The Langlands program aims to relate systems of polynomial equations with integer coefficients to automorphic forms, i.e. functions on symmetric spaces with a large number of discrete symmetries. The focus of the trimester will be on some manifestations of this program, including:

moduli spaces of shtukas
p-adic techniques in local Langlands and the relation to geometric Langlands
Shimura varieties and more general spaces in global Langlands

Conference dedicated to the memory of Bas Edixhoven

The Richmond Geometry Meeting will focus on emergent research topics while bringing together researchers in algebraic geometry, low-dimensional topology, and mathematical physics. In summer 2023, we will highlight developments in moduli theory together with new perspectives in Floer homology and low-dimensional topology. This year's format will be in-person. This meeting is supported by NSF award DMS-2240741.

Topic: Motivic homotopy theory involves the study of algebraic varieties and schemes using methods not only from algebraic geometry, but also from algebraic topology. A basic idea is to use techniques from homotopy theory, such as the construction of homotopy groups and the use of homotopical invariants, to investigate topological and geometric properties of these varieties. It was developed in the late 20th century as a way to extend classical homotopy theory, which studies topological spaces up to continuous deformations, to the realm of algebraic geometry.

One of the fundamental problems in motivic homotopy theory over F is to calculate the homotopy groups π_t,w(1) of the motivic sphere spectrum 1. Here the integers t, w ∈ Z refer to the topological degree and the weight, respectively. In a precise sense, these groups are the universal motivic invariants because the motivic sphere is the unit for the tensor product on motivic spectra. All the relations witnessed in the graded ring π_*,*1 hold in every other theory representable in the stable motivic homotopy category, such as algebraic cobordism, algebraic and hermitian K-theory, motivic cohomology, and higher Witt theory.

The goal of the workshop is to discuss “Why, what, and how” on specific computations in stable motivic homotopy theory.

Please see the preliminary syllabus for more detailed information and references.

Suggested prerequisites:

Mentors: The 2023 Talbot workshop will be mentored by Prof. Oliver Röndigs of the Osnabrück University and Paul Arne Østvær of University of Milan, Italy and University of Oslo, Norway.

Format: The workshop discussions will have an expository character and a majority of the talks will be given by participants. Breaks will be built into the schedule for informal discussions and collaborations. The workshop will take place in a communal setting, with participants sharing living space and cooking and cleaning responsibilities.

The workshop will be held entirely in-person. Participants should expect to follow mitigation measures such as masking in indoor common spaces and eating meals in a socially distanced/outdoor setting.

Timeline: The 2023 Talbot workshop will take place June 4-10, 2023.

Funding: We cover all local expenses, including lodging and food. We also have limited funding available for participant travel costs.

Who should apply: Talbot is meant to encourage collaboration among young researchers, particularly graduate students. To this end, the workshop aims to gather participants with a diverse array of knowledge and interests, so applicants need not be an expert in the field. In particular, students at all levels of graduate education are encouraged to apply. Our decisions are based not on applicants' credentials but on our assessment of how much they would benefit from the workshop. As we are committed to promoting diversity in mathematics, we also especially encourage women and minorities to apply.

Inclusiveness statement: In accordance with the Statement of Inclusiveness, this workshop will be open to everybody, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity. We are committed to ensuring that the Talbot Workshop is a supportive, inclusive, and safe environment for all participants, and that all participants are treated with dignity and respect.

Contact Information: Please email the organizers at talbotworkshop(at)gmail.com if you have any questions.

This summer school series aims at training their participants in key strategic problems in mathematics and their applications, with the core idea that theory and applications strengthen each other. The school is focused in training of young researchers whilst opening new fields for senior ones.

The Hypatia Graduate Summer School will consist in two keynote courses on subjects of exceptional promise and scientific importance delivered by highly distinguished speakers in the area plus a high-level colloquium on a complementary subject.

The Hypatia Graduate Summer School will be developed in an informal atmosphere based on discussions, exchange of ideas and critical analysis of results. Moreover, to honour its namesake, it is committed to work under a friendly gender perspective that highlights the role of women in mathematics and encourages and helps the participation and promotion of young female researchers at a professional level.

