Calendar

Posted September 10, 2025
Last modified September 23, 2025

Geometry and Topology Seminar Seminar website

Colin Crowley, University of Oregon
TBA

TBA

Posted September 29, 2025

Geometry and Topology Seminar Seminar website

Scott Baldridge, Louisiana State University
What does the Four Color Theorem have to do with the sound a drum makes?

Mark Kac famously asked in 1966, “Can one hear the shape of a drum?” While the answer to this question is now known to not be true in general, it popularized an investigation into eigenvalues of Laplacians that continues to this day. One formulation of it is as follows: two closed Riemannian manifolds are said to {\em isospectral} if the eigenvalues of their Laplace-Beltrami operator, counted with multiplicities, coincide. Modern questions ask to what extent having the same eigenvalues determine the geometry of the two manifolds. In this talk, we introduce a Laplace-de Rham operator on a cochain complex derived from a cellularly embedded graph into a surface. (When the surface is a $2$-sphere, this is simply a plane graph.) In degree zero, the dimension of the subspace of the harmonic solutions to this operator counts the number of $4$-face colorings of the graph. Therefore, there are zero eigenvalue solutions for a plane graph if and only if the graph does not have a bridge (the Four Color Theorem). The nonzero eigenvalues of this operator are also quite interesting, which leads us to pose the following isospectral conjecture by the end of the talk, "Can one hear the shape of the CW structure of a surface?”

Posted September 26, 2025

Geometry and Topology Seminar Seminar website

Naageswaran Manikandan, Max Planck Institute
TBA

Posted September 1, 2025
Last modified September 23, 2025

Geometry and Topology Seminar Seminar website

Matthew Haulmark, UT Rio Grande Valley
TBA

TBA

Posted September 1, 2025
Last modified September 23, 2025

Geometry and Topology Seminar Seminar website

Chen Zhang, Stony Brook University
TBA

TBA