Seminar: Shannon Rubin - A hotomotopical invariant of Weinstein surfaces (Mar 31, 2026)

Speaker: Shannon Rubin (Yau Mathematical Sciences Center - Tsinghua University)
Title: A hotomotopical invariant of Weinstein surfaces
Time: March 31, 2026 at 16:00 Istanbul local time (21:00 Beijing local time)
Place: Online
Meeting ID: 935 6390 4955
Passcode: 699568
Abstract: An symplectic geometry, a Weinstein surface W can be understood by combinatorial data on its skeleton, which is generically a finite trivalent graph G. Motivated by the microlocal theory of sheaves, there is a naturally associated diagram D of differential-graded categories, defined over the quiver which replaces each edge of G by a cospan. We call such quivers 'graphic'. After adding in appropriate homological shifts, the homotopy limit of D yields an invariant of W, so we are motivated to find explicit presentations for these homotopy limits.

Abstracting the story above, we fix an arbitrary graphic quiver Q. Given any model category M (above we had M = dg-categories) we consider M-valued diagrams over Q. In this talk I will present a combinatorial characterization of all such diagrams D which are suitably 'fibrant,' which in particular implies that the homotopy limit of D is just its classical limit. Analogous to the calculation of derived functors in homological algebra, this yields an explicit formula for the homotopy limit of any diagram.