## Thursday, March 18, 2021

### Christian Krattenthaler (University of Vienna) March 18, 2021 - 3:55 PM-5:00 PM (IST)

The next talk is by Christian Krattenthaler. I hope this time the live broadcast works. Here is the announcement.

Talk announcement

Title: Determinant identities for moments of orthogonal polynomials

Speaker: Christian Krattenthaler (University of Vienna, Austria)

When: March 18, 2021 - 3:55 PM - 5:00 PM (IST)

Abstract: We present a formula that expresses the Hankel determinants of a linear combination of length d+1 of moments of orthogonal polynomials in terms of a d x d determinant of the orthogonal polynomials. As a literature search revealed, this formula exists somehow hidden in the folklore of the theory of orthogonal polynomials as it is related to "Christoffel's theorem". In any case, it deserves to be better known and be presented correctly and with full proof. (During the talk I will explain the meaning of these somewhat cryptic formulations.) Subsequently, I will show an application of the formula. I will close the talk by presenting a generalisation that is inspired by Uvarov's formula for the orthogonal polynomials of rationally related densities.

## Thursday, March 11, 2021

### Announcement: Atul Dixit (IIT, Gandhinagar) awarded the 2021 Gabor Szego award by OPSF SIAM

Dear all,

We are happy to report that Atul Dixit, one of the co-organizers of this seminar, has been awarded the 2021 Gábor Szegö Prize. This prize is awarded every two years by the SIAM Activity Group on Orthogonal Polynomials and Special Functions (SIAG/OPSF). It is awarded to an early-career researcher for outstanding research contributions within 10 years of obtaining a Ph.D.

The selection committee for the 2021 award consists of Peter Clarkson (Chair), University of Kent; Kerstin Jordaan, University of South Africa; Adri Olde Daalhuis, The University of Edinburgh; Sarah Post, University of Hawaii; and Yuan Xu, University of Oregon.

The selection committee in its letter to him cited his “impressive scientific work solving problems related to number theory using special functions, in particular related to the work of Ramanujan.”

Atul obtained his Ph.D. under the direction of Bruce Berndt in 2012 from the University of Illinois at Urbana-Champaign. Subsequently he did a post-doc at Tulane with Victor Moll as his mentor. Currently, he is in IIT, Gandhinagar and has quickly developed a reputation among young and upcoming mathematicians in this country that has attracted a bright set of Ph.D. students and post-docs to his team.

We wish Atul continued success, both personally and for the group he is leading.

Gaurav Bhatnagar and Krishnan Rajkumar (co-organizers with Atul of this seminar).

1. Atul's talk in this seminar earlier.

## Thursday, March 4, 2021

### Liuquan Wang (Wuhan University) March 4, 2021 - 3:55 PM (IST)

The next talk is by Liuquan Wang of Wuhan University.

Talk announcement

Title: Parity of coefficients of mock theta functions

Speaker: Liuquan Wang (Wuhan University, PRC)

When: March 4, 2021 - 3:55 PM - 5:00 PM (IST)

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

Abstract: We study the parity of coefficients of classical mock theta functions. Suppose $g$ is a formal power series with integer coefficients, and let $c(g;n)$ be the coefficient of $q^n$ in its series expansion. We say that $g$ is of parity type $(a,1-a)$ if $c(g;n)$ takes even values with probability $a$ for $n\geq 0$. We show that among the 44 classical mock theta functions, 21 of them are of parity type $(1,0)$. We further conjecture that 19 mock theta functions are of parity type $(\frac{1}{2},\frac{1}{2})$ and 4 functions are of parity type $(\frac{3}{4},\frac{1}{4})$. We also give characterizations of $n$ such that $c(g;n)$ is odd for the mock theta functions of parity type $(1,0)$.