Classifying crystalline interacting topological phases through equivariant cohomology

Speaker: Omar Antolín (Instituto de Matemática - UNAM)

Abstract: I'll describe joint work with Daniel Sheinbaum in which we explain how to compute how many distinct topological phases there are for crystalline interacting gapped systems given their symmetry group. Our answer is given in terms of a tool from algebraic topology called equivariant cohomology. I'll explain in broad strokes how this classification arises from natural assumptions and will compare both the classification and those assumptions with those from other proposals you can find in the literature.