Pedro Ribeiro (Porto, Portugal) - Thursday, Feb 22, 2024 - 4:00 PM (IST)

 Dear all,

This week's talk is by Pedro Ribeiro of the University of Porto, Portugal. We apologize for the late notification. The talk announcement follows. 

Talk Announcement: 

Title:  Generalizations (in the spirit of Koshliakov) of some formulas from Ramanujan's Lost Notebook

Speaker:  Pedro Ribeiro (University of Porto, Portugal) 
When: Feb 22, 2024, 4:00 PM- 5:00 PM IST (10:30 am Western European Time (WET)) 

Where: Zoom:

Live Link: https://youtube.com/live/yq4SVSlTD2o?feature=share

Abstract

In his lost notebook, Ramanujan recorded beautiful identities. These include earlier versions of Guinand's formula for the divisor function and the transformation formula for the logarithm of Dedekind's -function. 

In our presentation we will describe some generalizations of these formulas using a beautiful theory due to the forgotten mathematician N. S. Koshliakov. Our work will be presented under the point of view initiated by A. Dixit and R. Gupta, the first mathematicians of our century who have extended Koshliakov's theory in several directions. 

This talk is based on joint work with Semyon Yakubovich. 

Arvind Ayyer (IISc.) - Thursday, Feb 8, 2024 - 4:30 PM (IST)

 Dear all,

The next talk is by Arvind Ayyer of the Indian Institute of Science, Bangalore, India. The talk announcement follows. Please note that the talk is half an hour later than our usual meeting time. 

Talk Announcement: 

Title: A new combinatorial formula for the modified Macdonald polynomials

Speaker:  Arvind Ayyer (IISc, Bangalore, India)
When: Feb 8, 2024, 4:30 PM- 5:30 PM IST (Note special time) 

Where: Zoom: Please write to the organisers for the link

Live Link: https://youtube.com/live/udOYGrz0zaI?feature=share

Abstract

Macdonald polynomials are a remarkable family of symmetric
functions that are known to have connections to combinatorics, algebraic
geometry and representation theory. The modified Macdonald polynomials 
are obtained from the Macdonald polynomials using an operation called 
plethysm. A combinatorial formula for the latter was given by Haglund, 
Haiman and Loehr in a celebrated work (JAMS, 2004). We will give a new 
combinatorial formula (ALCO 2023).

Recently, a formula for the symmetric Macdonald polynomials was given by 
Corteel, Mandelshtam and Williams in terms of objects called multiline 
queues, which also compute probabilities of a statistical mechanics 
model called the multispecies ASEP on a ring. It is natural to ask 
whether the modified Macdonald polynomials can be obtained using a 
combinatorial gadget for some other statistical mechanics model. We 
answer this question in the affirmative via a multispecies totally 
asymmetric zero-range process (TAZRP) in (arXiv:2209.09859).

These are joint works with J. Martin and O. Mandelshtam.