Calendar

Posted March 17, 2026
Last modified March 30, 2026

Algebra and Number Theory Seminar Questions or comments?

Shahriyar Roshan-Zamir, Tulane University
Interpolation in Weighted Projective Spaces

Over an algebraically closed field, the double point interpolation problem asks for the vector space dimension of the projective hypersurfaces of degree d singular at a given set of points. After being open for 90 years, a series of papers by J. Alexander and A. Hirschowitz in 1992--1995 settled this question in what is referred to as the Alexander-Hirschowitz theorem. In this talk, we primarily use commutative algebra to prove analogous statements in the weighted projective space, a natural generalization of the projective space. For example, we introduce an inductive procedure for weighted projective space, similar to that originally due to A. Terracini from 1915, to demonstrate an example of a weighted projective plane where the analogue of the Alexander-Hirschowitz theorem holds without exceptions and prove our example is the only such plane. Furthermore, Terracini's lemma regarding secant varieties is adapted to give an interpolation bound for an infinite family of weighted projective planes. There are no prerequisites for this talk besides some elementary knowledge of algebra.

Event contact: Gene Kopp

Posted March 27, 2026
Last modified April 5, 2026

Informal Analysis Seminar Questions or comments?

Yixing Miao, Louisiana State University
Spectra of Magnetic Schrodinger Operators on Hexagonal Graph

In this presentation, I will talk about my ongoing work on the spectral analysis of Hamiltonians defined on the hexagonal graph with delta-like interactions, which is a generalization of previous work by Becker, Han, and Jitomirskaya. The methodology is to reduce the study of spectra of Hamiltonians to that of quasi-periodic Jacobi operators. The main difficulty is due to the parameters of we introduced in the delta-like boundary conditions. It requires us to modify the proofs of several theorems related to the spectral analysis of quasi-periodic Jacobi operators, and results in various spectral types dependent on those parameters. Numerous tools from ODE, Fourier analysis, functional analysis, complex analysis, dynamical systems, etc... are involved.

Posted January 15, 2026
Last modified April 7, 2026

Informal Geometry and Topology Seminar Questions or comments?

Nilangshu Bhattacharyya, Louisiana State University
Spanning tree complex and Khovanov homology

This talk will give an introduction to the spanning tree model for Khovanov homology. Starting from a knot or link diagram, one can associate a planar graph by checkerboard coloring, and the spanning trees of this graph turn out to capture an important part of the structure of the Khovanov complex. I will explain how this viewpoint leads to a simpler complex generated by spanning trees, why it is natural from the perspective of the Jones polynomial, and how it helps illuminate the combinatorial structure underlying Khovanov homology. The emphasis will be on the main ideas and examples, with the goal of making the spanning tree complex accessible to a broad audience.

Posted March 20, 2026

Applied Analysis Seminar Questions or comments?

Tan Bui-Thanh, The University of Texas at Austin Professor and the Endowed William J. Murray, Jr. Fellow in Engineering
Rigorous Model-Constrained Scientific Machine Learning for Digital Twins: A Computational Mathematics Perspective

Digital twins (DTs) are high-fidelity virtual representations of physical systems and processes. At their foundation lie mathematical and physical models that describe system behavior across multiple spatial and temporal scales. A central purpose of DTs is to enable "what-if" analyses through hypothetical simulations, supporting lifecycle monitoring, parameter calibration against observational data, and systematic uncertainty quantification (UQ). For DTs to serve as a reliable basis for real-time forecasting, optimization, and decision-making, they must reconcile two traditionally competing requirements: mathematical rigor and physical fidelity, and computational efficiency at scale. This has motivated a new generation of approaches that combine classical tools from numerical analysis, partial differential equations, inverse problems, and optimization with the expressive power of Scientific Machine Learning (SciML). In this talk, I will outline a principled pathway from traditional computational mathematics to rigorously grounded SciML. I will then present recent Scientific Deep Learning (SciDL) methods for forward modeling, inverse and calibration problems, and uncertainty quantification, emphasizing mathematical structure, stability, and generalization. Both theoretical results and numerical demonstrations will be shown for representative problems governed by transport, heat, Burgers, Euler (including transonic and hypersonic regimes), and Navier- Stokes equations.

Event contact: Robert Lipton

Posted February 5, 2026
Last modified February 6, 2026

Control and Optimization Seminar Questions or comments?

Wonjun Lee, Ohio State University
Linear Separability in Contrastive Learning via Neural Training Dynamics

The SimCLR method for contrastive learning of invariant visual representations has become extensively used in supervised, semi-supervised, and unsupervised settings, due to its ability to uncover patterns and structures in image data that are not directly present in the pixel representations. However, this success is still not well understood; neither the loss function nor invariance alone explains it. In this talk, I present a mathematical analysis that clarifies how the geometry of the learned latent distribution arises from SimCLR. Despite the nonconvex SimCLR loss and the presence of many undesirable local minimizers, I show that the training dynamics driven by gradient flow tend toward favorable representations. In particular, early training induces clustering in feature space. Under a structural assumption on the neural network, our main theorem proves that the learned features become linearly separable with respect to the ground-truth labels. To support the theoretical insights, I present numerical results that align with the theoretical predictions.

Posted March 27, 2026
Last modified April 6, 2026

Geometry and Topology Seminar Seminar website

Chris Manon, University of Kentucky
Toric tropical vector bundles   

A toric vector bundle is a vector bundle over a toric variety which is equipped with a lift of the action action of the associated torus. As a source of examples, toric vector bundles and their projectivizations provide a rich class of spaces that still manage to admit a combinatorial characterization. Toric vector bundles were first classified by Kaneyama, and later by Klyachko using the data of decorated subspace arrangements. Klyachko's classification is the foundation of many interesting results on toric vector bundles and has recently led to a connection between toric vector bundles, matroids, and tropical geometry. After explaining some of this background, I'll introduce the notion of a tropical toric vector bundle over a toric variety. These objects are discrete analogues of vector bundles which still have notions of positivity, a sheaf of sections, an Euler characteristic, and Chern classes. The combinatorics of these invariants can reveal properties of their classical analogues as well as point the way to new theorems for tropical vector bundles over a more general base. Time permitting, I will discuss some new results on higher Betti numbers of a tropical vector bundle.

Posted February 9, 2026
Last modified March 9, 2026

LSU SIAM Student Chapter

Michael Kurtz, ExxonMobil
Industry Speaker

Motivation for, Challenges to, and Progress in the Use of Advanced Data Science Methodologies for Improved Chemical Manufacturing

Event contact: Maganizo Kapita, Laura Kurtz