## EVENT DETAILS AND ABSTRACT

**Graduate Student Seminar**
**Title:** Inequalities for Riemannian surfaces

**Speaker:** Grigory Papayanov

**Speaker Info:**

**Brief Description:**

**Special Note**:

**Abstract:**

If f: X -> Y is a holomorphic map between two compact hyperbolic Riemannian surfaces, then degree of f is less or equal than (g(X)-1)/(g(Y)-1).
This is very easy to prove using either Schwarz lemma or Riemann-Hurwitz formula. What if f is not holomorphic, but only continious? Then the
formula (called Kneser's inequality) still holds, but it becomes harder to prove it by conventional topological tools. I want to tell how to
prove this inequality by putting an L^1-norm on the space of singular chains of a surface. If time permits, I will tell how to use these methods
to prove Milnor-Wood inequality: if a vector bundle over a surface $X$ admits a flat connection, then its Euler number is less or equal than g(X)-1.

**Date:** Friday, February 15, 2019

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Yajit Jain

**Contact email:** ykjain@math.northwestern.edu

**Contact Phone:** 847-467-6255

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