Registration deadline 21 / 05 / 2023

COURSE 1: Contact geometry and the many facets of complexity of hydrodynamics

Lecturer: Eva Miranda (UPC-CRM) / Daniel Peralta (ICMAT)

Abstract: In this course we will unveil various connections between three seemingly unconnected topics: contact geometry, fluid mechanics, and Turing machines.

The point of departure will be Euler’s equations with a focus on the study of stationary solutions. Our constructions combine techniques from various areas of mathematics that we will thoroughly analyze in this course. An important ingredient will be the close inspection of various notions of complexity of our constructions: dynamic, computational and logical. Several applications to Celestial mechanics will also be discussed.

COURSE 2: Symbolic Dynamics in Celestial Mechanics

Lecturer: Susanna Terracini (Dipartimento di Matematica “Giuseppe Peano”)

Abstract: it is part of the mathematical folklore that Dynamical Systems featuring many nonlinear interactions should display chaotic behavior and possess complex dynamics, whatever this means.

On the other hand, for natural systems, this lacks a rigorous statement and even more, a rigorous proof, specially when we are leaving the perturbative setting.

The purpose of the minicourse is to illustrate how to contstruct complex trajectories by the use of global variational methods in some relevant models from Celestial Mechanics.

We are excited to announce the Arithmetic, Birational Geometry, and Moduli Spaces conference the week of June 12-16 2023 at Brown University in celebration of Dan Abramovich’s 60th birthday. We hope you will be able to attend.

The webpage for the conference is at the following URL:

https://sites.google.com/view/abgms2023/

There is a registration form on the webpage. There are funds to support some students and early researchers. The registration deadline is May 1, 2023, but we encourage all participants to register as soon as possible. Please register even if you are not requesting funding support: this helps us with preparation and logistics.

This conference will be on various aspects of the local Langlands correspondence over p-adic fields and methods from p-adic Hodge theory. Topics will include the usual local Langlands correspondence, the p-adic local Langlands correspondence and the relation to coherent sheaves on spaces of Galois representations, and the geometry and cohomology of local Shimura varieties.

We believe that number theory should be not only accessible, but enjoyable to everyone. Join us for a joyful collaborative research experience, where people are valued and uplifted. Help us rethink the graduate school and postdoc experience, research seminars, hiring process, conferences, grant applications, and other aspects of our profession.

Microlocal sheaf theory, mainly based on the notion of microsupport of sheaves, is a creation of M. Kashiwara and P. Schapira after M. Sato’s foundational ideas. Beyond its application to the study of systems of linear partial differential equations (D-modules), P. Schapira and his collaborators used microlocal sheaf theory to bring light and progress to many areas: analysis (Sobolev spaces), symplectic geometry and topology (connection with Tamarkin’s results), deformation by quantization, regular and irregular holonomic D-modules, Ind-sheaves, persistent homology, and the list is not exhaustive.

The aim of this journey is to present recent results which were influenced by Schapira’s work.

In the early 1920s, Emmy Noether introduced the fundamental concept of a Noetherian ring, a notion that has had a remarkably broad impact on mathematics over the last century. In this conference, we celebrate Noether's legacy with research talks from many areas of algebra, broadly construed, including algebraic geometry, commutative algebra, number theory, and representation theory.

This, the 16th in a series of Workshops in Alpbach, will feature minicourses given by world class researchers and invited talks by younger researchers, covering topics in arithmetic geometry related to Galois representations and heights. The emphasis includes not only deep theoretical developments, but also applications of a more concrete/computational nature. Minicourses presenting a broad overview of these topics, delivered by top international experts, will be complemented by invited talks highlighting recent progress.

Interest in specialization of polynomials and Galois groups goes back at least to the work of Hilbert on the inverse Galois problem. This theory has found an abundance of applications in Algebra, Number Theory, Group Theory, and Arithmetic Geometry. In recent years, the area is blooming and we see striking results that open completely new horizons: The discovery of Hilbert irreducibility properties of algebraic groups, its connection with expanders and random walks, the interrelation with arithmetic-geometric properties of parametrizing varieties, and the exciting progress on the Cohen-Lenstra heuristics. The conference aims to bring together leading experts and young researchers interested in the area. We plan to leave an abundance of free time, dedicated to informal discussions. We believe that this will encourage the transfer of ideas, techniques, and will foster new collaborations and new research directions.

