This month-long program is hosted in the Bernoulli Center, EPFL, Lausanne,
it includes a 2-weeks Summer School and a 1-week Workshop.
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.
Organization
To reach the organization committee write to fouvry73[at]math.ethz.ch
please 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)
Registration
Application 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 Information
The 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 School
August 17-28, 2026
Two 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 Combinatorics
Stephanie Chan (University College London) Arithmetic Statistics
This 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 forms
Kevin Destagnol (Laboratoire de Mathématiques d'Orsay) Analytic number theory and rational points
Given 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 functions
Random 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 applications
The 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.
Accomodation, in the form of shared bedrooms will be provided to selected participants. We will not fund travel.
There will be short talks sessions for participants to advertise their work, the talks should be exaclty 8 min long.
°⺣ Schedule ⺣°
This is a tentative preliminary schedule it will change.
Workshop
August 31 - September 4, 2026
°⺣ Confirmed speakers ⺣°
°⺣ Schedule ⺣°
tbd
°⺣ Titles and abstracts ⺣°
Brandon Alberts (Eastern Michigan University)
TBA
Abstract:
tba
Dante Bonolis (Graz University of Technology)
TBA
Abstract:
tba
Martin Čech (Charles University)
TBA
Abstract:
tba
Alexander Dunn (Georgia Tech)
Recent developments in non-vanishing for higher order Hecke L-functions and CM elliptic curves
Abstract:
In this talk I will describe recent progress on the non-vanishing problem for cubic and quartic Hecke L-functions over number fields. Important ingredients include the large sieve and inputs from the theory of metaplectic forms. The cubic case is based on a joint work with A. de Faveri, C.David, and J.Stucky. The quartic case is joint work with C.Castillo and A. de Faveri. We also will discuss some recent unconditional results on the non-orthogonality of the cubic and quartic large sieve. This is a joint work with A.de Faveri and J.Hoffstein.
Peter Koymans (Utrecht University)
Value sets of binary forms.
Abstract:
Given a binary form $F$ with integer coefficients, we define its value set $\mathrm{Val}(F)$ to be the set $\{F(x, y) : x, y \in \mathbb{Z}\}$. For two binary forms $F$ and $G$, what can we say if $\mathrm{Val}(F) = \mathrm{Val}(G)$? The goal of this talk is to show how one may give a complete answer to this question. This is joint work with Étienne Fouvry.
Junxian Li (University of California Davis)
TBA
Abstract:
tba
Kaisa Matomäki (University of Turku)
TBA
Abstract:
tba
Lilian Matthiesen (Goettingen University)
TBC
Abstract:
tbc
Jori Merikoski (University of Helsinki)
TBA
Abstract:
tba
Alexandru Pascadi (University of Bonn)
Bilinear forms with Kloosterman sums via quadratic characters
Abstract:
We discuss recent work, joint with Valentin Blomer, on bilinear forms with $S(m, n; c)$. Our results apply for general moduli c and save $c^{-1/32}$ for sums of square-root length, improving the savings of Kowalski--Michel--Sawin for prime moduli. We rely on a new connection to sums of quadratic Dirichlet characters, as well as on the representation theory of $\mathrm{SL}_2(\mathbb{Z}/c\mathbb{Z})$ (building on a ''non-abelian amplification'' argument from previous work). Time permitting, we briefly mention applications to moments of twisted $L$-functions and the $\mathrm{GL}_2$ exceptional-spectrum large sieve.
Cédric Pilatte (University of Oxford)
TBA
Abstract:
tba
Julia Stadlmann (University of Illinois Urbana-Champaign)
TBA
Abstract:
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Damaris Schindler (Goettingen University)
Quantitative weak approximation and quantitative strong approximation for certain quadratic forms
Abstract:
In this talk we discuss recent results on optimal quantitative weak approximation for certain projective quadrics over the rational numbers as well as quantitative results on strong approximation for quaternary quadratic forms over the integers. We will also discuss how a Brauer-Manin obstruction can affect the growth of coprime integer points of bounded height on a quaternary quadratic form. This is joint work with Zhizhong Huang and Alec Shute.
K. Soundararajan (Stanford University)
TBC
Abstract:
tbc
Cathy Swaenepoel (Université Paris Cité)
Prime numbers with an almost prime reverse
Abstract:
Let $b\geq 2$ be an integer. For any integer $n\geq 0$, we call reverse of $n$ in base $b$ the integer obtained by reversing the digits of $n$.
The existence of infinitely many prime numbers whose reverse is also prime remains an open problem.
In a joint work with Cécile Dartyge and Joël Rivat, we show that there are infinitely many primes with an almost prime reverse.
More precisely, we show that there exist an explicit $\Omega_b\in \mathbb{N}$ and $c_b>0$ such that, for at least $c_b b^{\lambda} \lambda^{-2}$ primes $p \in [b^{\lambda-1},b^{\lambda}[$, the reverse of $p$ has at most $\Omega_b$ prime factors.
Our proof is based on sieve methods and on establishing a result in the spirit of the Bombieri-Vinogradov theorem concerning the distribution in arithmetic progressions of the reverse of prime numbers.
Gerald Tenenbaum (Institut Elie Cartan de Lorraine)
TBA
Abstract:
tba
Maryna Viazovska (EPFL)
TBC
Abstract:
tbc
Victor Wang (Institute of Mathematics, Academia Sinica)
TBA
Abstract:
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Katharine Woo (Stanford University)
TBA
Abstract:
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Max Xu (Courant Institute)
TBA
Abstract:
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Asif Zaman (University of Toronto)
TBA
Abstract:
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