Topology Seminar

This seminar is held on Tuesdays at 3pm in 210 Deady.

October 8, Eric Ramos (UO)
Spanning subspace configurations and representation stability

Abstract: Let V_1, V_2, V_3,… be a sequence of Q-vector spaces where V_n carries an action of S_n for each n. Representation stability is one notion of when the sequence {V_n} has a limit. In this talk, we will introduce the tools of representation stability as they apply to the homology groups of the variety X_{n,k} of spanning configurations. That is, the variety of n-tuples (L_1,…,L_n) of lines in C^k that satisfy L_1 + … + L_n=C^k as vector spaces. Using representation stability, we will study stability phenomena for the homology groups H_q(X_{n,k}) as the parameter (n,k) grows. This is joint work with Brendan Pawlowski and Brendon Rhoades.

October 15, Boris Botvinnik (UO)
Spin manifolds with fibered singularities: geometry and topology

October 22, Nikolai Saveliev (U. Miami)
On the monopole Lefschetz numbe

Abstract: Given an involution on a rational homology 3-sphere Y making it into a branched cover of S^3, we prove a formula for the Lefschetz number of the map induced by this involution on the reduced monopole homology of Y. This formula is motivated by a variant of Witten’s conjecture relating the Donaldson and Seiberg-Witten invariants of 4-manifolds. It has various applications in 4-dimensional topology, gauge theory, knot theory, and contact geometry, and a recent extension to higher order diffeomorphisms. This is a joint project with Jianfeng Lin and Daniel Ruberman.

November 5, Tadayuki Watanabe (Shimane U.)
Special Time: 11am in 210 Deady Hall

November 13, Tom Hockenhull (Glasgow)
Special Time: 12pm in 206 Deady Hall

Math Department of Mathematics