202425 Department of Mathematics and Statistics Events 

October, 2024 
Wednesday 
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:
Snacks are always available! See you there! 
Thursday 
Crypto Café Speaker: Dr. Veronika Kuchta, Assistant Professor, Florida Atlantic University FLYER Title: Proximity gaps for ReedSolomon Codes and their Application in Interactive Oracle Proofs of Proximity and ZKSNARKs Abstract: ReedSolomon codes have long been a fundamental tool of error correction and data integrity, but their applications extend far beyond traditional coding theory. In this talk, I will explore the concept of proximity gaps within ReedSolomon codes—specific measures of how far a received word is from the closest codeword—and their critical role in the design and analysis of advanced cryptographic protocols, such as ZeroKnowledge Succinct NonInteractive Arguments of Knowledge (ZKSNARKs) and Interactive Oracle Proofs of Proximity (IOPPs). 
Thursday 
Analysis and Applications Speaker: Professor Tomas Schonbek, Florida Atlantic University Title: The Helmholtz decomposition Miniabstract: I will discuss the Helmholtz decomposition of a vector field into a gradient and a divergence free vector field, a fundamental tool in fluid dynamics, and give my take on the proof. 
Friday 
Math Colloquium Speaker: Sri Namachchivaya, Professor, University of Waterloo Title: Random and Data Driven Dynamical Systems Abstract: I will present a general overview of several engineered and natural systems with uncertain mathematical models, the multidisciplinary methods required for their analysis, and relevant results. The collection of new mathematical techniques that I will describe lies at the confluence of three important areas: dynamical systems; control and estimation (data assimilation); and information theory. The first part of the talk focuses on the challenges in data assimilation that arise from the interactions between uncertainties, nonlinearities, and observations. I will present rigorous reducedorder data assimilation techniques for high dimensional multiscale problems. In particular, I will outline how scaling interacts with filtering via stochastic averaging. Optimal sensor placement based on information theoretic concepts will also be discussed. The second part of the talk deals with the almostsure stability of a noisy nonlinear autoparametric system. This work brings together two interesting themes in dynamical systems — resonances and Lyapunov exponents. The subtleties of their interactions are explored in a canonical way by combining the ideas from dynamical systems and the Oseledets multiplicative ergodic theory. — Joint work with Peter H. Baxendale (USC), Ryne Beeson (Princeton) and Nicolas Perkowski (Free University of Berlin). This talk is dedicated to the memory of the late Professor Yukweng Michael Lin, formerly Charles E. Schmidt Eminent Scholar Chair in Engineering and the Founding Director of FAU Center for Applied Stochastics Research, who was for more than 50 years a leading figure in stochastic and engineering mechanics. Refreshments including brownies cookies and coffee will be served! All are welcome! 
Saturday 
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 7, 2024. 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 
Thursday 
Crypto Reading Seminar Join the faculty and students of Cryptography for a biweekly reading seminar on fully homomorphic encryption. 
Wednesday 
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:
Snacks are always available! See you there! 
Thursday 
Crypto Café Speaker: Ruslan Ospanov, Eurasian National University, Kazakhstan Title: The MCDMRLbased Framework for Consensus Protocol Selection for IoT networks. Abstract: This topic is a part of my PhD research topic: “Design and analysis of cryptographic algorithms and protocols for solving the problem of consensus in distributed ledger technologies”. Reinforcement learning (RL) has played a key role in the rapid development of artificial intelligence technologies that has been observed over the past decade. Reinforcement learning methods have shown impressive results in a range of fields. Specifically, RL is widely applied in robotics, control systems, and the Internet of Things (IoT) to address challenges in automation, optimization, and the management of complex systems. The IoT is also a major area for the implementation of distributed ledger and blockchain technologies, which provide effective solutions to overcome the limitations of conventional IoT applications. A key element of the distributed ledger reference architecture is the consensus layer, which handles agreement among network nodes, ensuring the ledger’s state remains consistent while maintaining data security, accuracy, and protection. The selection of a consensus protocol plays a crucial role in determining the performance and security of the blockchain system. This talk is devoted to the issue of selection a blockchain consensus protocol for IoT networks using the combined application of multicriteria decision making (MCDM) and reinforcement learning (RL) methods. In this talk, I will consider an idea of integration multicriteria decision making and reinforcement learning methods to blockchain consensus protocol selection for IoT. It proposes a combined consensus protocol selection and management system for IoT networks based on the multicriteria decision making method and reinforcement learning. Bio: Ruslan Ospanov has been engaged in scientific and educational activities in the field of mathematics and cryptography for more than 20 years, has dozens of scientific and scientificmethodological works, as well as several copyright certificates from Qazpatent (National Institute of Intellectual Property of the Ministry of Justice of the Republic of Kazakhstan (NIIP)). He worked as a teacher in various universities of Kazakhstan (Karaganda State University named after academician E.A. Buketov, L.N. Gumilyov Eurasian National University and other). He is also a research fellow at the Research Institute of Information Security and Cryptology of L.N. Gumilyov Eurasian National University. Since September 2022, he has been a doctoral student at the Eurasian National University named after L.N. Gumilyov, specializing in Information Security Systems. 
Thursday 
Analysis and Applications Speaker: Jorge Gonzalez, Florida Atlantic University Title: Validated enclosure of renormalization fixed points Abstract: I will discuss recent work with Maxime Breden and Jason Mireles James where we develop a framework for proving existence, uniqueness, and stability results for real analytic fixed points of mth order FeigenbaumCvitanović renormalization operators. The universality properties associated to the fixed points, first discovered by Feigenbaum for m=2 in the context of population dynamics, in general describe different routes to chaotic behavior in multiple contexts in Mathematics and the physical sciences. We obtain general formulas for the Jacobian of the mth order operator and use Chebyshev expansions to approximate the fixed points. The advantage of Chebyshev series is that they are naturally adapted to spaces of real analytic functions, in the sense that they converge on ellipses containing real intervals. We prove the existence of multiple renormalization fixed points of order m = 3, . . . , 10, and compute validated bounds on the values of their universal constants. We also reprove the existence of the classical m = 2 Feigenbaum renormalization fixed point and compute its universal constants to about 500 correct decimal digits. Preprint on arxiv: https://arxiv.org/pdf/2409.20457

