Colloquium: Algebraic geometry, analysis and combinatorics in the study of periodic graph operators

Abstract: In this talk, we will  discuss the crucial role that the algebraic properties of complex Bloch and Fermi varieties play in the study of periodic graph operators. I will begin with an introduction to the basics of periodic graph operators, followed by a discussion of recent discoveries, particularly focusing on the irreducibility of Bloch and Fermi varieties. Next, I will demonstrate how these algebraic properties, combined with techniques from analysis and combinatorics, can be applied to address spectral and inverse spectral problems arising from periodic operators.

Host: Xiang Tang

Reception to follow at Cupples I, Room 200 (Lounge) from 2:00 - 3:00 pm.