# Symplectic Geometry Seminar Winter 2018

Wednesdays - 5:15 p.m.
McHenry Library Room 4130

• January 10, 2018

TBA

January 17, 2018

TBA

January 24, 2018

TBA

**SPECIAL DAY & TIME**

Thursday, February 1, 2018 - 3:00pm

Kei Irie, Simons Center/Kyoto University

Denseness of Minimal Hypersurfaces for Generic Metrics

We prove that, on a smooth closed manifold of dimension 3 < = d < = 7 with a C^{\infty} generic Riemannian metric, the union of closed embedded minimal hypersurfaces is dense. This is joint work with F. Marques and A. Neves.

The proof is based on min-max theory for the volume functional on the space of codimension 1 (flat) cycles, which was originally developed by Almgren and Pitts. The key ingredient of the proof is the Weyl law" (proved by Liokumovich, Maques, and Neves), which says that the asymptotic of min-max values in this theory recovers the volume of a Riemannian manifold.

February 7, 2018

TBA

February 14, 2018

TBA

February 21, 2018

TBA

February 28, 2018

TBA

March 7, 2018

TBA

SPECIAL DAY & TIME

Tuesday, March 20, 2018 1:00-2:00pm

McHenry 4130

Ciprian Manolescu, UCLA

A sheaf-theoretic model for SL(2,C) Floer homology

I will explain the construction of a new homology theory for three-manifolds, defined using perverse sheaves on the SL(2,C) character variety. Our invariant is a model for an SL(2,C) version of Floer's instanton homology. I will present a few explicit computations for Brieskorn spheres, and discuss the connection to the Kapustin-Witten equations and Khovanov homology. This is joint work with Mohammed Abouzaid.

March 21, 2018

TBA