Time & Location: All talks will be in Gibson Hall 126A on Thursdays at 3:30 pm unless otherwise noted. In order to have time to talk informally with the speakers, we will schedule a time we call “Tea with the speaker” that everyone is welcome to join.
Organizer: Tommaso Buvoli and SamuelPunshon-Smith
Thursday, September 12
Colloquium
Topic: On the flow of zeros of derivatives of polynomials
Andrei Martinez-Finkelshtein - Baylor University (Host: Ken McLaughlin)
Abstract: Assume we have a sequence of polynomials whose asymptotic zero distribution is known. What can be said about the zeros of their derivatives? Especially if we differentiate each polynomial several times, proportional to its degree? This simple-to-formulate problem has recently attracted the attention of researchers. Both the problem and the methods of its solution have exciting connections with free probability, random matrices, and approximation theory on the complex plane. In this talk, I will explain some known results in this direction and our approach to the problem, which uses only some elementary complex analysis. This is a joint work with E. Rakhmanov from the University of South Florida.
Location: Dinwiddie Hall 108
Time: 3:30 pm
Thursday, October 10
Colloquium
Topic: Invariant Embeddings
Shlomo Gortler - Harvard (Host: Bernstein)
Abstract: Fix a dimension d and graph H, with n vertices and m edges. Let p be a configuration of n points in R^d. Then we can measure the configuration, mod the Euclidean group, by recording the squared length between each point pair associated with an edge of H. When H is generically globally rigid in d-dimensions, then this measurement map is an almost everywhere injective map from R^{nd}/E(d) to R^m. In this talk, I will discuss the general question of how one can create fully injective maps from R^{nd}/G to R^m where G is some group and m is roughly 2nd.
Location: Gibson Hall 126A
Time: 3:30 pm
Thursday, October 24
Colloquium
Topic: Extreme first passage times for populations of identical rare events
Jay Newby - University of Alberta (Host: McKinley)
Abstract: A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit to infinity as a positive parameter scaling the noise magnitude is reduced to zero. In contrast, previous work has shown that the mean of the fastest event time goes to zero in the limit of an infinite number of walkers. The combined limit is studied. In particular, the mean time and the most likely path taken by the fastest random walker are investigated. Using techniques from large deviation theory, it is shown that there is a distinguished limit where the mean time for the fastest walker can take any positive value, depending on a single proportionality constant. Furthermore, it is shown that the mean time and most likely path can be approximated using the solution to a variational problem related to the single-walker rare event.
Location: Gibson Hall 126A
Time: 3:30 pm
Thursday, October 31
Colloquium
Topic: Subsets of Groups in Public-Key Cryptography
Antonio Malheiro - Universidade Nova de Lisboa, Portugal (Host: Mahir Can)
Abstract: This presentation introduces group-based cryptography, focusing on a novel method that employs algebraic subsets instead of subgroups in public-key cryptography. The initial part reviews the essential concepts of public-key cryptography and the motivation for using groups, including a brief introduction to formal languages and algebraic subsets.
The second part presents an adaptation of well-known protocols, such as those by Shpilrain and Ushakov, where finitely generated subgroups are replaced by algebraic subsets. Examples are provided to illustrate how these subsets offer greater resistance to length- and distance-based attacks. The practical challenges associated with implementing this approach are also discussed. The presentation concludes by proposing new group-theoretic problems arising from this technique and exploring potential applications in other cryptographic systems.
This is joint work with André Carvalho (University of Porto, Portugal)
Location: Gibson Hall 126A
Time: 3:30 pm
Thursday, November 7
Colloquium
Topic: The partition function and modular forms
Scott Ahlgren - University of Illinois at Urbana-Champaign (Host: Olivia Beckwith)
Abstract: The partition function p(n), which counts the number of ways to break a positive integer into parts, is a basic function in additive number theory and combinatorics.
Modular forms are hyper-symmetric complex functions which play a central role in number theory.
The fact that the generating function for partitions is a modular form opens the door to study its properties using the theory of modular forms. There are two branches to this study; the analytic side involves Maass forms and spectral theory and the arithmetic side involves holomorphic modular forms and Galois representations. In all cases the study can be viewed as a "testing ground” for more general theorems about modular forms.
I will discuss (in a non-technical way) the history of this subject as well as a number of results which have been proved with various collaborators in the last few years.
Location: Gibson Hall 126A
Time: 3:30 pm
Thursday, November 14
Colloquium
Topic: KPZ limit theorems
Jinho Baik - University: University of Michigan (Host: Gustavo Didier)
Abstract: In probability theory, various models often exhibit similar fluctuation behaviors as the system size or time increases, leading to the formation of universality classes. One such class is the KPZ universality class, which includes randomly growing interfaces, interacting particle systems, and directed polymers. This concept was first introduced by physicists Kardar, Parisi, and Zhang in 1985. We will discuss some key results from the past twenty-five years related to the KPZ universality class, focusing on the last passage percolation models.
Location: Gibson Hall 126A
Time: 3:30 pm
Tuesday, November 19
Special Colloquium
Topic: Topological deep learning on graphs, manifolds, and curves
Dr. Guo-Wei Wei - Affiliation: Michigan State University (Host: Tai Ha)
Abstract: In the past few years, topological deep learning (TDL), a term coined by us in 2017, has become an emerging paradigm in artificial intelligence (AI) and data science. TDL is built on persistent homology (PH), an algebraic topology technique that bridges the gap between complex geometry and abstract topology through multiscale analysis. While TDL has made huge strides in a wide variety of scientific and engineering disciplines, it has many limitations. I will discuss our recent effort in extending TDL from graphs to manifolds and curves, using algebraic topology, geometric topology, and differential geometry. I will also discuss how TDL led to victories in worldwide annual competitions in computer-aided drug design, the discoveries of SARS-CoV-2 evolutionary mechanism, and the accurate forecasting of emerging dominant viral variants.
Special Location: Boggs 243
Special Time: 2:00PM – 3:00PM
