Titre: FOUVRY - 73
Week 1-2 (17 August- 28 August 2026): Summer school
Week 3 (31 August -4 September 2026): Workshop
Week 4 (7-11 September 2026): Scientific collaborations
General summary:
Analytic number theory refers, very broadly, to studies of properties of arithmetic objects based on methods of analytic nature. Some of the foundational problems, which remain topics of considerable research interest, include distribution problems for prime numbers (e.g., what are the smallest or largest gaps that can occur between prime numbers of a certain size? are there infinitely many prime numbers which are of the form n^2 + 1?), for squares or for other polynomial values (e.g., how many times can a positive integer be written as sum of a fixed number of squares? which numbers are sums of three cubes?).
By its very nature, analytic number theory involves a very broad array of methods and tools. It has been instrumental in developing a number of important areas of mathematics, such as representation theory, from the characters of finite abelian groups, used by Dirichlet to study primes in arithmetic progressions, to the representation theory of reductive Lie groups, which is an essential component of the Langlands program. In recent years, important breakthroughs have been achieved using tools borrowed, for instance, from ergodic theory and homogeneous dynamics, from additive combinatorics, or from very fine aspects of probability theory (such as the so-called Gaussian Multiplicative Chaos).
It is because of the truly kaleidoscopic aspect of analytic number theory that young researchers benefit immensely from broad instructional programs where they can get first exposure to some of the new techniques which may be of critical importance in their own research. The four-week period at the Bernoulli Center which we propose aims at giving exactly this type of insight to PhD students and postdocs.
Organisateurs:
Régis de la Bretèche: regis.de-la-breteche@imj-prg.fr
Lucile Devin: lucile.devin@univ-littoral.fr
Florent Jouve: florent.jouve@math.u-bordeaux.fr
Emmanuel Kowalski: kowalske@ethz.ch
Philippe Michel: philippe.michel@epfl.ch