Monday, September 27, 2021

Jaban Meher (NISER, Bhubaneswar) - Thursday Sept 30, 2021; 3:55-5:00 PM

Dear all,

The next talk is by Jaban Meher of NISER, Bhubaneswar. The announcement is as follows.

Talk Announcement:

Title: Modular forms and certain congruences

Speaker: Jaban Meher (NISER, Bhubaneswar)

When: Thursday, September 30, 2021 - 4:00 PM - 5:00 PM (IST)

Where: Zoom: (Please write to sfandnt@gmail.com for the link)

Live Link: https://youtu.be/vYs5YGuS_L4

Tea or Coffee: Please bring your own.

Abstract:

In this talk we shall discuss about modular forms and certain types of congruences among the Fourier coefficients of modular forms. We shall also discuss about the non-existence of Ramanujan-type congruences for certain modular forms.

Gaurav Bhatnagar (Ashoka), Atul Dixit (IIT, Gandhinagar) and Krishnan Rajkumar (JNU)

sfandnt@gmail.com

Thursday, September 16, 2021

Neelam Saikia (University of Virginia), Thursday, September, 16, 2021 - 3:55 PM (IST)

Dear all,

The next talk is by Neelam Saikia who is currently a post-doc with Ken Ono at the University of Virginia.

Talk Announcement:

Title: Frobenius trace distributions for Gaussian hypergeometric functions

Speaker: Neelam Saikia (University of Virginia)

When: Thursday, September 16, 2021 - 4:00 PM - 5:00 PM (IST)

Where: Zoom: Please write to sfandnt@gmail.com for a link.

Live Link: https://youtu.be/o7qNW8BhgJI

Tea or Coffee: Please bring your own.

Abstract:

In the 1980's, Greene defined hypergeometric functions over finite fields using Jacobi sums. These functions possess many properties that are analogous to those of the classical hypergeometric series studied by Gauss, Kummer and others. These functions have played important roles in the study of supercongruences, the Eichler-Selberg trace formula, and zeta-functions of arithmetic varieties. We study the distribution (over large finite fields) of the values of certain families of these functions. For the $_2F_1$ functions, the limiting distribution is semicircular, whereas the distribution for the $_3F_2$ functions is the more exotic \it{Batman distribution.}

Gaurav Bhatnagar (Ashoka), Atul Dixit (IIT, Gandhinagar) and Krishnan Rajkumar (JNU)

sfandnt@gmail.com