Michael Schlosser (University of Vienna) - Thursday, Sept 11 , 2025 - 4:00 PM (IST)

 Dear all,

Welcome back from the summer break. We hope you had an exciting summer, filled with new theorems and fresh collaborations.

The first talk of the season is by Michael Schlosser on Sept 11. The announcement is below.

Talk Announcement: 

Title: Asymptotic formulas for the Fourier coefficients
of infinite $q$-products

Speaker: Michael Schlosser (University of Vienna)

When: Sept 11, 2025, 4:00 PM- 5:00 PM IST (12:30 PM CEST)

Where: Zoom: (Write to the organisers for a link)

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

Abstract:

We derive asymptotic expansions for weighted partition
numbers satisfying certain conditions. As applications we
partially settle some conjectures by Berkovic and Garvan,
and by Seo and Yee, on the nonnegativity of the coefficients
of certain infinite products, and a conjecture by Chan and
Yesilyurt on the periodicity of the signs of the coefficients of
a non-theta product. This is joint work with Nian Hong Zhou.

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: 

Title: 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

Live Link: https://youtube.com/live/VO3hTqh8TSw?feature=share

Abstract 

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.).

Michael Schlosser (University of Vienna) - October 22, 2020 - 3:55 PM-5:00 PM (IST)

The next talk in the seminar is by Michael Schlosser.  This talk is a longer version of a talk he presented recently in an AMS regional meeting. Please note that this time the talk will be on Zoom. 

Talk announcement

Title: Basic hypergeometric proofs of two quadruple equidistributions of Euler-Stirling statistics on ascent sequences

Speaker: Michael Schlosser (University of Vienna, Austria).

When: Thursday October 22, 3:55 PM-5:00 PM

Where: ZOOM this time. Please write to sfandnt@gmail.com to get the link to the talk. It is best to write a day in advance.  (The link will be open at 3:30 PM for the organizers to test their systems)

Tea or Coffee: Please bring your own.

Abstract: 

In my talk, I will present new applications of basic hypergeometric series to specific problems in enumerative combinatorics. The combinatorial problems we are interested in concern multiply refined equidistributions on ascent sequences. (I will gently explain these notions in my talk!) Using bijections we are able to suitably decompose some quadruple distributions we are interested in and obtain functional equations and ultimately generating functions from them, in the form of explicit basic hypergeometric series. The problem of proving equidistributions then reduces to applying suitable transformations of basic hypergeometric series. The situation in our case however is tricky (caused by the fact how the power series variable $r$ appears in the base $q=1-r$ of the respective basic hypergeometric series; so being interested in the generating function in $r$ as a Maclaurin series, we are thus interested in the analytic expansion of the nonterminating basic hypergeometric series in base $q$ around the point $q=1$), as none of the known transformations appear to directly work to settle our problems; we require the derivation of new identities. Specifically, we use the classical Sears transformation and apply some analytic tools to establish a new non terminating ${}_4\phi_3$ transformation formula of base $q$, valid as an identity in a neighborhood around $q=1$. We use special cases of this formula to deduce two different quadruple equidistribution results involving Euler--Stirling statistics on ascent sequences.  One of them concerns a symmetric equidistribution, the other confirms a bi symmetric equidistribution that was recently conjectured in a paper (published in JCTA) by Shishuo Fu, Emma Yu Jin, Zhicong Lin, Sherry H.F. Yan, and Robin D.B. Zhou. 

This is joint work with Emma Yu Jin. For full results (and further ones), see https://arxiv.org/abs/2010.01435