obits is attached to some of these points. In this talk, we investigate how such Lagrange points organize the dynamics of the systems. First, we will observe and compare the homoclinic dynamics in the planar and spatial case. Then, we will study the heteroclinic case which, in conjunction with Smale Horseshoe theorem, provides the existence of a family of periodic orbit orbits revolving around all three primaries.

All are cordially invited.

Saturday
Oct. 28
2:30-4 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!    Register Here for Fall, 2023 Math Circles

Tuesday
Oct. 31
10:00 am
ZOOM
Virtual only

Doctoral Dissertation Defense

Speaker:  Amish Bishal

Title:  Topological Data Analysis for Data Science: The Delaunay-Rips Complex, Triangulation Stabilities, and Protein Stability Predictions

Advisor: Dr. Francis Motta

Abstract:  Topological Data Analysis (TDA) is a relatively new field of research that utilizes topological notions to extract discriminating features from data. Within TDA, persistent homology (PH) is a robust method to compute multi-dimensional geometric and topological features of a dataset. Because these features are often stable under certain perturbations of the underlying data, are often discriminating, and can be used for visualization of structure in high-dimensional data and in statistical and machine learning modeling, PH has attracted the interest of researchers across scientific disciplines and in many industry applications. However, computational costs may present challenges to effectively using PH in certain data contexts, and theoretical stability results may not hold in practice. In this dissertation, we develop an algorithm that can reduce the computation burden of computing persistent homology on point cloud data. Naming it Delaunay-Rips (DR), we define, implement, and empirically test this computationally tractable simplicial complex construction for computing persistent homology of Euclidean point cloud data. We demonstrate the practical robustness of DR for persistent homology in comparison with other simplical complexes in machine learning applications such as predicting sleep state from patient heart rate. To justify the theoretical stability of DR, we prove the stability of the Delaunay triangulation of a pointcloud P under perturbations of the points of P. Specifically, we impose a notion of genericity on the points of P to ensure stability. In the final chapter, we contribute to the field of computational biology by taking a data-driven approach to learn topological features of designed proteins from their persistence diagrams. We find correlations between the learned topological features and biochemical features to investigate how protein structure relates to features identified by subject-matter experts. We train several machine learning models to assess the performance of incorporating topological features into training with biochemical features. Using cover-tree differencing via entropy reduction (CDER), we identify distinguishing regions of the persistence diagrams of stable/unstable proteins. More notably, we find statistically significant improvement in classification performance (in terms of average precision score) for certain designed secondary structure topologies.

Please contact Dr. Hongwei Long <hlong@fau.edu>  for an electronic copy of the dissertation.

Zoom Meeting information (Zoom Only):

Amish Mishra is inviting you to a scheduled Zoom meeting.

Join Zoom Meeting:
https://fau-edu.zoom.us/j/86460096194?pwd=c0o4eHRyNm4xWGJjSUZ4SWhJU2tlZz09

Meeting ID: 864 6009 6194

Passcode: John1:14

All are cordially invited

 

September 2023

Tuesday
September 12
10:00 am
SE 215
ZOOM

Crypto Cafe

Speaker :  Paul Zimmermann, Directeur de Recherche at INRIA/LORIA (Nancy, France)

Bio : Paul Zimmermann's research interests include asymptotically fast arithmetic, computer algebra, and computational number theory. Together with Richard Brent, he has written the book "Modern Computer Arithmetic," and he has coordinated the book "Computational Mathematics with SageMath." He has contributed to some of the record computations in integer factorization and discrete logarithm. He is the author or co-author of several computer packages, including the GNU MPFR library providing arithmetic on floating-point numbers with correct rounding, and CADO-NFS, an implementation of the number field sieve for integer factorization. His latest project is CORE-MATH, an implementation of mathematical functions with correct rounding for the IEEE 754 standard formats.

Title : Deciphering Charles Quint (A diplomatic letter from 1547)

Abstract
: An unknown and almost fully encrypted letter written in 1547 by Emperor Charles V to his ambassador at the French Court, Jean de Saint-Mauris, was identified in a public library, the Bibliothèque Stanislas (Nancy, France). As no decryption of this letter was previously published or even known, a team of cryptographers and historians gathered together to study the letter and its encryption system. First, multiple approaches and methods were tested in order to decipher the letter without any other specimen. Then, the letter has now been inserted within the whole correspondence between Charles and Saint-Mauris, and the key has been consolidated thanks to previous key reconstructions. Finally, the decryption effort enabled us to uncover the content of the letter and investigate more deeply both cryptanalysis challenges and encryption methods.

Video Recording

Thursday
September 14   
11:00 am
SE 215  

Analysis and Applications Seminar

Speaker:     Dr. Erik Lundberg, Florida Atlantic University

Title:     Arclength null quadrature domains and vortex dynamics

Abstract:  A planar domain (viewed as a region in the complex plane) is referred to as an arclength null quadrature domain if the integral with respect to the arclength of any (complex) analytic function (in the Smirnov space—the appropriate function space for integrating with respect to arclength) along the boundary vanishes. We use classical results from complex analysis and potential theory (due to Havinson-Tumarkin and Denjoy-Carleman-Ahlfors) in order to prove the existence of a roof function (a positive harmonic function whose gradient coincides with the inward-pointing normal along the boundary) for any arclength null quadrature domain having finitely many boundary components. This bridges a gap toward the classification of arclength null quadrature domains by removing an a priori assumption from previous classification results. This result also strengthens a known connection between arclength null quadrature domains and a free boundary problem for Laplace’s equation that has applications in fluid dynamics (equilibrium solutions for dynamics of vortices with constant pressure core) that will be explained in the talk.  This is joint work with Dmitry Khavinson.