Saturday 
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 7, 2024. 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 
Wednesday 
Analysis and Applications Speaker: Joseph Cummings (Notre Dame  Applied and Computational Mathematics & Statistics) Title: Algebraic Invariants of Level1 Phylogenetic Networks Abstract: Algebraic techniques in phylogenetics have historically been successful at proving identifiability results and have also led to novel reconstruction algorithms. In this talk, we will find a Gröbner basis for the ideal of phylogenetic invariants of the CavenderFarrisNeyman (CFN) model on level1 phylogenetic networks, that is the vanishing ideal of the set of all possible probability distributions on the leaves arising from the model. We will show that the vanishing ideal can be completely determined by analyzing the covariance matrix instead of the whole probability distribution. Moreover, we will show that the ideal is cut out by 2 x 2 and 3 x 3 minors of the covariance matrix which can be determined from the topology of the network. This research is joint with Elizabeth Gross, Ben Hollering, Sam Martin, and Ikenna Nometa. 
Wednesday 
Crypto Seminar at New College Speaker: Edoardo Persichetti, Associate Professor, Florida Atlantic University Title: On Digital Signatures from Cryptographic Group Actions” Abstract: Cryptography based on group actions has been studied since 1990. In recent years, however, the area has seen a revival, partially due to its role in postquantum cryptography. In this work, we present a unified taxonomy of a variety of techniques used to design digital signature schemes. We describe all techniques in a single fashion, show how they impact the performance of the resulting protocols and analyze in detail how different techniques can be combined for optimal performance. Everyone welcome! Seminar Locatiion: New College of Florida, Sarasota Zoom link https://ncf.zoom.us/j/92611790452?pwd=7QQ4l7n2NLhlU9qDjOWBnUugdjNW5u.1 
Thursday 
Crypto Reading Seminar Join the faculty and students of Cryptography for a biweekly reading seminar on fully homomorphic encryption. The following paper will be discussed: 
Thursday 
Analysis and Applications Speaker: Jorge Gonzalez, Florida Atlantic University Title: Validated enclosure of renormalization fixed points Abstract: I will discuss recent work with Maxime Breden and Jason Mireles James where we develop a framework for proving existence, uniqueness, and stability results for real analytic fixed points of mth order FeigenbaumCvitanović renormalization operators. The universality properties associated to the fixed points, first discovered by Feigenbaum for m=2 in the context of population dynamics, in general describe different routes to chaotic behavior in multiple contexts in Mathematics and the physical sciences. We obtain general formulas for the Jacobian of the mth order operator and use Chebyshev expansions to approximate the fixed points. The advantage of Chebyshev series is that they are naturally adapted to spaces of real analytic functions, in the sense that they converge on ellipses containing real intervals. We prove the existence of multiple renormalization fixed points of order m = 3, . . . , 10, and compute validated bounds on the values of their universal constants. We also reprove the existence of the classical m = 2 Feigenbaum renormalization fixed point and compute its universal constants to about 500 correct decimal digits. Preprint on arxiv: https://arxiv.org/pdf/2409.20457 
Wednesday 
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:
Snacks are always available! See you there! 
Thursday 
Crypto Café Speaker: Francesco Sica, Assistant Professor, Florida Atlantic University FLYER Title: Group Actions and the Discrete Log Problem Abstract: The discrete logarithm problem (DLP) asks to compute, in a cyclic group $G=\langle g \rangle$, given $x\in G$ and $y= x^k$, the exponent $k$. This problem can be generalized to a situation when $G$ acts on a set $X$, and gives rise to the analogous vectorization problem (VP), asking to recover $\gamma\in G$ from knowledge of $x\in X$ and $y=\gamma \cdot x$. We will discuss generic algorithms to solve the VP, in particular in the presence of hints $z=\gamma^d \cdot x$, rephrasing a 2006 argument of Cheon. 

