The purpose of this lecture series is to introduce the audience to basic ideas of specific areas of contemporary pure mathematics. Each lecture shall present an area: where it comes from, where it currently is, where it goes. Lectures will be given by prominent mathematicians twice a year: in the Spring and in the Autumn. Before and after each lecture we will organize reading seminars to prepare the audience for the lecture and to dig further into the topic of the lecture. With the lecturer’s consent, lectures will be recorded, slides and/or lecture notes will be provided if available.

The purpose of the school is to present a self-contained proof of a famous theorem of Serre in 1972. This theorem tells us that the representation associated to the Galois action on the p-torsion points of an elliptic curve is surjective for p great enough. This theorem had a very great impact in the field of arithmetic geometry and opened the field to numerous problems that are, for some, still open today. After introducing the students to the topics needed to understand the proof, illustrating the theory through exercises and computer sessions, we will present the proof itself.

This Thematic Month aims to cover topics related to singularity theory of algebraic or analytic spaces, algebraic study of differential equations, and their applications to questions of transcendence. This 5-week program covers different themes that are often not closely related. One of the main objectives is to make them interact. To encourage participants (especially the youngest ones) to attend the entire month and foster interactions outside each one’s expertise zone, the scientific program of each week of the month will consist of courses accessible to non-experts, as well as more specialized presentations. This month will consist of five successive weeks: – Logarithmic and non-archimedean methods in Singularity Theory. The first week will focus on recent results based on methods in logarithmic geometry and non-archimedean geometry in singularity theory. – Foliations, birational geometry and applications. The second week will cover topics in birational geometry, including singularity resolution, MMP (Minimal Model Program), algebraic foliation theory, and local holomorphic dynamics. – Tame Geometry. The third week will address tame geometry in various forms: o-minimality, transseries, Hardy fields, non-archimedean analogs of tame geometry, and their applications to number theory. – Galois differential Theories and transcendence. The fourth week is devoted to differential Galois theory and its applications to questions of functional transcendence and number theory, as well as the study of periods and E and G-functions. – Enumerative combinatorics and effective aspects of differential equations. The last week is dedicated to enumerative combinatorics and certain effective aspects of differential equations, especially applications in enumerative combinatorics of techniques presented in the previous week, or as effective results on topics covered in the preceding weeks.

The workshop is aimed at algebraic and arithmetic geometers curious about the potential application of model theory in their research, as well as at model theorists who are keen to learn how their tools may be extended to answer questions of geometric interest.

Speakers:

 Charlotte Chan
 Jessica Fintzen
 Florian Herzig
 Tasho Kaletha 

This is a 4-day workshop that aims to explore connections between p-adic Arthur and ABV packets and geometric representation theory/the geometric Langlands program. It will feature talks from experts in both areas. The primary goal of this workshop is to foster new research directions and collaborations.

Harmonic analysis on homogeneous spaces is a fundamental area of research that simultaneously generalizes classical harmonic analysis on groups and on Riemannian symmetric spaces. It naturally relates to many areas of mathematics, playing a central role in representation theory and the theory of automorphic forms.

This workshop will be an occasion to introduce recent developments in some of these areas. It will also aim to explore new connections between them and extend the fruitful interactions between C*-algebras, harmonic analysis and representation theory beyond the classical setting of groups to the general setting of homogeneous spaces.

Topics will include:

• C*-algebraic approaches to the tempered dual of non-Riemannian symmetric spaces;
• Harmonic analysis and Plancherel theory for spherical spaces;
• Connections with the Langlands program and periods of automorphic forms;
• Recent approaches to the theta correspondence via C*-algebras

The goal of this workshop is to present a panorama of hot topics, and their recent progress, in arithmetic geometry (incl. p-adic Hodge theory, Shimura varieties and their cohomology, L-functions, Berkovich spaces, homotopy and anabelian geometry, Galois theory, condensed mathematics, vanishing cycles, motivic theory, birational geometry,...). Talks will include introductory presentations for graduate students and for PhD researchers.

A conference on automorphic forms and related topics. The topics include mock modular forms, Maass wave forms, elliptic curves, Siegel and Jacobi modular forms, special values of L-functions, random matrices, quadratic forms, applications of modular forms, and many others. In addition to research talks, the workshop has, in the past years, featured panel discussion sessions. We expect to have many contributed talks and a mix of students and faculty.