Thursday
September 21
11:00 am
SE 215

Analysis and Applications Seminar

Speaker:     Dr. Parker Edwards, Florida Atlantic University

Title:  A computational viewpoint on distance functions and applications

Abstract:  One of the main theoretical approaches in computational geometry and topology runs as follows: Let d_X:R^n\to R be the distance-to-X function for a compact subspace X in R^n and let P be a "good" finite sample of X. The goal is usually to show that an algorithm of interest correctly extracts information about d_X when using the point set P as input.

The critical point theory for distance functions initiated by Grove and Shiohama in 1977 is precisely the right framework for analyzing this behavior. For most subspaces, d_X is not differentiable everywhere. With the right definition of critical points and values, however, one recovers Morse-function type behavior for d_X.

In this first of two talks, I will give a gentle introduction to this theory in the computational geometry context, accompanied by a motivating application from robotics.

Saturday
September 23
2:30 pm-4:00 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!   

Tuesday
September 26
10:00 am
SE 215
Zoom

Crypto Café

Speaker: Dr. Zhijun Yin, Instructor, Florida Atlantic University

Title: Exploring the Power of Multivariate Public Key Cryptography (MPKC) 

Abstract:  Multivariate Public Key Cryptography (MPKC) leverages multivariate quadratic polynomial mappings over finite fields as the foundation for its trapdoor one-way functions. This innovative approach offers remarkable efficiency in both encryption and decryption processes, making it a compelling choice for secure communications.

In contrast to traditional cryptographic methods, attacking MPKC involves solving a system of nonlinear equations over the finite field, a significantly more complex challenge than NP-hard problems like Boolean satisfiability, which is equivalent to solving equations over the finite field GF(2).

In this presentation, we will delve into MPKC through a simplified example featuring three variables within the finite field of GF(2). This illustrative toy example will demystify key concepts such as public and secret keys, encryption, decryption, and cryptanalysis. Join us as we unravel the intriguing world of MPKC and its potential impact on modern cryptography.

Video Recording

Tuesday
September 26
1:30 pm
SE 215

MS Exam

Speaker:     Ian Morgan, MS Candidate, Florida Atlantic University

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.

All are cordially invited.

Wednesday
September 27
1:00 pm
SE 271

Algebra Seminar

Speaker:  Matthew Trang, Florida Atlantic University

Title:     Covering Relations in Neural Codes

Abstract:   How does my brain do this? This is a question that everyone must have asked themselves at least once in their lifetime. Brains are composed of billions of neurons and mysteriously they manage to use these neurons to encode the data of external stimuli from the real world via neuron firing events. This
motivates researchers from different disciplines to collaborate in order to study how the brain functions. To mimic these neuron firing events, mathematicians introduced combinatorial neural codes. These are algebraic objects that keep track of the collections of neurons firing together. Using these neural codes to
infer properties of a stimulus space is one of the tasks of neuroscience. For instance, does a combinatorial neural code have a convex realization? In 2020, Jeffs introduced morphisms of neural codes that preserve some combinatorial properties of corresponding stimuli in order to study the convexity of these
codes. As an attempt to verify a conjecture about the convexity of codes, we have built a method together with Jeffs to enumerate the neural codes covering a given code via some morphisms. In this talk, we will give an overview of neural codes and describe this joint research. 

Thursday
September 28
11:00 am
SE 215

Analysis and Applications Seminar

Speaker:     Dr. Parker Edwards, Florida Atlantic University

Title:    Real, algebraic, and computational geometry/topology

Abstract:   Semialgebraic spaces are the sets of real solutions to systems of polynomial equations and inequalities. A finite list of polynomials defining such a space is a complete specification and algorithms for computing a space's geometric or topological properties using that list as input have been studied for decades. Most of those algorithms are unimplemented, however, as they were designed primarily to investigate computational complexity.

In this second talk, I will discuss some recent work with colleagues to design and implement efficient algorithms in the real algebraic geometry context using a computational geometry/topology approach. While we have made progress, the story is far from settled. I will therefore also present some related open questions/directions in this area.

Saturday
September 30
2:30 pm-4:00 pm
PS 112

Math Circle at FAU

Welcome to Math Circle!  The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023.

It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk.

Source of the Problems:  The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source.

Registration is FREE!     

 

August, 2023

Tuesday
Aug. 29  
10:00 am     SE 215
ZOOM

Crypto Café

Speaker: Adam Yergovich, Regional Cybersecurity Officer, Department of State, Bureau of Diplomatic Security

Title: Challenges in Securing a Worldwide Enterprise Network Footprint - The Basics from Australia to Zimbabwe.  

Abstract:  Many modern theories on Information Security rely on sophisticated and efficient infrastructure we take for granted in developed countries.  When operating in nearly every country in the world it is necessary to focus on the basics.  There might be questionable infrastructure or even openly hostile host nations, but basic "hygiene" is often the best roadmap to securing information and communication - and often the most neglected.

Biography: Adam Yergovich works for the Department of State, Bureau of Diplomatic Security as a Regional Cyber Security Officer currently stationed in Fort Lauderdale Florida.  He has previously been stationed in Frankfurt Germany, Bangkok Thailand, and Moscow Russia but traveled extensively within those regions.  He graduated from from the University of California Davis with a degree in Computer Science and Engineering and worked for several years designing single board computers for a small California company before joining State.  

Video Recording