Calendar

Posted December 17, 2025
Last modified February 8, 2026

Applied Analysis Seminar Questions or comments?

Tuoc Phan, University of Tennessee–Knoxville
On Lin type Hessian estimates for solutions to a class of singular-degenerate parabolic equations

We disscuss a class of parabolic equations in non-divergence form with measurable coefficients that exhibit singular and/or degenerate behavior governed by weights in a Muckenhoupt class. We present new results on weighted F.-H. Lin type estimates of the Hessian matrices of solutions. As examples, we demonstrate that the results are applicable to equations whose leading coefficients are of logistic-type singularities, as well as those are of polynomial blow-up or vanishing with sufficiently small exponents. A central component of the approach is the development of local quantitative lower estimates for solutions, which are interpreted as the mean sojourn time of sample paths, a stochastic-geometric perspective that generalizes the seminal work of L. C. Evans. By utilizing intrinsic weighted cylinders and perturbation arguments alongside with parabolic ABP estimates, we effectively manage the operator's degeneracies and singularities. We also briefly address regularization and truncation strategies that ensure our estimates are robust. We conclude with a discussion of future applications and related developments in the field.

Posted January 15, 2026
Last modified February 3, 2026

Student Colloquium

Joshua Sabloff, Haverford College
Informal Discussion with Joshua Sabloff

Join us for an informal discussion with Joshua Sabloff. We will be discussion what it is like working in a primarily undergraduate institution.

Posted February 3, 2026
Last modified February 4, 2026

Student Colloquium

Joshua Sabloff, Haverford College
How to Tie Your Unicycle in Knots: An Introduction to Legendrian Knot Theory

You can describe the configuration of a unicycle on a sidewalk using three coordinates: two position coordinates x and y for where the wheel comes into contact with the ground and one angle coordinate t that describes the angle that the direction the wheel makes with the x axis. How are the instantaneous motions of the unicycle constrained (hint: do you want your tire to scrape sideways)? How can we describe that constraint using generalizations of tools from vector calculus? The system of constraints at every point in (x,y,t)-space is an example of a "contact structure," and a path that obeys the constraints is a "Legendrian curve." If the curve returns to its starting point, then it is called a "Legendrian knot." A central question in the theory of Legendrian knots is: how can you tell two Legendrian knots apart? How many are there? In other words, how many ways are there to parallel park your unicycle? There will NOT be a practical demonstration.

Posted January 22, 2026

Informal Analysis Seminar Questions or comments?

Matthew McCoy, Louisiana State University
Crash Course on Schrödinger Operators (Part 2)

An expository talk in spectral theory.

Posted January 28, 2026
Last modified February 3, 2026

Geometry and Topology Seminar Seminar website

Joshua Sabloff, Haverford College
On the Non-Orientable Genera of a Knot: Connections and Comparisons

We define a new quantity, the Euler-normalized non-orientable genus, to connect a variety of ideas in the theory of non-orientable surfaces bounded by knots.  We use this quantity to explore the geography of non-orientable surfaces bounded by a fixed knot in 3 and 4 dimensions.  In particular, we will use the Euler-normalized non-orientable genus to reframe non-orientable slice-torus bounds on the (ordinary) non-orientable 4-genus and to bound below the Turaev genus as a measure of distance to an alternating knot.  This is joint work with Julia Knihs, Jeanette Patel, and Thea Rugg.

Posted February 4, 2026
Last modified February 5, 2026

Informal Geometry and Topology Seminar Questions or comments?

Justin Lanier, Louisiana State University
Every Surface is a Leaf

We'll start by discussing the fact that every closed 3-manifold admits foliations, where the leaves are surfaces. This fact raises the question: for a given closed 3-manifold, which surfaces can appear as leaves of some foliation of that 3-manifold? Kerékjártó and Richards gave a classification up to homeomorphism of noncompact surfaces, which includes surfaces with infinite genus or infinitely many punctures. In their 1985 paper "Every surface is a leaf", Cantwell–Conlon prove a universality theorem: for every closed 3-manifold M and every orientable noncompact surface L, M has a foliation where L appears as a leaf. We will discuss their paper and the surrounding context.

Posted February 6, 2026

Actuarial Student Association

ASA x Cabe C.

We will be joined by the President of Lewis and Ellis (LSU Alumni!!!) Pizza Will be served

Posted November 26, 2025
Last modified January 29, 2026

Control and Optimization Seminar Questions or comments?

Anthony Bloch, University of Michigan AMS, IEEE, and SIAM Fellow
Control, Stability and Learning on Dynamic Networks

In this talk we consider various aspects of dynamics, control and learning on graphs. We discuss diffusively coupled network dynamical systems and the role of coupling in stabilizing and destabilizing such systems. We also discuss dynamic networks of this type and in particular Lyapunov-based methods for analyzing the stability of networks undergoing switching. In addition we analyze the problem of learning the dynamics of switched systems from data, including linear and polynomial systems and systems on graphs. In addition we consider the control and dynamics of systems on hypergraphs which have applications to biological networks.

Posted February 8, 2026

Combinatorics Seminar Questions or comments?

Yiwei Ge, Louisiana State University
Extremal connectivity in graphs

A $k$-connected graph is minimally (respectively, critically) $k$-connected if the deletion of any edge (respectively, vertex) results in a graph that is not $k$-connected. A graph is uniformly $k$-connected if there are exactly $k$ internally disjoint paths between every pair of vertices. These classes have played a prominent role in graph connectivity theory. We introduce super-minimally $k$-connected graphs, defined as $k$-connected graphs with no proper $k$-connected subgraph. In this talk, we will give a brief introduction to these connectivity classes, with particular emphasis on extremal problems for $3$-connected graphs.