# TGTS Tetrahedral Geometry/Topology Seminar

Sponsored by Elizabethtown College, Franklin and Marshall College,
Lebanon Valley College, Millersville University, and West Chester University

### Speakers Fall 2024

Sep 2024: NO TGTS this month
4 Oct 2024: Ron Umble, Millersville University
1 Nov 2024: Jeremy Brazas, West Chester University

TGTS is a regional mathematics seminar/colloquium. We meet at 4:30
p.m. on the first Friday of each month during the academic year (with
some exceptions, as noted in the schedule above). The public is
cordially invited to attend.

### Next Talk

**Date/Time:** 4 October 2024, 4:30pm ET
**Location:** Franklin and Marshall College, 215 Stager Hall
**Zoom:** https://fandm.zoom.us/j/94928313369
**Speaker:** Ron Umble, Millersville University
**Title:** Gerstenhaber-Schack Bialgebras
**Abstract:** A \emph{Gerstenhaber-Schack bialgebra} (GSb) consists
of a graded Hopf algebra $A$ together with three multilinear operations
$\{\omega^{n,m}\in Hom^{3-m-n}(A^{\otimes m},A^{\otimes n}) :m+n=4\}$
whose sum is a $2$-cocycle in the Gerstenhaber-Schack (G-S) complex of
$A$. A \emph{G-S extension} of $A$ is a GSb containing it. G-S
extensions of $A$ are classified up to isomorphism by the degree -1
component of the G-S cohomology group $H_{GS}^{2}(A;A)$. We exhibit a
space $X$ and a non-trivial topologically induced GSb structure on
$H^{\ast}\left(\Omega X;\mathbb{Z}_{2}\right) $.

### Past Seminars

### Contact Information