Calendar

Posted February 9, 2026
Last modified February 23, 2026

Informal Analysis Seminar Questions or comments?

Gustavs Tobiss, Louisiana State University
Bloch's Theorem, Wannierization, and Tight-binding

This talk presents the mathematical framework and numerical methods behind tight-binding models for electrons in a one-dimensional periodic potential, focusing on the transition from Bloch states to Wannier functions. We start by revisiting Bloch’s theorem, which leads to a decomposition into independent Hamiltonians for each wavevector in the Brillouin zone. This immediately allows us to describe the system in terms of its band structure. We then introduce Wannier functions, localized eigenstates derived from band eigenfunctions. The Wannier functions possess many nice qualities, such as being exponentially localized and orthonormal, with the decay tied to the analyticity of the band structure. Next, we derive the tight-binding Hamiltonian by projecting onto a single band subspace. This Hamiltonian is expressed as a sum of hopping terms, with hopping amplitudes related to the band structure, providing a link to the system's dispersion relation and physical properties. Finally, we discuss how this simple model will be used to analyze more complicated structures.

Posted January 28, 2026
Last modified February 17, 2026

Geometry and Topology Seminar Seminar website

Nir Gadish, University of Pennsylvania
Letter braiding invariants of words in groups

How can we tell if a group element can be written as k-fold nested commutator? One way is to find a collection of computable function that vanish only on nested commutators. This talk will introduce letter-braiding invariants - these are elementarily defined functions on words, inspired by the homotopy theory of loop-spaces and carrying deep geometric content. They give a universal finite-type invariant for arbitrary groups, extending the influential Magnus expansion of free groups that already had countless applications in low dimensional topology. As a consequence we get new geometric formulas for braid and link invariants, and a way to linearize automorphisms of general groups that specializes to the Johnson homomorphism of mapping class groups.

Posted January 15, 2026
Last modified February 20, 2026

Informal Geometry and Topology Seminar Questions or comments?

Hailey Garcia, Louisiana State University
The Cohomology of the Complement of Hyperplane Arrangements

We consider linear hyperplane arrangements 𝓐 in V=ℂ^n. Of interest is the complement of the arrangement M(𝓐)=M(𝓐)=V\(∪_{H_i∈𝓐}H_i). We will demonstrate the definition and some properties of the Orlik-Solomon algebra A(𝓐) of 𝓐. Then, by considering the deletion-restriction triple (𝓐',𝓐,𝓐''), we demonstrate that the cohomology ring of M(𝓐) is isomorphic to A(𝓐) and hence determined by the combinatorics of the intersection lattice L(𝓐).

Posted January 8, 2026

Control and Optimization Seminar Questions or comments?

Lars Gruene, University of Bayreuth SIAM Fellow
Can Neural Networks Solve High Dimensional Optimal Feedback Control Problems?

Deep reinforcement learning has established itself as a standard method for solving nonlinear optimal feedback control problems. In this method, the optimal value function (and, in some variants, the optimal feedback law also) is stored using a deep neural network. Hence, the applicability of this approach to high-dimensional problems relies crucially on the network's ability to store a high-dimensional function. It is known that for general high-dimensional functions, neural networks suffer from the same exponential growth of the number of coefficients as traditional grid based methods, the so-called curse of dimensionality. In this talk, we use methods from distributed optimal control to describe optimal control problems in which this problem does not occur.

Posted February 9, 2026

LSU AWM Student Chapter LSU AWM Student Chapter Website

Discussion session with Amber Schreve

The AWM Student Chapter is pleased to host a special discussion session with Amber Schreve, a PhD student in Finance at LSU and an actuary at the Louisiana Department of Insurance. She will share her experience as a mathematician working in the actuarial field, discussing her journey from studying mathematics to becoming an actuary. This offers a great opportunity for students to interact with Amber and ask questions about her career motivations and professional path behind transitioning from academia to industry.

Event contact: jgarc86@lsu.edu

Posted February 24, 2026

Combinatorics Seminar Questions or comments?

Steven Noble, University of Leeds
Critical groups for embedded graphs

Critical groups are finite Abelian groups associated with graphs. They arise in many different ways, for example, via the chip-firing game, through the Laplacian and via fundamental cycles and cocycles. Several results in the literature on critical groups only hold for planar graphs and their proofs rely on a plane drawing. This suggests the natural setting for the critical group might be graphs embedded on surfaces. We show how various definitions of the critical group may be extended to embedded graphs, and crucially that they give isomorphic groups. No knowledge of topology or group theory is required!

Posted February 10, 2026

Mathematical Physics and Representation Theory Seminar

Milo Moses, Caltech
Four-colorings, recoverability, and topological quantum matter

In ongoing joint work with A. Kitaev, D. Ranard, I. Kim, we have been developing a formalism for exploring topologically ordered quantum states using recovery maps. In this talk, I will explain the potential applicability of these recovery maps to the study of 4-colorings of planar graphs. Conditioned on an unproven technical lemma (which perhaps someone in the audience can demonstrate!), I can show that bridgeless planar graphs quasi-isometric to the Euclidean plane obey a medley of properties reminiscent of topological quantum order.

Posted February 9, 2026

Informal Analysis Seminar Questions or comments?

Basit Abdulfatai, Louisiana State University
Dolapo Onifade, Louisiana State University
Introduction to deep adaptive sampling and physics informed neural networks

Posted January 19, 2026

Geometry and Topology Seminar Seminar website

Ettore Marmo, Università degli Studi di Milano-Bicocca
TBA

Posted January 15, 2026
Last modified January 16, 2026

Informal Geometry and Topology Seminar Questions or comments?

Benjamin Appiah, Louisiana State University
TBD

TBD