Speaker: Yosuke Kubota (Shinshu Univ.)

Title: Crystallographic T-duality in twisted equivariant K-theory

Time/Date: 4:45-6:15pm, November 30 (Tue.), 2021

Room: This will be an online seminar on Zoom. Please ask Kawahigashi for the Zoom link.

Abstract: Associated to a crystallographic group (a proper cocompact subgroup of the Euclidean motion group), there are two finite group actions (and twists) on the tori. Crystallographic T-duality is an isomorphism of their twisted equivariant K-groups. This is regarded as a topological version of the Fourier-Mukai transform, and is defined by a composition of fundamental maps in K-theory; pull-back, cup product, and push-forward. This talk deals with the isomorphism of this kind for a generalized version of twisted equivariant K-theory in the sense of Freed-Moore. This generalization is motivated by condensed-matter physics because one of the twisted equivariant K-groups is known to classify the symmetry-protected topological phases of matter. We also discuss some applications. This is a joint work with Guo Chuan Thiang and Kiyonori Gomi.