Amanda Folsom (Amherst College)- Mock modular and quantum modular forms                                                                                                                                                                                                                                                                                                                                                                  Abstract

Modular forms, functions which possess a type of symmetry on the upper half of the complex plane, have played central and far-reaching roles in number theory and mathematics over the last two centuries. What can be gained by perturbing modular symmetries? We will discuss this theme from past to present, in the context of mock modular forms and quantum modular forms, both of which are younger descendents of modular forms. Some topics of current of interest in this direction have their roots in the first half of the 20th century dating back to Ramanujan and Gauss, while some fascinating and surprising answers come from just the last 15 years. In this talk, we will give an accessible introduction to these intertwined topics and some of their recent applications.                                                                                                                                                                                                                                                                                                                                                                                                                                            Zoom Link: https://ccny.zoom.us/j/92057419965                                                                                                                                                                    Zoom ID: 92057419965