Focused Workshop on Khovanov homology and exotic manifolds

Four-dimensional manifolds hold a special place in the field of smooth manifolds. It is the lowest dimension in which we see exotic manifolds, and arguably the least understood of all dimensions: for example the generalised Poincare conjecture is still open only in dimension 4. 

Historically, the most popular tool to study 4-manifolds from a smooth perspective is gauge theory, in its many forms ranging from Donaldson's seminal work, to the Seiberg-Witten invariants, instanton Floer homology, and Heegaard Floer homology, just to name a few. What all these gauge theories have in common is that their definition is based on some PDE and heavy analysis.

Very recently, Ren and Willis showed that sometimes exotic pairs of 4-manifolds can be detected with a combinatorial invariant defined by Morrison-Walker-Wedrich, which in turn is based on the popular Khovanov homology for knots and links.

The main goal of the focused workshop is to extend Ren and Willis's approach to study exotic manifolds.