202324 Department of Mathematics Events 

September 2023 
Tuesday 
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 coauthor of several computer packages, including the GNU MPFR library providing arithmetic on floatingpoint numbers with correct rounding, and CADONFS, an implementation of the number field sieve for integer factorization. His latest project is COREMATH, an implementation of mathematical functions with correct rounding for the IEEE 754 standard formats.
Title
: Deciphering Charles Quint (A diplomatic letter from 1547)

Thursday 
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 HavinsonTumarkin and DenjoyCarlemanAhlfors) in order to prove the existence of a roof function (a positive harmonic function whose gradient coincides with the inwardpointing 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 
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 distancetoX 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 Morsefunction 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 
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 
Crypto Café
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 oneway 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 NPhard 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. 
Tuesday 
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 
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 
Thursday 
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 
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 
Crypto Café
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. 