# Topology Seminar

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

### Fall Quarter, 2019

- October 1, Organizational Meeting
- 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.

- October 29,
**Clover May** (UCLA)
- November 5,
**Yoosik Kim** (Boston U.)
- November 5,
**Tadayuki Watanabe** (Shimane U.)

**Special Time:** 11am in 210 Deady Hall
- November 12,
**Heather Lee** (U. Washington)
- November 13,
**Tom Hockenhull** (Glasgow)

**Special Time:** 12pm in 206 Deady Hall
- December 3, Course Organization Meeting

### Winter Quarter, 2020

- February 11,
** Maggie Miller** (Princeton)

Topology Seminar

Previous years: 2019 2018 2017 2016 2015 2013 2012 F11 S10 W10 F09 F08 S08 W08 F07 S07 W07 F06 F05-S06 F04-S05 F03-S04 F02-S03 F00-S01 F99-S00 F98-S99 F97-S98