The conference "Number Theory, Quantum Chaos and their Interfaces” aims at gathering distinguished researchers working in either of the disciplines to discuss recent research advances in these fields, and serve as a playground for the exchange of ideas between these, rather diverse, research communities. Another purpose of our conference is to provide a solid educational platform for more junior researchers who aspire to conduct research in the relevant fields and expose them to some of the outstanding results and open problems.

This meeting will take place on the occasion of the 60th birthday of Francesco Pappalardi. This event honours his outstanding contributions to number theory, and will also be a recognition of his exceptional activity in promoting mathematics in countries which need it the most. In particular, Francesco is a driving force for mathematical cooperation between Kurdistan Iraq and other countries, including Italy. This conference will be an opportunity to feature outstanding international mathematicians in Erbil and showcase the scientific potential of Kurdistan Iraq.

This is a graduate student workshop on discrete groups in topology and algebraic geometry. This includes topics like fundamental groups of varieties and mapping class groups. This is the second week of a three week long thematic program. The conference the following week may also be of interest to graduate students.

This is a conference on discrete groups in topology and algebraic geometry, which includes topics like fundamental groups of varieties and mapping class groups. This is the third week of a thematic program on the topic.

RNT6 will be a remote collaborative research experience for the weeks of June 16 through June 27, 2025. The goal is for participants to learn new math, get to know colleagues, and have a joyful, affirming research experience. You must apply to participate! Team leaders have planned projects for participants to work on during the workshop. You can read more about the 6 projects on our website.

To ensure that all participants can share in this joyful research experience, we ask that all who apply to participate be committed to equity and justice. We will also make time to imagine a different way to do math: How can our profession be transformed to welcome and support everyone?

RNT aims to foster diversity; we particularly encourage applications from historically underrepresented people in mathematics (including Black and Indigenous people, people of color, women, LGBTQ+ members of the community, and people with disabilities), scholars at undergraduate institutions, and in general scholars at all stages of their career who believe they would benefit from this experience. Please share this announcement with any groups, students, post docs, and scholars at all points in their careers who might be interested in participating in this workshop.

In recent years, there has been an explosion of activity surrounding algebraic points on curves, from many different perspectives. These include the study of measures of irrationality, isolated and parametrized points, computational methods to determine algebraic points, and the arithmetic statistics of algebraic points. In this workshop, we aim to bring together researchers from these diverse perspectives, with the particular goal of developing bridges between them. The workshop will include overview talks on the various perspectives, research talks, an open problem session, and structured time for collaboration.

The René 25 conference's purpose is to celebrate the research interests of René Schoof.

Part of a series of conferences: NTDU

During the 2025-26 academic year the School will have a special program on Arithmetic Geometry, Hodge Theory, and O-minimality. Jacob Tsimerman, University of Toronto will be the Distinguished Visiting Professor.

The purpose of this special year will focus on recent developments in hodge theory and o-minimality and their applications to arithmetic geometry. There has been much progress over the last 15 years in using transcendental uniformization maps to study arithmetic questions (general shafarevich theorems, results on unlikely intersections, general bounds on rational point counts). It has become increasingly clear that hodge theory (both classical and P-adic) and the resulting period maps form a natural home for these kinds of investigations to arise. In the other direction, O-minimality has been applied with success to make progress on questions in Hodge theory (Griffiths conjecture, definable period maps), and has recently had its own explosion of results (sharply O-minimal sets, the resolution of Wilkie's conjecture).

The goal of this year will be to bring together researchers in these different fields, with the aim of extending the collaboration between areas, share key insights, and investigate how far existing methods can be pushed.

Senior participants: Gal Binaymini, Ben Bakker (to be confirmed), Jonathan Pila and Claire Voisin (STV)

The Geometric and Analytic Number Theory conference will bring together world leading researchers to present talks on the latest advancements in the fields of geometric and analytic number theory with a view towards rational points on varieties and counting number fields. Attendees will have the opportunity to engage with pioneering work and connect with peers from around the world, fostering collaboration and knowledge exchange within the number theory community.

The Algorithmic Number Theory Symposium (ANTS) is the premier international forum for the presentation of new research in computational number theory and its applications, devoted to algorithmic aspects of number theory and related fields, including elementary number theory, algebraic number theory, analytic number theory, the geometry of numbers, arithmetic geometry, finite fields, cryptography, and coding theory.

On the occasion of 40+ years after the seminar paper of Gross--Zagier, we bring together experts to deliver lectures on a broad range of topics connected with the Gross-Zagier formula, its generalizations, related future directions, and other works that it has inspired.