Categorical Donaldson-Thomas Theory for Local Surfaces

Prof. Yukinobu Toda received his PhD from the University of Tokyo in 2006, and held a JSPS postdoctoral position at the University of Tokyo from 2006 to 2007. Subsequently, he started at the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) in 2008, initially as a project assistant professor, and since 2017, he has held the position of full professor at Kavli IPMU. He was an ICM invited speaker in 2014 in Seoul.

• - Introduction.- Koszul duality equivalence.- Categorical DT theory for local surfaces.- D-critical D/K equivalence conjectures.- Categorical wall-crossing via Koszul duality.- Window theorem for DT categories.- Categori ed Hall products on DT categories.- Some auxiliary results.