TOMORROW - Special Lecture: Modular forms and differential equations - Don B. Zagier

[ICTP Math Section]

> *_Special Lecture: Modular forms and differential equations_*
>
> *Don B. Zagier (MPI, Bonn - ICTP-IGAP)*
>
> Tuesday, 17 March at 16:30 -  Leonardo Building, Budinich Lecture Hall 
> (in-person) - https://indico.ictp.it/event/11309/
>
> *
> *
>
> *Abstract:*
>
> In the theory of special functions, the central question is usually 
> whether they satisfy any kind of differential equation, like Bessel or 
> Legendre functions. Strangely enough, modular forms, which are 
> ubiquitous both in pure mathematics and in mathematical physics, do 
> satisfy differential equations, and even of several different kinds, 
> but these facts are not widely known and used.
>
> I will give a very brief introduction to modular forms, followed by a 
> survey of the three principal kinds of dfferential equations, each of 
> which is important in several parts of mathematics and mathematical 
> physics:
>
> (i) Non-linear differential equations of Painleve type, the 
> proto-example being the so-called Chazy equation.  These are relevant 
> in the theory of integrable systems, which also has many applications 
> in the study of moduli spaces and in string theory.
>
> ii) Linear equations of Picard-Fuchs type. These have applications 
> both in number theory (e.g. in Apery's proof of the irrationality of 
> zeta(3)) and in the study of Calabi-Yau manifolds, again important in 
> string theory.
>
> iii) Finally, the so-called modular linear differential equations that 
> are now playing an increasing role in conformal field theory and the 
> study of VOAs.
>
> *This lecture is part of the KMPB-Ukraine Workshop programme (in 
> Berlin): https://indico.desy.de/event/52099/*
>
> All are welcome to join.
>
-- Micol Stock Secretariat of the ICTP Math Section Abdus Salam 
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