Time: Friday, April 5, 2019
Time: 3:30 – 4:30 (coffee & refreshments starting at 3:00)
Place: HP 4351 (Macphail Room), School of Mathematics & Statistics, Carleton University
Speaker: Sarah Harrison (McGill University)
Title: Quantum Modularity in Topology in Physics


I will discuss a set of inter-related phenomena in topology, physics, and number theory. A natural question in topology is the construction of homological invariants of 3-manifolds. These turn out to be related to certain special 3-dimensional quantum field theories in physics. Both of these scenarios exhibit a fascinating number theoretic phenomenon: quantum modularity. Quantum modular forms, introduced by Zagier, are functions defined only at rational numbers, and in the most general cases are neither analytic nor modular. It is still an open question to develop a general theory which encompasses their behavior. I will overview these relations and discuss recent advances which may shed light on some of these questions.