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 follow-up to the 2015, 2017, 2019 and 2022 Students' Conference on Tropical and Non-Archimedean Geometry, will take place in Regensburg from July 22, 2024 to July 26, 2024. The goal of the conference is to gather mainly PhD students and young post-docs in tropical, Arakelov or non-archimedean geometry in a friendly setting and foster new collaborations.

The conference will begin with three introductory lectures on tropical, Arakelov and non-archimedean geometry respectively, aimed in particular at new PhD students. Those will then be followed by more traditional research talks. We also encourage participants to apply for giving a talk.

The aim of this conference is to help narrow the gap between computational mathematicians and mathematical cryptographers, driven by the many new hardness assumptions that are emerging in the context of post-quantum cryptography. The conference will be organized along the four main mathematical themes in post-quantum cryptography: lattices, error-correcting codes, systems of non-linear equations, and isogenies.

The Journal of Number Theory hosts a number theory conference every two years to publicize recent advances in the field. The JNT also sponsors the David Goss Prize, a 10K USD prize awarded every two years to a young researcher in number theory and presented at the JNT Biennial.

The aim of this meeting is to bring together people attacking key problems in number theory via techniques involving concrete or computable descriptions. Here, number theory is interpreted broadly, including algebraic and analytic number theory, Galois theory and inverse Galois problems, arithmetic of curves and higher-dimensional varieties, zeta and L-functions and their special values, and modular forms and functions. Considerable attention is paid to computational issues, but the emphasis is on aspects that are of interest to the pure mathematician.

Because of limited space, participation is by invitation only.

The workshop is primarily aimed at researchers on the doctoral and early postdoctoral level. Besides some already announced mini-courses and research talks, we will offer selected participants the opportunity to present their own work.

This is a summer school aimed at advanced Masters students and PhD students. There will be three courses,

Class Field Theory (Tamás Szamuely)

Elliptic Curves (TBA)

Cohen-Lenstra Heuristic (Alex Bartel),

with lectures in the morning and exercise sessions in the afternoon. The number of participants will be limited to 50 and we have funds to cover the accommodation costs of about 35 participants. Registration is open until 20 May.

The purpose of the Annual International Conference of the Georgian Mathematical Union is to bring together mathematicians from various fields to present their original research results and provide opportunities to establish new connections within the fields of pure and applied mathematics, as well as science, engineering, and technology. The conference also provides valuable networking opportunities for you to meet great personnel in these fields. Sections: • Algebra and Number Theory • Differential and Integral Equations, and Their Applications • Geometry and Topology • Logic, Language, Artificial Intelligence • Mathematical Education and History • Mathematical Logic and Discrete Mathematics • Mathematical Modeling and Numerical Analysis • Mathematical Physics • Probability Theory and Statistics, Financial Mathematics • Real and Complex Analysis

Automorphic forms are present in almost all areas of modern number theory. Over the past few decades, there has been an explosion of activity and progress in this vast field, leading to exciting new directions of research, new applications, and connections to other fields. The Building Bridges conferences are a central element in this evolution of the subject. The Building Bridges conference is an international biennial event, the 2024 edition will be the sixth. These meetings, which last two weeks, consist of a summer school, followed by a one-week workshop. Each summer school consists of three 2-day mini-courses, taught by teams of internationally renowned researchers. The courses are given by pairs of teachers- made up of a European and an American researcher, giving meaning to the idea of a bridge between the research carried out in the two continents. The workshop is organized in a very dynamic way and is well known and well received by the experts. The format of the conference is special: there are no guest speakers, but the time is shared equally between all speakers, following the advice of the scientific committee. The objective is to promote young researchers by giving them the same time to present their research as experienced scientists in the field. There will also be several awareness round tables on themes of social interest.

In 2019, the organizers created a workshop called Number Theory in the Americas, which brought together junior and senior mathematicians from North, Central, and South America, to work together on research projects. The workshop resulted in at least seven publications, and served as a first collaboration experience for many of the junior researchers. The organizers propose to create a follow-up workshop in order to provide collaboration opportunities for the PhD students and postdocs who were too young to participate the last time. The workshop will be held in Spanish in order to erase the additional obstacle of communicating in English. We will welcome native and non-native speakers alike.

Our workshop is modeled after several other workshops that have been successful at fostering mathematical collaboration. Participants will be divided into small project groups (3-5 participants) containing a mix of junior and senior researchers. Each group will be led by one or two senior mathematicians. Project groups will be assigned based on research area, with care taken to ensure that each group contains researchers from both continents who have not previously worked together. Background reading will be sent to project group members several months in advance so that they are prepared to work on their respective problems together when they arrive in Oaxaca. The bulk of the workshop will be devoted to working in the project groups, but there will be introductory talks on the first day and final reports on the last day. There will also be panel discussions on topics of particular interest to junior researchers. The expectation is not that each project group will write a paper by the end of the week. Rather, it is meant to be an opportunity to exchange ideas and a starting point for potential future collaboration.

This workshop is motivated by recent developments in geometric representation theory, related to wild ramification in the geometric Langlands program and non-abelian Hodge theory. The goal is to bring together researchers in these fields and researchers working on irregular singularities (in particular Stokes phenomena), to stimulate future interactions.

It will feature research talks from experts in the field, a poster session for early-career researchers as well as three mini-courses by

Jean-Baptiste Teyssier (Sorbonne Université), Valerio Toledano-Laredo (Northeastern University) and Zhiwei Yun (Massachusetts Institute of Technology).

CIMPA/AESIM introductory school of number theory for developing countries

The Early Number Theory Researchers Workshop 2024 (ENTR 24) aims to foster colloborations and interactions among young researchers in number theory, in particular L-functions, Shimura varieties and p-adic Langlands program. The workshop has three plenary talks in these three directions. Participants are strongly encouraged to give a talk within these topics.

The Palmetto Number Theory Series (PANTS) is a series of number theory meetings held at colleges and universities in the Southeast since 2006.

The Maple Conference is dedicated to exploring different aspects of the math software Maple, including its impact on education, new symbolic computation algorithms and techniques, the wide range of applications and research Maple enables, and new and upcoming advancements in Maple and related technologies.

Come to this free virtual event to:

-Discover the work done by Maple users around the world, as well as new products and initiatives from Maplesoft
-Learn about valuable techniques and features to enhance your use of Maple
-Share experiences and ideas with members of the community and with the Maplesoft product team

The workshop is aimed at young researchers such as PhD students and postdocs, and it features three mini-courses on different aspects of rational points.

Speakers:

• Damaris Schindler (Universität Göttingen)

• Anthony Várilly-Alvarado (Rice University)

• Bianca Viray (University of Washington)

See the website for details on the subject matter of the workshop.

Per MFO rules, participation is generally limited to invited mathematicians. However, we have reserved a small number of places for early-career mathematicians, who may apply to participate by completing a short application.

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.

Speakers:

 Charlotte Chan
 Jessica Fintzen
 Florian Herzig
 Tasho Kaletha 

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

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.

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.

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.

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)