Sunday, May 21, 2023

Michael Schlosser (Vienna, Austria) - Thursday May 25, 2023 - 4:00 PM (IST)

 Dear all,

The next talk is by Michael Schlosser of the University of Vienna, Austria. 

After this talk we will be taking a break for the summer. Hopefully, we will get an opportunity to meet in person during this time. 

Talk Announcement: 

Bilateral identities of the Rogers-Ramanujan type

Speaker: Michael Schlosser (University of Vienna, Austria)
When: May 25, 2023, 4:00 PM- 5:00 PM IST (12:30 PM CEST)
Where: Zoom. Please write to the organisers for a link

The first and second Rogers-Ramanujan (RR) identities have a prominent history. They were originally discovered and proved in 1894 by Leonard J. Rogers, and then independently rediscovered by the legendary self-taught Indian mathematician Srinivasa Ramanujan some time before 1913. They were also independently discovered and proved in 1917 by Issai Schur. About the RR identities Hardy remarked

`It would be difficult to find more beautiful formulae than the
``Rogers-Ramanujan'' identities, ...'

Apart from their intrinsic beauty, the RR identities have served as a stimulus for tremendous research around the world. The RR and related identities have found interpretations in
various areas including combinatorics, number theory, probability theory, statistical mechanics, representations of Lie algebras, vertex algebras, knot theory and conformal field theory.

In this talk, a number of bilateral identities of the RR type will be presented. We explain how these identities can be derived by analytic means using identities for bilateral basic hypergeometric series. Our results include bilateral extensions of the RR and
of the Göllnitz-Gordon identities, and of related identities 
by Ramanujan, Jackson, and Slater.

Corresponding results for multiseries are given as well, including multilateral extensions of the Andrews-Gordon identities, of Bressoud's even modulus identities, and others.

This talk is based on the speaker's preprint arXiv:1806.011153v2 (which has been accepted for publication in Trans. Amer. Math. Soc.).

Sunday, May 7, 2023

Bishal Deb (University College, London) - Thursday May 11, 2023 - 4:00 PM (IST)

 Dear all,

The next talk is by Bishal Deb of University College, London. Here is the announcement. 

Talk Announcement: 

The "quadratic family" of continued fractions and combinatorial sequences

Speaker: Bishal Deb (University College, London)
When: May 11, 2023, 4:00 PM- 5:00 PM IST (11:30 AM BST)
Where: Zoom:

We will begin this talk by introducing some combinatorial sequences whose Stieltjes-type continued fraction coefficients increase linearly. We briefly mention the work of Sokal and Zeng where they systematically studied multivariate generalisations of these continued fractions for factorials, Bell numbers and double factorials. 

Next, we will define the Genocchi and median Genocchi numbers and  introduce D-permutations, a class of permutations which enumerate these numbers. We mention some multivariate continued fractions counting various statistics on D-permutations.

Finally, we move to the secant numbers and introduce cycle-alternating permutations; these are another class of permutations  which enumerate the secant numbers. We mention some multivariate continued fractions counting various statistics on cycle-alternating permutations. We then describe the entries in the Jacobi-Rogers matrix of our continued fraction using alternating Laguerre digraphs, which are a class of directed graphs. If time permits, we will briefly state some remarks on the Jacobian elliptic functions.

This talk will be based on joint work with Alan Sokal.