TOPICS
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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,
Berkovichspaces, and NewtonOkounkov bodies.
Algebrogeometric 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 padic fields and number
fields. This should be covered by Olivier Wittenberg and
other mathematicians around him.
SCHOOL
1115 September 2017
There will be four lecturers, and each will give a series of four onehour lectures.
Time  Monday  Tuesday  Wednesday  Thursday  Friday 

09:3010:30  Registration +coffee 
David Eisenbud Lecture 1 
David Eisenbud Lecture 2 
June Huh Lecture 3 
June Huh Lecture 4 
10:3011:00  opening  C O F F E E  
11:0012:00  Peter Scholze Lecture 1 
June Huh Lecture 1 
June Huh Lecture 2 
Duco van Straten Lecture 4 
IMAGINARY 
12:0014:00  
L U N C H 
@13:00 Contemporary Music concert 

.  
14:0015:00  Peter Scholze Lecture 2 
Peter Scholze Lecture 3 
Peter Scholze Lecture 4 
David Eisenbud Lecture3 

15:0015:15  B R E A K  
15:1516:15  Duco van Straten Lecture 1 
Duco van Straten Lecture 2 
Duco van Straten Lecture 3 
David Eisenbud Lecture 4 
CONFERENCE
1822 September 2017
Time  Monday  Tuesday  Wednesday  Thursday  Friday 

08:3009:00  Registration  Registration  Registration  Registration  Registration 
09:0010:00  D. Eisenbud  O. Wittenberg  M. Mustaţă  A. Corti  S. Galkin 
10:0011:00  F.O. Schreyer  M. Hering  J. Poineau  I. Cheltsov  B. Rémy 
11:0011:30  C O F F E E B R E A K  
11:3012:30  A. Caraiani  A. Conca  A. Werner  F. Ambro  Y. André 
12:3014:15  
L U N C H 
@13:00 Contemporary Music concert 

.  
14:1515:15  A. Dimca  C. Raicu  M.E. Rossi  J. Wisniewski  
15:1515:20  B R E A K  NO BREAK  
15:2016:20  G. Farkas  S. Kovács  F. Nicolas ^{ ♬ }  M. Verbitsky 
Composer François Nicolas will lecture about "Musical heterophony and its possible echoes in mathematics" 
The talks are 50 minutes, ending about 30 minutes before the concerts at the Enescu Festival start.
THE ENESCU FESTIVAL 2017
224 September 2017
The George Enescu Festival is held in Bucharest every other year, and is maybe the most important music festival in Eastern Europe. In 2017 Zubin Mehta will be the Honorary President. The festival consists of three weeks of concerts, and every weekend special events dedicated to contemporary music will take place.
PROGRAMME
You can find the programme here. Ticket sales will start in November 2016.
INTERACTION WITH THE FESTIVAL
In the frame of the conference, composer François Nicolas will talk to mathematicians about music. Further joint public discussions with musicians and mathematicians will be organised. Among others, some of the composers presenting their work in the contemporary music workshop will be part of these discussions. A joint social event is also being planed.
IMAGINARY
In the foyers of the concert halls an IMAGINARY exhibition will be shown. It will contain a part about algebraic surfaces, and interactive exhibits about the overalps of music and mathematics.
VENUES
The main concert halls are Sala Palatului and Ateneul Român. Both are less than 800m away from the conference venue. The workshop "Music of the 21st Century" will take place every weekend (Friday to Sunday) at Sala Radio  another 1.2 km further away.
Klaus Altmann (FU Berlin)
Marian Aprodu (U Bucharest & IMAR)
Alexandru Constantinescu (INdAM & IMAR)
Hélène Esnault (FU Berlin)
Institute of Mathematics of the Romanian Academy
Florin Ambro (IMAR)
Marian Aprodu (U Bucharest & IMAR)
Alexandru Constantinescu (U Genova & IMAR)
Cezar Joiţa (IMAR)
Cătălin Gherghe (U Bucharest)
Marius Vlădoiu (U Bucharest)
Victor Vuletescu (U Bucharest)
Clay Mathematics Institute 
ERC Advanced Grant  Compositio Foundation  George Enescu Festival 2017  AXXESS CAPITAL / SEGES S.A. 
The Research Insitute of the University of Bucharest  