# 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**