Bott Periodicity Seminar

The seminar is going to be on Bott periodicity. After the introductory meeting, a speaker will present a proof of the Bott periodicity theorem every week. Tentative meeting location and times are as follows:

• Location: SC 232
• Day/Time: Thursday 5:15pm to 6:15pm
The first meeting will be on 7th February 2019.

# Schedule

#### 7 Feb 2019, Introductory Meeting (Dexter Chua)

I will go through the various ways to state the Bott periodicity theorem. Afterwards we will discuss some administrative affairs.

Notes: HTML PDF

#### 14 Feb 2019, Morse theory (Kai Xu)

We will be meeting at 5:30pm instead of the usual time.

#### 21 Feb 2019, Simplicial methods (Dexter Chua)

I will present the proof of Bruno Harris in his paper Bott Periodicity via Simplicial Spaces. The proof is extremely short if one assumes the simplicial machinery employed, and the talk will focus on explaining the underlying machinery that goes into the proof.

#### 4 Apr 2019, Fredholm operators (Maxim Jeffs)

We will be meeting at 5:30pm instead of the usual time.

The study of holomorphic disks with Lagrangian boundary conditions is an important tool in symplectic geometry. In this talk, I'll explain how to use them to give a proof of orthogonal Bott periodicity, by combining ideas of Atiyah on Fredholm operators with unpublished work of de Silva and Seidel.

𝄆 $\mathbf{Z}\;\; \mathbf{Z}_2\;\mathbf{Z}_2\;0\;\;\mathbf{Z}\;\;0\;\;0\;\;0$ 𝄇