Graduate Student Seminar- Gram Determinants of Type Mb

Date and Time: February 21, 2025 (1:00 PM – 2:00 PM)

Location: Phillips Hall, Room 736

Speaker: Anthony Christiana

Title: Gram Determinants of Type Mb

Abstract: As classically defined, Gram Determinants are essential tools in linear algebra and function theory. In this talk, we lift the motivating idea behind Gram Determinants to define a Gram Determinant of Type Mb - a polynomial value which encodes the interactions between basis elements of the Relative Kauffman Bracket Skein Module. We begin by understanding crossingless connections between 2n points on the mobius band such that we can define the bilinear form between such crossingless connections. Then, we will discuss recent work which has allowed for the computation of this bilinear form algorithmically. All this is in service of proving a general formula for the Gram Determinants of Type Mb and other related values.

Attendance is required for all graduate students. We look forward to your participation.