Calendar

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 April 8, 2026

Combinatorics Seminar Questions or comments?

Tong Jin, Vanderbilt University
Representation theory of orthogonal matroids.

Orthogonal matroids generalize maximal isotropic spaces just as matroids generalize linear spaces, and they are Coxeter matroids of type D_n in the sense of Borovik--Gelfand--White, and even \Delta-matroids or tight 2-matroids in the sense of Bouchet. In this talk, we construct the foundation F_M of an orthogonal matroid M, which processes the universal property that the set of equivalence classes of representations of M over a field F is naturally in one-to-one correspondence with Hom(F_M, F). We also give an explicit presentation of the foundation F_M as an algebra over the regular partial field. The presentation here has a different set of generators from the matroid case in the work of Baker--Lorscheid, and a central theorem in this approach is a new characterization of representations of orthogonal matroids by circuits. We end this talk with some interesting examples of foundations of orthogonal matroids that are representable over all fields, and we will see phenomena that don’t appear in matroids.

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

Posted April 8, 2026

Informal Analysis Seminar Questions or comments?

Arif Ali, Louisiana State University
TBD

TBD

Posted March 9, 2026
Last modified April 6, 2026

Harmonic Analysis Seminar

Alexander Burgin, Georgia Tech
Integer Cantor sets: Harmonic-analytic properties & arithmetic applications.

Integer Cantor sets, which consist of a set of integers in a fixed base and a fixed set of digits, have many interesting properties, including uniform distribution, metric pair correlation, and mean ergodic theorems. In particular, their Fourier transform factorizes. I’ll begin with a motivation from ergodic theory, and proceed to discuss some recent results of myself, Fragkos, Lacey, Mena, and Reguera. If time permits, I will discuss some arithmetic applications of these estimates.

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

Anurakti Gupta, Louisiana State University
TBD

TBD

Posted December 27, 2025
Last modified February 25, 2026

Control and Optimization Seminar Questions or comments?

Aris Daniilidis, Technische Universität Wien
Variational Stability of Alternating Projections

The alternate projection method is a classical approach to deal with the convex feasibility problem. We shall first show that given two nonempty closed convex sets $A$ and $B$, the consecutive projections $x_{n+1} = PB(PA(x_n))$, $n \ge 1$ produce a self-contacted sequence, providing in particular an alternative way to establish convergence in the finite dimensional case [2]. In infinite dimensions, a regularity condition is required to ensure convergence of the above sequence $\{x_n\}_{n\ge 1}$ [4]. In [3], it was established that a regularity condition from [1] also ensures the variational stability of the above method. In this talk, we shall complete this result and show that variational stability is actually equivalent to the aforementioned regularity assumption. REFERENCES: [1] H. Bauschke, J. Borwein, On the convergence of von Neumann’s alternating projection algorithm for two sets, Set-Valued Anal. 1 (1993), 185–212. [2] A. Bohm, A. Daniilidis, Ubiquitous algorithms in convex optimization generate self-contracted sequences, J. Convex Anal. 29 (2022) 119–128. [3] C. De Bernardi, E. Miglierina, A variational approach to the alternating projections method, J. Global Optim. 81 (2021), 323-350. [4] H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. 57 (2004), 35–61.