Graduate Student Seminar - Mohabat Tarkeshian (Math)

Title: Jacobians of graphs and starfish 

Speaker: Mohabat Tarkeshian

Abstract: Graphs can be viewed as discrete analogues of various mathematical structures, such as algebraic curves and Riemann surfaces. A finite graph has an associated finite abelian group called the Jacobian group, denoted Jac(G) (also called the critical, sandpile, or Picard group). We will discuss these groups and a special type of k-regular graph called a starfish graph. A starfish is similar to a hyperelliptic curve since each can be viewed as a (ramified) double-cover of a simply connected object. It is a graph S exhibited as a double-cover S→T of a tree T with ramification locus equal to the leaves of T. We will discuss how varying the starfish can give rise to natural questions such as how often S is Ramanujan and how S→T can be viewed as a harmonic morphism of graphs. We will also briefly examine induced maps on Jacobians and their connection to harmonic morphisms. 

As always, great food, coffee and drinks will be provided!

We hope to see you all this Friday! We encourage your participation in the seminar to provide continuity to this project. 

You can visit the Grad Seminar website at https://uwomathgrad.github.io/editions/winter2020/.