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Abstracts for Special colloquium for Don Zagier

Alternatively have a look at the program.

Modular forms and optimization in the Euclidean space

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Speaker: 
Maryna Viazovska
Zugehörigkeit: 
EPFL Lausanne
Datum: 
Mit, 2019-06-26 13:45 - 14:45
Location: 
MPIM Lecture Hall

Arithmetic support and monodromy

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Speaker: 
Maxim Kontsevich
Zugehörigkeit: 
IHES
Datum: 
Mit, 2019-06-26 15:00 - 16:00
Location: 
MPIM Lecture Hall

In my talk on Arbeitstagung 2017 I introduced a strange series with rational coefficients related to p-curvatures of certain family of algebraic linear differential equations (Heun equations). This series has zero radius of convergence p-adically for any prime p, which seems to be a new phenomenon, and it is extremely hard to calculate (e.g. using first 40000 primes one can get only first 250 coefficients of the series).

Single-valued integration

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Speaker: 
Francis Brown
Zugehörigkeit: 
All Souls College, Oxford
Datum: 
Mit, 2019-06-26 17:00 - 18:00
Location: 
MPIM Lecture Hall

This talk was originally inspired by Zagier's construction of single-valued polylogarithms and regulators in the late 80's. 

In short, single-valued functions are ubiquitous in mathematics and physics, since well-defined problems have well-defined answers. On the other hand, the solution to such a problem is often given by an integral, which is usually a multi-valued function of its parameters.  The reason is that integration is a pairing between differential forms and chains of integration, and the latter are ambiguously defined.

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