We are going to organize a week long conference during June 26-30, 2023, hosted by the Alfred Renyi Institute of Mathematics in Budapest, Hungary. The topic of the conference will emphasize the rich interactions between complex analysis and complex geometry, within the context of geometric analysis.

In addition, the conference will serve as an opportunity to celebrate the 70+1th birthday of Laszlo Lempert.

This workshop is organized around the themes of using refined invariants of algebraic varieties to study enumerative questions, with ideas coming from motivic homotopy theory, quadratic enumerative geometry, hermitian K-theory and beyond.

Géométrie Algébrique en Liberté, also known as GAeL, is an annual workshop organized by and for young algebraic geometers. The aim of this workshop is to gather young mathematicians in this field of research and give them an opportunity to discuss freely without having to fear that their questions or viewpoints might be silly: hence the name of the workshop.

The first 13 editions of GAeL were organized at the Centre International des Rencontres Mathématiques in Marseille (France), then GAeL became an itinerant workshop. Recently, GAeL has been held in Trieste (Italy), Leuven (Belgium), Nesin Maths Village (Turkey), Bath (UK), Strasbourg (France), Bucharest (Romania), Loughborough (UK) and Orsay (France).

If you have any questions, please do not hesitate to email any member of the organizing committee.

Victor P. Snaith (1944 – 2021) was distinguished not just as an outstanding mathematician who made deep and lasting contributions in algebraic topology and number theory but also as a charismatic leader who enthusiastically developed research communities and generously supported young researchers.

The conference will bring together homotopy theory, cohomology of groups, algebraic K-theory and number theory, the main areas in which Vic worked. The aim is to feature important developments, paying special attention to synergies between these areas, as Vic did in much of his versatile research.

This will be a one week conference broadly focused on the topics of the LMFDB, mathematical databases, computation, number theory, and arithmetic geometry. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time set aside for research and collaboration. We plan to publish a proceedings volume that will include all of the accepted papers.

The last few years have witnessed an explosion of progress in algebraic K-theory. Derived algebraic geometry and non-commutative methods have been refined into powerful tools, especially through the theory of localizing invariants. Trace methods have brought K-theory and topological cyclic homology closer together than ever before. Perfectoid techniques mean that K-theory benefits from the recent progress in p-adic cohomology, such as prismatic cohomology. Condensed mathematics provides at long last a uniform approach to the K-theory of topological rings. Geometric foundations for motivic stable homotopy theory have been laid and new motivic filtrations have been unearthed.

The goal of the Summer School will be to help bring the participants up to date on these exciting developments, via research lectures, mini-courses, and an Arbeitsgemeinschaft on the topic of syntomic and étale motivic cohomology.

Following the highly-successful first AGNES Summer School on higher dimensional moduli in 2022, this school will focus on intersection theory on moduli spaces. The past few years have seen spectacular progress in explicit computations of the cohomology and rational/integral Chow rings of moduli spaces of curves and related objects. This school will introduce graduate students to a range of techniques in this active area through four mini-courses. A key component of the school will be afternoon working sessions, where participants will work together in groups on problems, ranging from exercises to open-ended examples and research problems, relating to the topics of the lectures.

This summer school is designed for graduate students who have completed a yearlong course covering the foundations of algebraic geometry (e.g., Hartshorne's Algebraic Geometry) and are working in the field.

The minicourses will be given by Andrea di Lorenzo, Eric Larson, Hannah Larson, and Angelo Vistoli.

This is the ninth Iwasawa conference following conferences in Besancon, Limoges, Irsee, Toronto, Heidelberg, London, Tokyo and Bordeaux. The conference is dedicated to the memory of John Henry Coates.

This workshop aims at bringing together the leading experts in the field, covering a broad spectrum reaching from the more theoretically-oriented over the explicit to the algorithmic aspects. The fundamental problem motivating the workshop asks for a description of the set of rational points X(Q) for a given algebraic variety X defined over Q. When X is a curve, the structure of this set is known, and the most interesting question is how to determine it explicitly for a given curve. When X is higher-dimensional, much less is known about the structure of X(Q), even when X is a surface. So here the open questions are much more basic for our understanding of the situation, and on the algorithmic side, the focus is on trying to decide if a given variety does have any rational point at all.

