Calendar

Posted February 1, 2026
Last modified February 2, 2026

Control and Optimization Seminar Questions or comments?

R. Tyrrell Rockafellar, University of Washington
Variational Analysis and Convexity in Optimal Control

Optimal control theory was considered by its originators to be a new subject which superseded much of the classical calculus of variations as a special case. In reality, it was more a reformulation of existing theory with different goals and perspectives. Now both can be united in a broader setting of variational analysis in which Lagrangian and Hamiltonian functions need not be differentiable or even continuous, but extended-real-valued, and convexity has a central role. The Control and Optimization Seminar for this talk will be held in person, with a Zoom option available for remote attendees.

Event contact: Gowri Priya Sunkara

Posted January 30, 2026

Combinatorics Seminar Questions or comments?

Tung Nguyen, University of Oxford, UK
Polynomial $\chi$-boundedness for excluding $P_5$

We discuss some ideas behind the recent resolution of a 1985 open problem of Gyárfás, that there is a positive integer k for which every graph with no induced five-vertex path has chromatic number at most the kth power of their clique number.

Posted December 29, 2025
Last modified February 3, 2026

Colloquium Questions or comments?

R. Tyrrell Rockafellar, University of Washington
Dual Problems of Optimization

A surprising discovery in the early days of optimization theory was the prevalence of a new kind of duality. Typical problems then of interest, in which a linear function was to be minimized subject to constraints consisting of equations or inequalities imposed on other linear functions, couldn't be solved without simultaneously solving a partnered problem of maximization in the same category. The solutions to the two problems could be viewed moreover as the best strategies for two opponents is a sort of zero-sum game. This theme is now understood much more broadly as a feature of optimization theory that has been important not only in the design of solution algorithms, but also in extending mathematical analysis beyond the traditions of calculus.

Posted December 17, 2025
Last modified January 30, 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.