In my talk I will conjecture existence of certain new homological
invariants of 3-manifolds. The invariants provide categorification of
the analytically continued WRT invariant and have some similarities
with Heegaard/monopole Floer homology. Physically such invariants can
be defined as Hilbert spaces of M-theory in certain backgrounds. I
will describe mathematical properties of such invariants, their
relation to open topological strings and how to calculate them for
some specific types of 3-manifolds. The talk is mainly based on a
joint work with S. Gukov, D. Pei and C. Vafa.
Speaker(s): Pavel Putrov (IAS)