MATH Seminar: “Lines generate the Picard group of a Fermat surface,” Alex Degtyarev, SA-141, 1:40PM November 25 (EN)

Dear Colleagues and Students,

You are cordially invited to the Topology Seminar organized by the Department of Mathematics.

Speaker: Alex Degtyarev (Bilkent)

“Lines generate the Picard group of a Fermat surface”

Abstract: I will explain a purely topological solution of a long standing algebra-geometric problem, viz. the so-called Shioda conjecture. After a brief introduction to the subject, I will state the problem and reduce it to the computation of the fundamental group (or, rather, properly understood Alexander module) of a certain arrangement of lines in the plane. Then, in the bulk of the talk, I will try to explain this computation in detail: We will discuss the braid monodromy, Zariski–van Kampen theorem (with its pros and contras) computing the fundamental group of a plane curve, and, essentially, Fox’ free calculus explained via cellular complexes.

The talk will largely be accessible to graduate and senior undergraduate students. At the end of the talk I am planning to discuss the generalizations to the so-called Delsarte surfaces and state a few open problems that may constitute a master or Ph.D. project.

Date: Monday, November 25, 2019
Time: 13:40
Place: Mathematics Seminar Room, SA – 141