Mathematics Colloquium
The UL Lafayette Mathematics Colloquium is an ongoing seminar series that features speakers from other universities and from our department. The topics cover all areas of mathematics and statistics. We try to schedule an interesting mix of topics ranging from very applied to more abstract in nature. These lectures are open to all UL Lafayette students, faculty and community members for the purpose of fostering continued discussion and networking in the various areas of mathematics. Please contact Jiaxin Jin or Calvin Berry with questions or suggestions about the colloquium series.
Our colloquia are normally held on Thursday at 3:30 p.m. in room 211 of Maxim Doucet Hall. Some colloquia may be presented via zoom instead. Refreshments are served at 3:15 in room 211. To accommodate outside speakers, the colloquium is occasionally held on a different day of the week, e.g., Tuesday at 3:30, instead of Thursday.
Remember, our colloquium is open to the public and everyone who is interested is encouraged to attend.
Fall 2025
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4 September 2025
Some Applications of Orthogonal Polynomials
Mourad Ismail
University of Louisiana at Lafayette
Abstract: I will discuss some applications of orthogonal polynomials and moment problems to probability, Schrodinger operators, and time permitting to some combinatorial problems. -
25 September 2025
How Fishing gives us a way to improve the design of Nanomachines
Erez Aghion
University of Louisiana at Lafayette
Abstract: A key challenge in the design of nanomachines is how to optimize their thermal efficiency. Nanomachines, like molecular motors, generate mechanical work from the random fluctuations of diffusing particles. In the process, however, a portion of this work may be wasted due to the emission of heat. Recent discoveries in the field of stochastic thermodynamics show that the rates of heat emission and work generation are bounded by stochastic speed limits. Can we optimize these machines for best performance under these bounds? According to the fishermen, it definitely seems so!
About the speaker: Dr. Aghion joined the physics department at UL Lafayette as an assistant professor in August 2024. He is very happy to be here. Erez completed his PhD at Bar-Ilan University, Israel, in 2019 under the supervision of Prof. Eli Barkai. His PhD research was on the physical applications of infinite-density functions for anomalous diffusion and nonequilibrium thermodynamics. Between 2021–2023, Erez worked as a postdoc in Jason R. Green's group at UMass Boston, where his research focused on stochastic thermodynamics. Before that, from 2019 to 2021, Erez worked as a visiting scientist at the Max Planck Institute (MPI-PKS) in Dresden, Germany, in the group of Holger Kantz. There, he focused on methods for deciphering anomalous diffusion in empirical time series. -
28 October 2025 (TUESDAY)
Quantitative topology
Fedya Manin
Department of Mathematics
University of Toronto
Abstract: Traditionally, algebraic and geometric topology focuses on classifying geometric objects (e.g. manifolds or knots) up to some equivalence relation. Typically an equivalence between two objects is realized by some third object (such as a mapping or deformation). Quantitative topology asks: how "obvious" is the equivalence relation? That is, if one takes two relatively simple equivalent objects, could it be that the simplest equivalence between them is extremely geometrically complicated? The answers turn out to vary greatly and rely on tools not just from algebraic topology and differential geometry, but also theoretical computer science and harmonic analysis among other areas. I will give an overview of a few of the things we have learned since the 1970s when Gromov initiated this program, and especially in the last decade. -
30 October 2025 (ON ZOOM)
(If you are not on our mailing list, please contact Calvin Berry to request the zoom link)
Towards Robust and Privacy-Preserving Federated Machine Learning
Thang Hoang
Department of Computer Science
Virginia Tech
Abstract: Secure aggregation protocols play a critical role in federated learning by protecting users’ data privacy and preventing the disclosure of local gradients during model training. However, many existing protocols introduce substantial computational and communication overhead and struggle to efficiently process the large update vectors typical of modern machine learning models.
