Ankush Goswami (IIT, Gandhinagar) - May 27, 2021 - 3:55 -5:00 PM (IST)

 

The next speaker in our series is Ankush Goswami of IIT, Gandhinagar. Until recently, Ankush was a post-doc in Linz (Austria).

Talk Announcement:

Title: Partial theta series with periodic coefficients and quantum modular forms

Speaker: Ankush Goswami (IIT, Gandhinagar)

 

When: May 27, 2021 - 3:55 PM - 5:00 PM (IST)

Where: Zoom (the link will be sent by email to our list)

 

Live link: https://youtu.be/W5av3JiovnI

Tea or Coffee: Please bring your own.

Abstract: Theta  series first appeared in Euler’s work on partitions, but was systematically studied later by Jacobi.  In his Lost Notebook, Ramanujan wrote down many identities (without proof) involving the so-called partial theta series. Unlike the theta series which are modular forms, the theory of partial theta series is not well understood. In this talk, I will consider a family of partial theta series and show their “quantum modular” behaviour. This is based on my recent joint work with Robert Osburn (UCD).

The talk should be accessible to graduate and advanced undergraduate students.

Siddhi Pathak - May 13, 2021 - 3:55 -5:00 PM (IST)

The next speaker in our series is Siddhi Pathak, S. Chowla Research Assistant Professor, Penn State University. The talk announcement is below.

Talk Announcement:

Title: Special values of L-functions

Speaker: Siddhi Pathak (Penn State)

 

When: May 13, 2021 - 3:55 PM - 5:00 PM (IST)

Where: Zoom (the link will be sent by email to our list)

 

Live link: https://youtu.be/SXl9IPgE2aI

Tea or Coffee: Please bring your own.

Abstract: In 1730s, Euler resolved the famous Basel problem by evaluating values of the Riemann zeta-function at even positive integers as rational multiples of powers of pi. Thus, we recognize that the values \zeta(2k) are transcendental and algebraically dependent. The situation is drastically different for odd zeta-values, that are not only expected to be transcendental, but also algebraically independent. Although we are far from proving this, there has been striking progress in the work of Apery, and more recently by Ball-Rivoal, Zudilin and others. In this talk, we discuss the analogous problem for Dirichlet L-functions, more generally, Dirichlet series with periodic coefficients.

This talk will be accessible to graduate students.