q-series and quantum modular forms

Seminar: 
Junior Colloquium
Event time: 
Friday, April 4, 2014 - 8:30am to 10:00am
Location: 
LOM 205
Speaker: 
Amanda Folsom (pre-talk: Susie Kimport)
Speaker affiliation: 
Yale University
Event description: 

The subject of weak Maass forms, certain nonholomorphic modular forms, has seen numerous advances over the last 9 years. Namely, these forms have played key roles in many areas of mathematics, including modular forms and number theory, combinatorics, arithmetic geometry, and mathematical physics. While relatively new, the subject has deep rooted origins dating back to Hardy and Ramanujan, whose original mock theta functions turn out to be related. In this talk we will discuss a recent application to the new theory of Quantum Modular Forms, initiated by Zagier in 2010. We revisit Ramanujan’s last letter to Hardy; we construct infinite families of quantum modular forms, and prove one of Ramanujan’s remaining claims. We will show how quantum modular forms underlie new relationships between combinatorial mock modular and modular forms. This is joint work with Ken Ono (Emory U.) and Rob Rhoades (Stanford U./CCR-Princeton).

Special note: 
Graduate Students only, please