Alok Shukla (Ahmedabad University)

The next talk is by Alok Shukla of Ahmedabad University. Alok has recently moved from the University of Manitoba and we welcome him back to India and this group 

Please note that we are now back into our usual time, one hour later than our previous talk. The talk is from 3:55 pm. 

The details are as follows.

Speaker: Alok Shukla (Ahmedabad University). 

Title: Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities

When: Thursday, July 30, 3:55 PM - 5:00 PM IST (GMT + 5:30)

Where: Zoom. Please write to sfandnt@gmail.com to get a link a few hours ahead of time.  

Tea or Coffee: Please bring your own.

Abstract: 

The Jacobi triple product identity and Rogers-Ramanujan identities are among the most famous $q$-series identities. We will present elementary combinatorial "tiling proofs" of these results. The talk should be accessible to a general mathematical audience.

Ali Uncu (RICAM, Austrian Academy of Sciences, Linz, Austria)

The next talk in the Topics in Special Functions and Number Theory seminar is by Ali Uncu.  This talk will again be on zoom. In case you wish to try out the software before the talk, please get in touch with one of the organizers. Further, requests for links should be made well before time. Some people did not get the link in time. In case you wish to be placed in the mailing list, please send an email to sfandnt@gmail.com.


Title: The Mathematica package qFunctions for q-series and partition theory applications


UPDATE: Please visit https://akuncu.com/qfunctions/ for a version of this talk (video) and materials mentioned in the talk. 

Speaker: Ali Uncu, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria

When: Thursday, July 16, 2020, 2:55 PM - 4:00 PM IST  (GMT+5:30)


Where: On zoom (link available on request).  Please write to sfandnt@gmail.com for the link a few hours before the talk. 


Tea or Coffee: Please bring your own. 


Abstract


In this talk, I will demonstrate the new Mathematica package qFunctions while providing relevant mathematical context. This implementation has symbolic tools to automate some tedious and error-prone calculations and it also includes some other functionality for experimentation. We plan to highlight the four main tool-sets included in the qFunctions package:

(1) The q-difference equation (or recurrence) guesser and some formal manipulation tools,
(2) the treatment of the method of weighted words and automatically finding and uncoupling recurrences,

(3) a method on the cylindrical partitions to establish sum-product identities,
(4) fitting polynomials with suggested well-known objects to guess closed formulas.

This talk is based on joint work with Jakob Ablinger (RISC).

Hjalmar Rosengren (Chalmers University of Technology and University of Gothenburg)

The next talk in the Topics in Special Functions and Number Theory seminar is by Hjalmar Rosengren on the Kanade-Russel identities. Please note that the talk will be one hour earlier than usual.

This talk will again be on zoom. In case you wish to try out the software before the talk, please get in touch with one of the organizers. 


Title: On the Kanade-Russell identities

Speaker: Hjalmar Rosengren, Chalmers University of Technology and University of Gothenburg, Sweden 

When: Thursday, July 2, 2020: 2:55-4:00 pm

Where: On Zoom: Link (available on request). Please send email to sfandnt@gmail.com a few hours before the talk. 

Tea or Coffee: Please bring your own. 

Kanade and Russell conjectured several Rogers-Ramanujan-type identities for triple series. Some of these conjectures are related to characters of affine Lie algebras, and they can all be interpreted combinatorially in terms of partitions. Many of these conjectures were settled by Bringmann, Jennings-Shaffer and Mahlburg. We describe a new approach to the Kanade-Russell identities, which leads to new proofs of five previously known identities, as well as four identities that were still open. For the new cases, we need quadratic transformations for q-orthogonal polynomials.