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The last week will be open for stay in residence. 
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. OrganizationTo reach the organization committee write to fouvry73[at]math.ethz.chplease note that this email is for organisation purpose only, registration for the workshop is by invitation only, and applications to the Summer School are now closed. °⺣ Organization Committee ⺣°Régis de la Bretèche (Université Paris Cité)Lucile Devin (Université du Littoral Côte d'Opale) Florent Jouve (Institut de Mathématiques de Bordeaux) Emmanuel Kowalski (ETH Zürich) Philippe Michel (EPF Lausanne) °⺣ Scientific Committee ⺣°Valentin Blomer (Universität Bonn)Tim Browning (IST Austria) Lillian Pierce (Duke University) RegistrationApplication to the Summer School is now closed, and all answers were sent.Due to limited room capacity, participation to the workshop is by invitation only. The organizers of this program are committed to fostering a safe, inclusive, and respectful environment for everyone. Participants are expected to uphold these values, behave respectfully toward others, and contribute to an atmosphere that supports diversity and gender balance. Practical InformationThe program takes place in the Bernoulli Center, their webpage contains information on how to get there.IMPORTANT WARNING: Scam / Phishing / SMiShing ! Note that ill-intentioned people may be trying to contact some of participants by email or phone to get money and personal details, by pretending to be part of the staff of our conference center. Participants should make their own accommodation arrangements in advance (if not supported by the conference funds) and be cautious when contacted by third parties who suggest they are associated with the conference. Summer SchoolAugust 17-28, 2026Two weeks of lectures given by world class mathematicians on important topics in Analytic Number Theory for PhD students and Postdocs researchers in the domain.°⺣ Lectures ⺣°Sarah Peluse (Stanford University)Additive CombinatoricsStephanie Chan (University College London) Arithmetic StatisticsThis course is an introduction to some topics in arithmetic statistics, centred around class groups of quadratic fields. We will start by recalling some basic background on class groups, and then move on to some classical results, including Davenport--Heilbronn. We will also discuss some other cases where aspects of the distribution of class groups have been studied, introducing some of the standard tools in the area as they arise.Paul Nelson (Aarhus University) Automorphic formsKevin Destagnol (Laboratoire de Mathématiques d'Orsay) Analytic number theory and rational pointsGiven an algebraic variety \(V\) defined over a number field \(k\), a natural question is to study its set of \(k\)-rational points \(V(k)\).(Q1) Is it empty or not? If it is empty, what are the obstructions to the existence of a rational point? (Q2) Is it finite or infinite? In the latter case, can we say something more quantitative? (Q3) The problem of deciding whether or not a given variety has a rational point is difficult. Can we say something about this problem on average in families? We will explain, during this mini-course, how analytic number theory can help us answer some of these questions. In particular, we will discuss a conjecture of Manin, which predicts the asymptotic behaviour of the number of rational points of height at most \(B\) on smooth Fano varieties as \(B\) goes to infinity. We will also discuss a conjecture of Loughran and Smeets regarding the number of varieties in families that have a rational points or a point everywhere locally. Finally, based on recent works, we will explain how to tackle such conjectures in two instances, highlighting two different approaches : the first based on Birch's circle method and the second one based on a descent method combined with the geometry of numbers. Adam Harper (University of Warwick) Introduction to random multiplicative functionsRandom multiplicative functions provide a model for certain functions of number theoretic interest, like Dirichlet characters. They can also be important tools for proving results about those functions, as well as an interesting probabilistic object in their own right.In these lectures, I will try to introduce and motivate random multiplicative functions; explain some ways of thinking about them, which have proved to be useful in various recent works; and present details of some proofs. At the end I hope to also have time to explain how one can (sometimes) transfer results from random multiplicative functions to deterministic ones. Emmanuel Kowalski (ETH Zürich) Trace functions and their applicationsThe course will survey the theory of trace functions, from their origin in the study of exponential sums over finite fields to current developments. We will focus on providing intuition and useful statements for applications (in particular convenient "black box" versions of Deligne's Riemann Hypothesis over finite fields), and highlight many applications of the theory to analytic number theory.James Maynard (University of Oxford) Sieve Theory°⺣ Participants ⺣°This workshop is aimed at PhD students (including those starting their PhD in 2026) and postdocs.Application for the Summer School is now closed. We hope to notify applicants of our decision by mid-April. Accomodation, in the form of shared bedrooms will be provided to selected participants. We do not expect to fund travel. click for more informationScheduletbdWorkshopAugust 31 - September 4, 2026°⺣ Confirmed speakers ⺣°click for more informationScheduletbd |