This website contains information and resources for the CIRGET learning seminar for the Winter term 2017 on stable homotopy theory and its connections to gauge theoretic invariants of low-dimensional manifolds. Talks will be:

Mondays, 3.00PM - 4.30PM,
PK5115, UQÀM, 201 Avenue du Président-Kennedy, Montréal

Conley index

Background: A few years ago, Ciprian Manolescu (among others) developed a way of understanding Seiberg-Witten theory and some Floer theoretic invariants in terms of stable homotopy theory. The general idea is that you take homology groups that may be defined using gauge theory of Floer theory and instead find a natural way to build a stable homotopy type whose homology recovers the given groups (but hopefully says something more). This new way of looking at things has been used to reprove gauge theoretic results like Donaldson's diagonalisation and the 11/8 Theorem. It was also the tool used to solve the Triangulation Conjecture recently.

The idea of the seminar is to understand some of the tools that go into all of this, hopefully making our way eventually to talking about the Triangulation Conjecture. We want to give a variety of different levels of talk so that everyone from students to faculty can have some interesting topics to give a lecture on.