# Michael Zhao Memorial Student Colloquium (Spring 2022)

Each week, the Michael Zhao Memorial Student Colloquium holds 45-minute talks by Columbia mathematics faculty about their own research. The talks are intended for current PhD students in mathematics at Columbia. If you are an undergraduate student or external graduate student and would like to come, please email kyc2130@columbia.edu or qy2266@columbia.edu.

- When: Tuesday 6:00 - 7:00 PM ET
- Where: Mathematics Building, Room 507 (when it's not on Zoom)
- Organizers: Kevin Chang, Vivian Yu

## Schedule

- 01/18
- Will Sawin (Zoom talk)
**Finite quotients of 3-manifold groups**
- Let G and H be two finite groups. Does there exist a
3-manifold whose fundamental group admits G as a quotient but not H?
We prove a theorem that determines the answers to questions of this
type. The proof relies on a probabilistic argument - we estimate the
probability that a random 3-manifold (according to a distribution
defined by Dunfield and Thurston) has a fundamental group with certain
quotients but not others. Our methods grew out of work in number
theory on the class groups of random number fields. This talk will
discuss the work in topology and its connections to number theory.
This is joint work with Melanie Wood.

### Past Seminars