Calendar

Posted January 28, 2026

Geometry and Topology Seminar Seminar website

Nilangshu Bhattacharyya, Louisiana State University
TBA

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 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