This is a workshop with about 50 participants. Participation is by invitation. Every participant is expected to contribute actively to the success of the event, by giving talks and/or by taking part in the discussions.

The goal is to produce a collaborative environment for discussions of recent developments about spectral gaps, that bring together groups of researchers with different perspectives and backgrounds. All participants will be given fully catered accommodation at Collingwood College Durham

This conference will be on various aspects of the global Langlands correspondence. Topics will include in particular the geometry and cohomology of Shimura varieties and more general locally symmetric spaces, or moduli spaces of shtukas.

Number theory mixes techniques from various branches of mathematics and reveals unexpected connections between them. The first conference organised by the International Centre for Mathematics in Ukraine aims to overview recent breakthroughs in this field.

The event will take place simultaneously in two grounds with a live connection between the audiences at The Kyiv School of Economics and Stefan Banach International Mathematical Center in Warsaw. Students and young scientists are encouraged to take part. There will be special sessions organised to discuss research and learning problems stated by the speakers.

This will be a workshop in arithmetic and algebraic geometry, similar to the previous iterations (in 2017 and online in 2020). The intended participant is a graduate student, or a postdoc, or even a senior researcher. You will work on a single topic, possibly related to the Stacks project, in a small group together with a mentor for a week. Part of this process will be seeing how one builds new theory from the foundations. There will also be one or two talks per day covering advanced topics in arithmetic or algebraic geometry.

The Stacks project workshop will have some optional activities you won't see at other workshops. Adding references to and finding mistakes in the Stacks Project (and fixing them) as well as activities related to LaTeX use, Git, and GitHub. Overall these will be aimed at helping you contribute efficiently to the Stacks project.

The workshop will be held at Bielefeld University, Germany, August 23 - 25, 2023. The workshop aims to gather young mathematicians in number theory, arithmetic and algebraic geometry, and zeta functions and L-series.

We are also delighted to announce our plenary speakers:

• Yajnaseni Dutta (University of Bonn)

• Joshua Maglione (Otto von Guericke University Magdeburg)

• Markus Schwagenscheidt (ETH Zürich).

For registration and more information, including financial support, please visit the website of ENTR23.

https://www.math.uni-bielefeld.de/entr23/

Deadlines:

June 28, 2023: registration with financial support

July 26, 2023: registration without financial support

If you have any questions, please contact us: [email protected]

QuINGs is a workshop for LGBTQ+ mathematicians who are early career researchers, from PhD students onwards. It is aimed at geometers and number theorists, but researchers in related areas and with an interest in these topics are welcome to apply. The event will take place at the West Lexham retreat in Norfolk for 3 days, from Wednesday, 30 August to Friday, 1 September 2023.

The retreat will be held in person, and we aim to have around 30 participants from the UK and Europe. We will cover accommodation and full board for all participants. A coach service between West Lexham and nearby train stations will be provided (details closer to the event), but we expect participants to cover the rest of their travel costs.

During the 2023-24 academic year the School will have a special program on the p -adic arithmetic geometry, organized by Jacob Lurie and Bhargav Bhatt, who will be the Distinguished Visiting Professor.

The last decade has witnessed some remarkable foundational advances in p-adic arithmetic geometry (e.g., the creation of perfectoid geometry and the ensuing reorganization of p-adic Hodge theory). These advances have already led to breakthroughs in multiple different areas of mathematics (e.g., significant progress in the Langlands program and the resolution of multiple long-standing conjectures in commutative algebra), have uncovered new phenomena that merit further investigation (e.g., the discovery of new structures on algebraic K-theory, new period spaces in p-adic analytic geometry, and new bounds on torsion in singular cohomology), and have made hitherto inaccessible terrains more habitable (e.g., birational geometry in mixed characteristic). This special year intends to bring together a mix of people interested in various facets of the subject, with an eye towards sharing ideas and questions across fields.

The conference will be held in a mixed format. Conference sections: 1. Algebra and Number Theory 2. Applied Mathematics, Informatics and Computing in Environmental Sciences 3. Differential Equations and Applications 4. Geometry and Topology 5. Logic, Language, Artificial Intelligence 6. Mathematical Education and History 7. Mathematical Logic and Discrete Mathematics 8. Mathematical Modeling and Numerical Analysis 9. Mathematical Physics 10. Probability Theory and Statistics, Financial Mathematics 11. Real and Complex Analysis Thematic Minisymposia

The aim of the conference is to bring together researchers at the crossroads of algebra and number theory working on dynamic or asymptotic aspects.

