[Club2] Invitation: From Kronecker's double series to context-free languages @ Mon Oct 15, 2018 14:00 - 15:00 (CEST) (club2 at mailbroy.informatik.tu-muenchen.de)

[julianbrunner at gmail.com]

You have been invited to the following event.

Title: From Kronecker's double series to context-free languages

Speaker: José Manuel Rodriguez Caballero
Abstract: In his 1881 memoir "Zur theorie der elliptischen Functionen"  
(Werke IV, pp 309-318), L. Kronecker determined the power series expansion  
of a quotient of theta functions which was previously used by C. G. J.  
Jacobi in mechanics. This identity, after a substitution due to C. Jordan,  
provides a generating function for topological invariants of a sequence of  
moduli spaces known as the Hilbert scheme of n points on the torus, where n  
= 1, 2, 3, etc. (T. Hausel, E. Letellier, F. Rodriguez-Villegas). These  
topological invariants can be interpreted in the setting of combinatorics  
over finite fields (C. Kassel and C. Reutenauer). The aim of this talk is  
to present a language-theoretic interpretation of Kronecker’s double series  
(after Jordan’s substitution) and to use this interpretation in order to  
derive new elementary number theoretic results. Prof. Hartmut F. W. Hoft  
developed a similar approach, called the symmetric representation of sigma  
(the sum of divisors), in order to prove some conjectures from the OEIS. A  
development of this theory in Isabelle/HOL will be presented.

References:
Hoft's approach: https://oeis.org/A241561/a241561.pdf
Caballero's approach:
https://link.springer.com/chapter/10.1007%2F978-3-319-66396-8_23
Repository:
https://github.com/josephcmac/Folklore-and-miscellaneous-results-in-number-theory
When: Mon Oct 15, 2018 14:00 – 15:00 Central European Time - Berlin
Where: MI 00.11.038 (John von Neumann)
Calendar: club2 at mailbroy.informatik.tu-muenchen.de
Who:
     * Julian Brunner - creator
     * club2 at mailbroy.informatik.tu-muenchen.de

Event details:  
https://www.google.com/calendar/event?action=VIEW&eid=MHUyN3Y2NGk2NmZxdHU5cHZxMzRnNHVyZ2wgY2x1YjJAbWFpbGJyb3kuaW5mb3JtYXRpay50dS1tdWVuY2hlbi5kZQ&tok=NTIjc2U2ZWJlM3RvZmY0Y2g1bm11bmlibTVtOThAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbTJhYWVkYzJkOGEwOTc5YTQ5MTg1NDBhNjgyYmU1NTk5Yzg3M2EyYzU&ctz=Europe%2FBerlin&hl=en&es=0

Invitation from Google Calendar: https://www.google.com/calendar/

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