# Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory

## Details

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

**Speakers and Courses:**

- Mohammed Abouzaid, Columbia University:
*Floer Homotopy* - Nate Bottman, Max Planck:
*Floer Homology Fundamentals* - Catherine Cannizzo, SCGP:
*Floer Homology Fundamentals* - Jeff Hicks, University of Edinburgh:
*Applications* - Cary Malkiewich, Binghamton University:
*Spectra and Smash Products* - Katherine Poirier, New York City College of Technology:
*String Topology* - Hiro Lee Tanaka, Texas State University:
*Operads and Ring Spectra*

**
School Structure:**

The summer school will consist of lecture courses with problem sessions; seminars on recent developments; and two panel discussions about professional development. The lecture courses will be:

__Week 1: July 11- 15__

Fundamentals of Floer Homology (9 lectures)

Operads and Ring Spectra (3 lectures)

String topology (3 lectures)

__Week 2:July 18- 22__

Spectra and smash products (4 lectures)

Operads and Ring Spectra continued (4 lectures)

Applications of Floer homology (3 lectures)

Floer homotopy theory (4 lectures)

Most days, an hour and a half will be set aside for problem sessions. There will also be two seminars on recent developments and one panel discussion on professional development each week.

**
Suggested Prerequisites:**

Basic algebraic topology (fundamental group, homology, cohomology, Poincaré duality) and basic differential geometry (smooth manifolds, vector fields, flows, transversality, differential forms, deRham cohomology). Some familiarity with generalized cohomology theories (K-theory, bordism, etc.) or spectra would be useful, but not absolutely required.

## Additional Information

### COVID-19 Reporting and Precautions for participants attending the summer school in person:

**Precautionary measures**:

- Wear you mask at all times indoors or in shared spaces.

- Maintain a safe distance from others (at least 1 metre), even if they don’t appear to be sick.

- Clean your hands often. Use soap and water, or an alcohol-based hand rub.

- Cover your nose and mouth with your bent elbow or a tissue when you cough or sneeze.

**Contact**:

Should you have any queries about this event, pleasae contact ruth@pims.math.ca.

**Scientific, Summer School**

**July 11–22, 2022**

**-**