Calendar

Posted January 28, 2026
Last modified February 17, 2026

Geometry and Topology Seminar Seminar website

Nilangshu Bhattacharyya, Louisiana State University
Steenrod Square on Khovanov Homology

Khovanov homology assigns a knot or a link to a bigraded homology theory that categorifies the Jones polynomial. It has concrete applications, for instance Rasmussen’s $s$-invariant, extracted from Lee’s deformation, which gives a lower bound on the smooth slice genus. At the same time, while the theory is very combinatorial and closely tied to the representation theory of $U_q(\mathfrak{sl}_2)$, it can be hard to see the underlying geometric picture directly from the homology groups. The stable homotopy refinement, introduced by Lipshitz and Sarkar, upgrades Khovanov homology to a space-level invariant: a spectrum whose cohomology recovers Khovanov homology while supporting additional structure that is invisible at the level of homology. This refinement induces stable cohomology operations, such as Steenrod squares, on Khovanov homology. In this talk, I will explain how to compute $Sq^1$ and $Sq^2$ on Khovanov homology.

Posted February 17, 2026

Discussion and Training in Combinatorics

Gyaneshwar Agrahari, LSU
An Introduction to the Crapo Beta Invariant in Matroid Theory

We will define the Crapo beta invariant of a matroid and prove a few of its fundamental properties, including how it behaves under standard matroid operations. We will also investigate the connection of certain matroid properties like connectivity with the invariant.

Event contact: Gyaneshwar Agrahari and Emmanuel Asante

Posted December 7, 2025
Last modified December 28, 2025

Control and Optimization Seminar Questions or comments?

Richard Vinter, Imperial College London IEEE Fellow
Control of Lumped-Distributed Control Systems

Lumped-distributed control systems are collections of interacting sub-systems, some of which have finite dimensional vector state spaces (comprising ‘lumped’ components) and some of which have infinite dimensional vector state spaces (comprising ‘distributed’ components). Lumped-distributed control systems are encountered, for example, in models of thermal or distributed mechanical devices under boundary control, when we take the control actuator dynamics or certain kinds of dynamic loading effects into account. This talk will focus on an important class of (possibly non-linear) lumped-distributed control systems, in which the control action directly affects only the lumped subsystems and the output is a function of the lumped state variables alone. We will give examples of such systems, including a temperature-controlled test bed for measuring semiconductor material properties under changing temperature conditions and robot arms with flexible links. A key observation is an exact representation of the mapping from control inputs to outputs, in terms of a finite dimensional control system with memory. (We call it the reduced system representation.) The reduced system representation can be seen as a time-domain analogue of frequency response descriptions involving the transfer function from input to output. In contrast to frequency response descriptions, the reduced system representation allows non-linear dynamics, hard constraints on controls and outputs, and non-zero initial data. We report recent case studies illustrating the computational advantages of the reduced system representation. We show that, for related output tracking problems, computation methods based on the new representation offer significantly improved tracking and reduction in computation time, as compared with traditional methods, based on the approximation of infinite dimensional state spaces by high dimensional linear subspaces.

Posted February 16, 2026

Combinatorics Seminar Questions or comments?

William Linz, University of South Carolina
On the maximum second eigenvalue of outerplanar graphs

A typical spectral Turan problem is to determine the maximum spectral radius of a graph in some given family of graphs on a fixed number of vertices. Spectral Turan problems have been well-studied in part because they are variations on classical Turan problems from extremal graph theory. Nikiforov proposed the much more general question of determining which graphs maximize a fixed linear combination of eigenvalues of a graph among a given family of graphs. In this talk, I will survey some of the results that are known about these problems. The main highlight of the talk will be a recent result on the maximum second eigenvalue of an outerplanar graph on a fixed number of vertices, a result which is joint work with George Brooks, Maggie Gu, Jack Hyatt and Linyuan Lu.

Posted February 17, 2026

LSU SIAM Student Chapter

Laura Kurtz, Louisiana State University
Rerun: Accesibility in LaTeX Workshop

Learn how to make your LaTeX documents readable by screen readers.

Posted February 3, 2026

Mathematical Physics and Representation Theory Seminar

Karl-Hermann Neeb, Universität Erlangen-Nürnberg
Coadjoint orbits carrying Gibbs ensembles

Coadjoint orbits are orbits for the action of a Lie group on the dual of its Lie algebra. They carry a natural symplectic structure and are models for homogeneous systems in classical mechanics. Gibbs measures on these orbits provide a natural setting for models of thermodynamic systems. We say that a coadjoint orbit carries a Gibbs ensemble if the set of all $x$, for which the function $\alpha \mapsto e^{-\alpha(x)}$ on the orbit is integrable with respect to the Liouville measure, has non-empty interior $\Omega_\lambda$. We describe a classification of all coadjoint orbits with this property. In the context of Souriau's Lie group thermodynamics, the subset $\Omega_\lambda$ is the geometric temperature, a parameter space for a family of Gibbs measures on the coadjoint orbit. The corresponding Fenchel--Legendre transform maps $\Omega_\lambda$ (modulo central shifts) diffeomorphically onto the interior of the convex hull of the coadjoint orbit $\cO_\lambda$. This provides an interesting perspective on the underlying information geometry.

Posted November 15, 2025
Last modified January 21, 2026

Algebra and Number Theory Seminar Questions or comments?

Marco Sangiovanni Vincentelli, Columbia University
An Euler system for the adjoint of a modular form

Euler systems have proven to be versatile tools for understanding Selmer groups and their connections to special values of $L$-functions. However, despite the key role they have played in making progress toward foundational conjectures in number theory, such as the Birch and Swinnerton-Dyer and Bloch–Kato Conjectures, only a handful of provably non-trivial Euler systems have been constructed to date. A significant obstacle to constructing Euler Systems lies in producing candidate Galois cohomology classes. This lecture series presents joint work with Chris Skinner that develops a method to overcome this obstacle. Using this method, we construct an Euler system for the adjoint of a modular form.

Event contact: Gene Kopp

Posted February 6, 2026

Actuarial Student Association

ASA Excel Workshop

We will be joined by our SOA Liason Matthew who will continue his Excel Workshop from last year! Pizza Will be Served

Posted February 9, 2026
Last modified February 10, 2026

Informal Analysis Seminar Questions or comments?

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

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 January 16, 2026

Informal Geometry and Topology Seminar Questions or comments?

Hailey Garcia, Louisiana State University
TBD

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