Livestream: https://www.youtube.com/live/AcnRxVLcRDM?si=RDVhqqe0akj2gObX(link is external)

These lectures will discuss instanton Floer homology for knots, links and webs (embedded trivalent graphs) in 3-manifolds. This provides a rich set of invariants that in some ways parallel Monopole, Heegaard Floer and Embedded contact homology but are definitely distinct. I’ll sketch the definition and move on to applications of the theory. Some things that might be covered depending on time are homology cobordism, relations with Khovanov homology and higher rank generalizations, the relationship with the 4-color map theorem. Mostly I will cover joint with Peter Kronheimer but many many people have contributed to this area starting with of course Floer, and including work of Uhlenbeck, Taubes, Donaldson, Friedman, Morgan, Furuta, Kotschick, Fintushel, Stern, Ruberman, Matic, Munoz, Baldwin, Sivek, Daemi, Li, Ye, Eismeier.