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: 9/30/2026
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: 11/4/2026
Pitcher's lecture
Speaker: Gerhard Huisken (University of Tübingen/Oberwolfach)
Title: TBD
Abstract: TBD