The study of rational points on varieties is a field of special interest to arithmetic geometers. Over the past few decades, many techniques have been used to decide whether a variety over a number field has a rational point or not, and even to describe those points completely. In this program, we are mainly interested in the study of rational points on modular curves.

Elliptic curves, modular forms and modular curves are central objects in arithmetic geometry. Modular curves can be thought of as moduli spaces for elliptic curves with extra level structures. The objective of this program is to understand the theoretical and computational aspects of determining K-rational points on modular curves X_H(K) for various fields K and subgroups H of GL_2(ℤ/Nℤ) for any natural number N.

In the mini-courses, we give an advanced introduction to the theory of rational points on modular curves, under both theoretical and computational aspects. These courses would include an introduction to the geometry of modular curves, their ℚ-rational points, classical and non-abelian Chabauty methods, and related computational aspects. We also attempt to strike a balance between the more advanced topics and the down-to-earth examples.

In the discussion meeting, we wish to bring many experts across the world in the area of arithmetic geometry together to share their ideas and the current state of research that will facilitate future research in this direction. We strongly encourage participation of young researchers.

CAIM series provide a forum for the review of the recent trends in applied and industrial mathematics either from a qualitative or from a numerical point of view.

The conference is about recent developments in Arithmetic Algebraic Geometry. Its central theme is the geometry of Shimura varieties and related spaces in all its facets. Topics to be covered include: Integral models of Shimura varieties and the geometry of their reductions, p-adic and perfectoid geometry, special cycles on Shimura varieties, moduli spaces of Galois representations and (φ, Γ)-modules.

The mathematical theory and practice of both cryptography and coding underpins the provision of effective security and reliability for data communication, processing and storage. This nineteenth International Conference in an established and successful IMA series on the theme of “Cryptography and Coding” solicits original research papers on all technical aspects of cryptography and coding. Submissions are welcome on any cryptographic or coding-theoretic topic including, but not limited to: • Foundational theory and mathematics; • The design, proposal, and analysis of cryptographic or coding primitives and protocols • Secure implementation and optimisation in hardware or software; and • Applied aspects of cryptography and coding. Call for Papers The proceedings will be published in Springer’s Lecture Notes in Computer Science series, and will be available at the conference. Submissions must not substantially duplicate work that any of the authors has published elsewhere or has submitted in parallel to a journal or any other conference or workshop with proceedings. Accepted submissions may not appear in any other conference or workshop that has proceedings. Authors of accepted papers must guarantee that their paper will be presented at the conference and must make a full version of their paper available online. All submissions will be blind-reviewed. Papers must be anonymous, with no author names, affiliations, acknowledgements, or obvious references. Submissions should begin with a cover page containing title, a short abstract, and a list of keywords. The body of the paper should be at most 14 pages, excluding the title page with abstract, the bibliography, and clearly marked appendices. Committee members are not required to review appendices, so the paper should be intelligible and self-contained within this length. The submission must be in Springer’s LNCS format (LaTeX). Submissions not meeting these guidelines risk rejection without consideration of their merits. Submissions should be submitted via https://easychair.org/account/signin?l=wkSzSmtr1OTY2v9Kuv3Kft
Important Dates Submission Deadline: 28 June 2023 Author Notification: 6 September 2023 Proceedings Version Deadline: 20 September 2023

Organising Committee Elizabeth Quaglia, RHUL (Chair) Angelo De Caro, IBM Maura Paterson, Birkbeck Chris Mitchell, RHUL

See conference website

This conference is devoted to the most recent results of Additive Combinatorics. The topic of the conference is aimed to emphasize the rich interactions between additive combinatorics, harmonic analysis and number theory. The conference will bring together some recognized experts of the field, junior researchers (postdoctoral fellows and graduate students), and senior researchers from various aspects of the main topic. Beside the discussion on the recent progress in the field, it is also aimed to initiate interaction and collaboration among the participants.

The biannual ANTS meetings are the premier international forum for the presentation of new research in computational number theory and its applications, including algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.

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.