In this talk, I will present e-SeaFL, an efficient and verifiable secure aggregation protocol that achieves aggregation in a single communication round. e-SeaFL enables the aggregation server to generate a proof of honest aggregation for all participants through the use of authenticated homomorphic vector commitments. The core idea is to leverage assisting nodes (i.e., lightweight entities that aid the aggregation server) under trust assumptions similar to those placed on participating users. Experimental results demonstrate that e-SeaFL provides an order-of-magnitude efficiency improvement over state-of-the-art approaches for high-dimensional gradient vectors with thousands of parameters.
Finally, I will discuss emerging challenges and open directions toward enabling robustness and privacy-preservation for federated learning in highly dynamic and adversarial environments. In particular, I will explore how robustness extends beyond privacy to address threats such as Byzantine behavior, model poisoning, and unreliable participation. These challenges motivate new designs that integrate secure aggregation with verifiable robustness mechanisms, enabling federated systems that remain both privacy-preserving and resilient under real-world operational conditions.
About the speaker: Thang Hoang is an Assistant Professor in the Department of Computer Science at Virginia Tech and a CCI Researcher. Prior to joining VT, he was a Postdoctoral Fellow at Carnegie Mellon University hosted by Prof. Elaine Shi. He received his Ph.D. from the University of South Florida in August 2020. His research spans the domains of cybersecurity and applied cryptography, with particular interests in privacy, secure and verifiable computation, zero-knowledge proofs, fuzzy cryptography, and trustworthy machine learning. -
6 November 2025
Norms of Chebyshev and Faber polynomials on curves with corners
Erwin Miña-Díaz
University of Mississippi
Abstract: The Chebyshev polynomial Tn=Tn,Γ of degree n associated to a compact set Γ of the complex plane is the monic polynomial of degree n with minimum supremum norm ||Tn||=maxz∊Γ|Tn(z)| over Γ. Determining the asymptotic behavior of ||Tn|| as n→∞ is a classical problem in the theory of approximation. For compact sets Γ of positive logarithmic capacity cap(Γ)>0, there is the well-known inequality
Wn ≔ [||Tn|| / cap(Γ)n] ≥ 1, n≥1
The behavior of the so-called Widom factors Wn has been established in a number of situations. When Γ is a sufficiently smooth Jordan curve, it is known from classic work of Widom that limn→∞Wn=1. This result makes use of the Faber polynomials Fn for the curve Γ. If, however, Γ has corners, the behavior of Wn has remained unknown. We will show that if Γ is a piecewise Dini-smooth Jordan curve, it is still the case that limn→∞Wn=1. To establish this limit we need to use instead a generalized (or weighted) version of the Faber polynomials. The talk will also present new asymptotic bounds for the supremum norm ||Fn|| of the Faber polynomials for a piecewise Dini-smooth Jordan curve, as well as a new limiting relation (as r→∞) between the Chebyshev polynomial Tn,r for the exterior r-level curve of a compact set and its Faber polynomial Fn. The work presented is in collaboration with Olof Rubin and Aron Wennman from KU Leuven. -
13 November 2025
Population Dynamics under Random Switching
Siddharth Sabharwal
Texas A&M University
Abstract: Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often, environmental stochasticity is modeled by systems of stochastic differential equations. However, this type of stochasticity is not always the best suited for ecological modeling. Instead, biological systems can be modeled using piecewise deterministic Markov processes (PDMP). For a PDMP the process follows the flow of a system of ordinary differential equations for a random time, after which the environment switches to a different state, where the dynamics is given by a different system of differential equations. Then this is repeated. The current paper is devoted to the study of the dynamics of n populations described by n-dimensional Kolmogorov PDMP. We provide sharp conditions for persistence and extinction, based on the invasion rates (Lyapunov exponents) of the ergodic probability measures supported on the boundary of the positive orthant $\partial \R_+^{n,\circ}$. In order to showcase the applicability of our results, we apply the theory in some interesting ecological examples.