# Jenya Sapir (Binghamton University)

Date

Friday November 12, 20212:30 pm - 3:30 pm

Location

Online (via Zoom)## Math & Stats Department Colloquium

**Friday, November 12th, 2021**

**Time:** 2:30 p.m. **Place:** Online (via Zoom)

**Speaker:** Jenya Sapir (Binghamton University)

**Title:** A projection from geodesic currents to Teichmuller space

**Abstract:** Given a genus $g$ surface $S$, we consider the space of projective geodesic currents $\mathbb{P}\mathcal{C}(S)$. This space contains many objects of interest in low dimensional topology, such as the set of all closed curves on S up to homotopy, the set of all marked, negatively curved metrics on $S$, as well as some higher Teichmuller spaces. We show that there is a mapping class group invariant, length minimizing projection from the space of filling projective currents onto Teichmuller space, and that this projection is continuous and proper. This is joint work with Sebastian Hensel.

**Jenya Sapir** is an Assistant Professor at Binghamton University. She got her Ph.D. in Mathematics from Stanford University in 2014, under Maryam Mirzakhani. She was a postdoc at the Max Planck Institute for Mathematics at Bonn, and at the University of Illinois at Urbana-Champaign. Her research areas are low dimensional topology and geometric group theory.