# Fall 2022 Colliquia

### October 7, 2022

#### Moon Duchin, Professor of Mathematics, Tufts University

**Tales from the Courtroom**

**Time:** 4:00 pm **Location:** JCC 280 **Reception:** JCC 501 5:00 pm **Abstract: **I spent several years preparing a mathematical framework for fairer redistricting. Then I tried it in court in seven states! This is an informal talk where I'll tell you how it went (so far) to try to deploy this civil rights math project in the real world.

### November 18, 2022

#### Melanie Matchett Wood, Professor of Mathematics, Harvard University

**Finite Quotients of 3-Manifold Groups**

**Time:** 4:00 pm **Location:** JCC 270 **Reception:** JCC 501 5:00 pm **Abstract:** It is well-known that for any finite group G, there exists a closed 3-manifold M with G as a quotient of the fundamental group of M. However, we can ask more detailed questions about the possible finite quotients of 3-manifold groups, e.g. for G and H_1,...,H_n finite groups, does there exist a 3 manifold group with G as a quotient but no H_i as a quotient? We answer all such questions. To prove non-existence, we prove new parity properties of the fundamental groups of 3-manifolds. To prove existence of 3-manifolds with certain finite quotients but not others, we use a probabilistic method, by first proving a formula for the distribution of the fundamental group of a random 3-manifold, in the sense of Dunfield-Thurston. This is joint work with Will Sawin.