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**

**Background:** A few years ago, Bauer and Furuta (independently) developed a way of understanding the 4-dimensional Seiberg-Witten equations in terms of stable homotopy theory. After this, Ciprian Manolescu developed methods to adapt and extend their ideas to the 3-dimensional Seiberg-Witten equations.

The general idea is that you take homology groups that may be defined using gauge theory or 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 Ciprian Manolescu used to build invariants that finally disproved the Triangulation Conjecture in dimensions >4.

**The idea of the seminar** is to understand some of the tools that go into all of this, starting with the 4-dimensional version and hopefully making our way to the 3-dimensional version. 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.