Seminar
Speaker
Aradhita Chattopadhyaya (Dublin Institute for Advanced Studies)
Date & Time
Wed, 08 February 2023, 15:00 to 16:30
Venue
Madhava Lecture Hall and Online
Abstract

We analyze the coefficients of partition functions of  Vafa-Witten theory for the complex projective plane  ℂℙ2. We experimentally study the growth of the coefficients for  gauge group SU(2) and SU(3), which are examples of mock modular  forms of depth 1 and 2 respectively. We also introduce the notion of ``mock cusp  form'', and study an example of weight 3 related to the SU(3) partition function.  Numerical experiments on the first 200 coefficients suggest that the  coefficients of a mock modular form of weight k grow as the  coefficients of a modular form of weight k, that is to say as nk−1. On the other hand the coefficients of the mock cusp form  appear to grow as n3/2, which exceeds the growth of classical  cusp forms of weight 3. We  provide bounds using saddle point analysis, which however largely exceed the  experimental observation.

Zoom link: https://icts-res-in.zoom.us/j/88092766911?pwd=R3ZrVk9yeW96ZmQ4ZG9KRzVhenRKZz09

Meeting ID: 880 9276 6911

Passcode: 232322