In Fall 2026, the Math Department Colloquium Series will be held on Wednesdays 3:30 pm at CU 218. Tea and refreshments available at 3:00 p.m. in the Assmus Conference Room (CU 212).
If you have any questions, please reach out to the organizers Daren Chen (dac726 AT lehigh DOT edu) and Ao Sun (aos223 AT lehigh DOT edu).
Date: 9/2/2026
Speaker: Mark Skandera (Lehigh)
Title: Picturing a change-of-basis matrix
Abstract: Much work in algebraic combinatorics involves the comparison of two different bases of a vector space, and pictorial formulas for entries of the change-of-basis matrix that relates the two bases. Such formulas tell us how to compute a matrix entry by drawing certain pictures and playing a game with them. In one vector space known as the Hecke algebra, a certain basis defined by Kazhdan and Lusztig and another natural basis are related by a change-of-basis matrix having no known elementary formula. We will look at pictures and games which describe some entries of this matrix, and at the open problem of describing the remaining entries.
This is joint work with Tommy Parisi, Ben Spahiu, and Jiayuan Wang.
The talk will be accessible to students who have taken linear algebra.
Date: 9/9/2026
Speaker: Joe Kramer-Miller (Lehigh)
Title: The complexity of power series in positive characteristic
Abstract: An amazing theorem of Christol from the 1980s states that a power series over a finite field is algebraic if and only if its coefficient sequence is p-automatic. Informally, this means that the coefficients of an algebraic series can be computed by a "finite machine". This theorem has since become a cornerstone in the study of transcendence in positive characteristic. In this talk we prove analogues of Christol's theorem for series that are solutions to iterative differential equations with moderate singularities.
Date: 9/16/2026
Speaker: Luya Wang (Princeton/IAS)
Title: Interactions between smooth and symplectic topology
Abstract: Symplectic structures lie between smooth topology and complex geometry and exhibit both flexible and rigid phenomena. However, we still do not have a good understanding of what a general symplectic manifold should look like. In this talk, I will begin by surveying some classical results of Gromov and McDuff from the 1980s, which use pseudoholomorphic curves to classify symplectic manifolds containing certain distinguished submanifolds. I will then discuss a question of Donaldson in the 1990s, which relates smooth structures in dimension four to symplectic structures in dimension six. Finally, I will describe some recent refinements of the Gromov-McDuff techniques and their applications to classification problems in the compact setting.
Date: 9/23/2026
Speaker: Lei Wu (Lehigh)
Title: Diffusive Limit of Transport Equations in Bounded Domains
Abstract: In this talk, I will discuss the transition from microscopic particle models to macroscopic continuum equations, a subject at the intersection of PDE and asymptotic analysis. I will focus in particular on the diffusive limit of the neutron transport equation, which serves as a prototype for more general hydrodynamic limits of kinetic equations. It also provides a setting that captures nearly all of the fundamental difficulties associated with boundary effects. In this survey-style talk, I will review these difficulties and discuss various approaches to addressing them. I will present our work over the past decade on three types of domains: smooth convex domains, smooth non-convex domains, and, most recently, polygonal domains. After a brief introduction to the Hilbert expansion, I will focus on the formulation and well-posedness of boundary layer and wedge layer problems.
Date: 9/30/2026
Speaker: Lisa Traynor (Bryn Mawr)
Title: Geometry with a Twist: The Restricted World of Legendrian Links
Abstract: Contact manifolds are smooth manifolds that have an extra geometric structure — with roots in physics — given by a “twisting” hyperplane field. Legendrian submanifolds are the maximal dimensional integral submanifolds of the hyperplane field. For example, a contact structure on Euclidean 3-space is given by a field of 2-dimensional planes, and its Legendrian submanifolds are smooth knots and links that have restricted shapes and movements. A motivating question is to understand when two Legendrian submanifolds, which are equivalent as smooth submanifolds, are not equivalent as Legendrian submanifolds. Through a series of examples, I will introduce Legendrian submanifolds and Legendrian invariants of increasingly sophisticated depths.
Date: 10/07/2026
Speaker: Gaoyong Zhang (NYU)
Title: Reconstruction of Convex Geometric Shapes and Monge-Ampère Equations
Abstract: Can a convex geometric shape be fully reconstructed from its local measurements? This fundamental question drives a number of geometric problems known as Minkowski-type problems. For example, a convex polytope can be recovered from its facet areas and unit normals, and a smooth closed convex hypersurface can be reconstructed from its Gauss curvature.
Solving these shape recovering problems relies on both analytical and geometrical tools. In the smooth setting, they translate into Monge-Ampère-type partial differential equations. When dealing with general, non-smooth shapes, they lead to singular Monge-Ampère and convex geometric measure equations.
This talk will introduce several of the Minkowski-type problems through accessible examples. We will talk about their analytical equations, recent developments, and open problems in the field.
Date: 11/4/2026
Pitcher's lecture
Speaker: Gerhard Huisken (University of Tübingen/Oberwolfach)
Title: TBD
Abstract: TBD
Date: 11/9/2026 (Note the special time)
3:15-4:15pm in CU 218
Speaker: Paulo Lima-Filho (Texas A&M University)
Title: TBD
Abstract: TBD
Date: 11/25/2026
Thanksgiving