2023-24 Department of Mathematics Events |
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November, 2023 |
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Wednesday |
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 |
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Thursday |
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 |
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Thursday Nov. 2 |
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! |
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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! Register Here for Fall, 2023 Math Circles |
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Monday |
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:
Snacks are always available! See you there! |
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Tuesday |
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. |
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Wednesday |
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). |
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Wednesday |
American Mathematics Competition - High School Students
The AMC-10/12A Contest will be held at FAU |
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Tuesday |
American Mathematics Competition - High School Students
The AMC-10/12B Contest will be held at FAU |
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Thursday |
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 |
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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. |
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Thursday |
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 |
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Thursday |
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. |
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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! Register Here for Fall, 2023 Math Circles |
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Monday |
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:
Snacks are always available! See you there! |
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Tuesday |
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. Meeting ID: 878 9825 0483 Passcode: gHJF6g All are cordially invited. |
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Tuesday |
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.
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Wednesday |
Algebra Seminar Speaker: Papiya Bhattacharjee, Florida Atlantic University Title: Max(dL) vs. Min(L), for M-Frames L
Abstract
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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♯- |
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Thursday |
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. |
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October 2023 |
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Wednesday |
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. |
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Thursday |
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. |
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Tuesday |
Crypto Café
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. Meeting ID: 878 9825 0483; Passcode: gHJF6g All are cordially invited. |
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Thursday |
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. |
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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! Register Here for Fall, 2023 Math Circles |
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Monday |
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 |
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Wednesday |
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:
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. |
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Thursday |
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. |
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Tuesday |
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. Meeting ID: 878 9825 0483 Passcode: gHJF6g All are cordially invited. |
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Wednesday |
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. |
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Thursday |
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. |
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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! Register Here for Fall, 2023 Math Circles |
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Tuesday |
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. Passcode: John1:14 All are cordially invited |
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September 2023 |
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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 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)
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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 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. |
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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 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. |
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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! |
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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 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. |
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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. |
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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 |
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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. |
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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! |
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August, 2023 |
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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. |
