A summer school and workshop will take place in Bucharest in September 2017. Their goal is to cover some active topics in algebraic geometry: homological methods, discrete and arithmetic aspects, and singularitiesFaculty of Mathematics and Computer Science, University of Bucharest

A special feature of this event will be a close relation to the George Enescu Music Festival . During the three weeks of the festival, an IMAGINARY math & music exhibition will be shown in the foyer of the Mihai Jora Concert Hall, while further events involving a direct interaction of mathematics and music - and of mathematicians and musicians - are planned.

Homological methods
Syzygies of a projective variety are very fine numerical invariants that control the embedding of the variety. From the syzygies, one can easily recover the Hilbert function, however, their outmost importance comes from the fact that they carry intrinsic geometric properties. They can be used to extract information on the geometry of moduli spaces of polarized varieties.

Discrete aspects
They originate in the theory of toric varieties linking algebraic varieties to convex geometry and combinatorics. Nowadays, the field has expanded into several directions like tropical geometry, Berkovich-spaces, and Newton-Okounkov bodies. Algebro-geometric theories like the minimal model program have counterparts in discrete geometry.

Singularities
Singularity theory is essential in the classification of algebraic varieties. While the classification in dimension one and two can be done in the smooth setting, from dimension three on the minimal model program heavily relies on singular varieties. Moreover, they play an interesting role in mirror symmetry where resolutions and deformations are interchanged.

Arithmetic geometry
With Peter Scholze being one of the speakers for a series of four lectures, we shall focus on perfectoid spaces, and integral de Rham theory. With Yves André being one of the lecturers, we shall have some emphasis on motivic theory over fields, and periods. In addition, we expect some activity around the study of rational points and the index of specific varieties over p-adic fields and number fields. This should be covered by Olivier Wittenberg and other mathematicians around him.