Alternatively have a look at the program.

## Historical remarks

Contact: Gaetan Borot (HU Berlin), Pieter Moree (moree@mpim-bonn.mpg.de)

## Reduction theory and periods of modular forms

Among Manin's most beautiful and influential contributions to number theory was his study of periods of modular forms, in particular the theory of modular symbols and his algebraicity theorem for the periods of cusp forms, both of which are related to the theory of continued fractions. After reviewing this material, I will turn to the inverse problem of determining a cusp form from its periods and will describe a complete solution for the case of the full modular group.

## The Last Lecture: Computability Questions in the Sphere Packing Problem

I will dedicate this last lecture of Manin's "Algebra, Geometry, and Physics" seminar to present his last work (and our last joint work) on computability questions arising naturally in the context of the sphere packing problem. I will show how our previous results on Kolmogorov complexity and the asymptotic bound for error correcting codes can provide some insight on this problem.

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