September, 2024 
Wednesday 
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:
Snacks are always available! See you there! 
Thursday 
Crypto Café Speaker: Dr. Edoardo Persichetti, Associate Professor, Florida Atlantic University FLYER Title: A Brief Introduction to CodeBased Cryptography Abstract: Codebased cryptographic primitives are among the main solutions for PostQuantum Cryptography, the area of study in charge of protecting our information and communication in the presence of quantum adversaries. In this talk, I will briefly walk through the history of this field, highlighting the main constructions, modern approaches, and recent developments. Everyone welcome! 
Thursday 
Analysis and Applications Speaker: Professor Markus Schmidmeier, Florida Atlantic University Title: Invariant Subspaces of Nilpotent Operators Abstract: Related to the invariant subspace problem in functional analysis, but heading in a more algebraic direction, this talk concerns the linear algebra problem of classifying invariant subspaces of linear operators acting on finite dimensional vector spaces, (with no conditions on the underlying basefield or on the topology of the space). Dependent on certain dimensions, the subspaces may either be sparse (and we can describe them) or plentiful (in the sense that there are parametrized families of pairwise nonequivalent subspace embeddings). Joint work with Claus Michael Ringelfrom Bielefeld, Germany. 
Saturday 
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 7, 2024. 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 
Thursday 
Crypto Reading Seminar Join the faculty and students of Cryptography for a biweekly reading seminar on fully homomorphic encryption. 
Wednesday 
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:
Snacks are always available! See you there! 
Thursday 
Speaker: Dr. Shi Bai, Associate Professor, Florida Atlantic University FLYER Title: Latticebased Cryptography: Construction and Analysis Abstract: Latticebased Cryptography holds a great promise for postquantum cryptography. It enjoys strong security based on the socalled worstcase to averagecase redution; relatively efficient implementations, as well as algorithmic simplicity. In this talk, we will discuss a postquantum scheme based on lattice; and several algorithms for evaluating the security of averagecase/worstcase problems in latticebased cryptography. 
Saturday 
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 7, 2024. 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 
Thursday 
Crypto Reading Seminar Join the faculty and students of Cryptography for a biweekly reading seminar on fully homomorphic encryption. 
Friday 
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! 

August, 2024 
Thursday 
Analysis and Algebra Seminar Speaker: Parker Edwards, Assistant Professor Title: On computing local monodromy (part IV) Abstract: A fundamental fact about zero sets of systems of polynomial equations over the complex numbers is that they decompose into a finite number of irreducible algebraic subsets. Knowing a thorough description of the irreducible components of an algebraic variety tells you quite a bit about it, and computing one is an essential preprocessing step to many numerical algorithms. Standard algorithms for computing this numerical irreducible decomposition combine some relatively sophisticated machinery. This week's talk will cover some background on monodromy actions and how they're used to detect irreducible components of algebraic varieties. A main component is computing the monodromy action of certain linear projection maps using numerical continuation. What if one is instead interested in studying the geometric properties of an algebraic variety localized at a point? This puts you into the realm of singularity theory in complex analytic geometry, which is a rich and ongoing area of theoretical development. Every zero set of a system of complexvalued analytic functions has a local irreducible decomposition at each point. Computing a corresponding numerical local irreducible decomposition is similarly essential to developing a local approach to numerical algebraic geometry. I will discuss some recent work with Jon Hauenstein which culminates in an algorithm for doing so. My aim for these seminars is to give a thorough enough overview of the background to understand what the algorithm is doing. If there's interest, we can discuss enough to get at the main ideas of the proof that it works. Here's the breakdown:

August, 59 
Young CryptograpHers Cybersecurity Summer Camp Young CryptograpHers is a Cybersecurity summer camp specially designed for high school girls. Participants will be introduced to the fundamental principles of cybersecurity and learn how to apply conceptual knowledge to realworld situations. The camp will focus on PostQuantum Cryptography, the area of math that is in charge of protecting our information in the era of quantum technology. The program includes lectures and activities by FAU faculty, alumni and speakers from industry and government. Our goal is to motivate and inspire talented students who are interested in a cybersecurity career. ( flyer ) 
Thursday 
Analysis and Applications Speaker: Turgay Bayraktar, Sabanci University (Istanbul) Title: Random Real Algebraic Geometry and Random Ameobas Abstract: Click here 