ICTP Mathematics Seminar on Monday 18 February

[math]

M A T H E M A T I C S   S E M I N A R S   2013


Monday, 18 February, at 15.00 hrs.


Dr. Anton Mellit
(ICTP)

Title: Multiplication laws for differential equations


Abstract:

With V. Golyshev.

This talk is an example of how some cases of Langlands'
correspondence for function fields can be interpreted very classically
and explicitly. Whenever we have an explicit description of Hecke
operators in the Langlands setup, we obtain some elementary identities 
between special functions. In particular, we see how formulas of 
Clausen's type and multiplication identities for Bessel functions arise 
this way.

As an application to arithmetic, our method gives a direct
correspondence between solutions of the Dwork's accessory parameter 
problem as studied by Beukers, and automorphic forms over P^1 with four 
marked points as described by Kontsevich.

VENUE: Luigi Stasi Seminar Room, first floor , ICTP Leonardo Building