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.


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

Fall 2021

Spring 2021

Fall 2020

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018