PhD defense Qingyuan Bai
Title: Variations on the theme of toric mirror symmetry
Abstract:
The theme of this thesis is an algebraic study of sheaves on real vector spaces. In the first part, we revisit the coherent constructible correspondence for toric varieties, which describes sheaves on Rn with prescribed singular support in terms of torus-equivariant quasi-coherent sheaves on a toric variety. Among other things, we show that such a correspondence can be lifted to the universal base ring , the sphere spectrum.
In the second part, we explain that this perspective can be used to describe all sheaves on Rn in the form of almost mathematics objects, following the work of Dmitry Vaintrob. This provides a natural interpretation of Efimov’s calculation of continuous K-theory for sheaves on Rn. We take this approach further to calculate the Picard group of sheaves on Rn under the convolution product.
The first part is a joint work with Yuxuan Hu, and the second part is a joint work with Robert Burklund.
Supervisor: Professor Dustin Clausen, IHES / University of Copenhagen
Co-supervisor: Professor Lars Hesselholt, Nagoya University / University of Copenhagen
Assessment committee:
Professor Nathalie Wahl (chair), University of Copenhagen
Assistant Professor Peter Haine, University of Southern California
Associate Professor Hiro Lee Tanaka, Texa State University