University of Connecticut

Algebra Seminar


+ Show/hide abstracts and details

Title: The origin of pictures
Speaker: Kiyoshi Igusa (Brandeis University)
Time: Wednesday, March 21, 2018 at 11:15 am
Place: MONT 313Abstract: Gordana Todorov, Jerzy Weyman, Kent Orr and I are working on a book about ``pictures'' which have gained renewed attention because they are equivalent to ``scattering diagrams''. This talk is about very old work that I did to introduce pictures and their relation to the cohomology of $\mathrm{GL}(n,\mathbb Z)$. In particular, I will discuss the pictures below (from our book!) and their relationship to $H^3(\mathrm{GL}(n,\mathbb Z),\mathbb Z/2)$. The algebraic side of this story is a fun topic. The cohomology class which detects the ``exotic element'' of $K_3(\mathbb Z)$ is the degree 3 class which counts the number of times (modulo 2) that commutativity of addition is used to prove that matrix multiplication is associative! This is an old result (about the obstruction to right distributivity in left near-rings) which I am happy to present in a new light.

Organizer: Liang Xiao