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) $.