The Principal Speaker of the 2019 Workshop will be Professor Ciprian Manolescu of the University of California, Los Angeles. He will be speaking on Triangulations, homology cobordisms, and Floer theories.
Titles and abstracts of the individual talks are as follows:
Talk 1: Triangulations of manifolds
Which manifolds are triangulable? Can any two triangulations of the same manifold be made equivalent after subdivision? I will survey the history of these questions, and explain the role of the three dimensional cobordism group in the study of triangulations.
Talk 2: Seiberg-Witten theory and homology cobordism
I will explain how invariants from gauge theory give information about homology cobordism. In particular, Pin(2)-equivariant Seiberg-Witten Floer homology can be used to prove that there are no elements of order 2 and Rokhlin invariant one in homology cobordism. This implies that non-triangulable manifolds exist in all dimensions at least five.
Talk 3: Involutive Heegaard Floer homology
I will describe an invariant of 3-manifolds called involutive Heegaard Floer homology, which gives further information about homology cobordism. The invariant was constructed in joint work with Kristen Hendricks, and has recently led to a proof (by Dai-Hom-Stoffregen-Truong) that the homology cobordism group has an infinite-rank summand.