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 "Dawn · Midi · Yofuke International Seminar" (DMY) is a hybrid and topic-oriented seminar with a focus on homotopy arithmetic geometry, between USA-France-Japan. This session:

Homotopy Galois Action

1. Sep. 08 (Colloquium) Arithmetic of fundamental groups, by C. Rasmussen (Wesleyan)
2. Sep. 09: Galois actions on pro-p fundamental groups of once-punctured CM elliptic curves, by S. Ishii (Keio)
3. Sep. 22: Arithmetic of elliptic curves related to Ihara's program, by C.McLeman (Michigan Flint)
4. Sep. 23: Galois l-adic polylogarithms, by D. Shiraishi (Tokoyo Univ. Sciences)

On website: Program & references and Registration

This workshop, sponsored by AIM and the NSF, will be devoted to new developments in wall-crossing for enumerative invariants of abelian categories, with a focus on identifying promising applications.

This workshop, sponsored by AIM and the NSF, will be devoted to new developments in wall-crossing for enumerative invariants of abelian categories, with a focus on identifying promising applications.

The year 2024 will mark the 30th anniversary of the resolution of Fermat’s Last Theorem, one of the most celebrated applications of the Langlands program. In the three decades since, many seemingly disparate areas of research within the Langlands program have blossomed, some inspired by the ideas introduced in the proof of Fermat, some with a more geometric flavor, made possible in part by the theory of perfectoid spaces, and some with a more representation-theoretic flavor.

The categorical Langlands program is an emerging conceptual framework that encompasses these disparate areas of research: the $p$-adic Langlands program, the geometrization of the local Langlands correspondence, and the cohomology of Shimura varieties in its many incarnations, just to name a few. This workshop brings together architects of the categorical Langlands program in the number field setting as well as emerging experts. The goals are to take stock of the state of the art in the field, and to chart a course for future developments, and to provide mentorship and support to a diverse group of early-career participants.

Due to limited space, in-person attendance at this meeting is by invitation only. However, we welcome applications for virtual participation in the workshop. If you are interested in virtual attendance, please apply at the following link: https://forms.gle/kPz15Cnj8CGKKkJy9.

For more information, please consult the conference web page:

With this conference we want to celebrate the 12th anniversary of the collaborative research centre (CRC) „Higher Invariants: interactions between arithmetic geometry and global analysis“. The aim of the conference is to highlight the current trends and future prospects of higher invariants and higher categorical methods as studied in our CRC.

The list of speakers is:

Federico Binda
José Burgos Gil
Dustin Clausen
Hélène Esnault
Hokuto Konno
Manuel Krannich
Akhil Mathew
Thomas Nikolaus
Viktoriya Ozornova
Maxime Ramzi
Charanya Ravi
Tomer Schlank
Peter Scholze
Georg Tamme
Inna Zakharevich

The ``Dawn · Midi · Yofuke International Seminar'' (DMY) is a hybrid and topic-oriented seminar with a focus on homotopy arithmetic geometry, between USA-France-Japan.

Talks of this session:

• Oct. 07: Colloquium :: Arithmetic of nonabelian Chabauty, by N. Dogra (King's London)
• Oct. 08: An Oda-Tamagawa criterion for fundamental groupoids of hyperbolic curves, by A. Betts (Cornell)
• Oct. 13: Explicit methods in Chabauty-Kim theory for rational points, by S. Hashimoto (Brown)
• Oct 14: Motivic aspects in genus 0, by I. Dan-Cohen (Ben-Gurion)

Registration for Zoom link and future annoucements on website.

This three-day conference celebrates the 60th birthday and influential career of Igor Kriz, whose groundbreaking contributions have shaped modern perspectives in homotopy theory and its interactions with physics. This special event will gather leading researchers and early-career mathematicians from around the world for a series of stimulating lectures, discussions, and collaborations.

The conference will spotlight cutting-edge developments in equivariant and motivic homotopy theory, as well as their deep connections to mathematical physics and symplectic topology. Invited talks by prominent experts will explore recent advances and open problems at the rich interface of these fields, honoring the wide-ranging impact of Kriz’s work.

We warmly invite you to be part of this celebration of mathematics, community, and visionary research. If you plan to attend, please complete the registration form below. We have some funding available for graduate students and junior researcher participants. If you wish to apply for travel funding, you may do so on the registration form.

Holomorphic-topological (HT) field theories form a fascinating class of quantum field theories. These theories combine features of topological quantum field theories (TQFT) and conformal field theories (CFT).

Due to the mixed holomorphic-topological nature of such theories, they create interactions between TQFT data (e.g., algbras, monoidal categories, etc) and CFT data (e.g., chiral algebras and chiral categories). This leads to exciting new mathematical structures, and connections to integrable systems, quantum topology and many other areas of mathematics. Recently. much progress has been made on the representation-theoretic aspects of HT theories. Examples include:

1. (Shifted) Poisson vertex algebras and their quantizations are constructed from local operators in HT theories.

2. Dimensional reduction of 4d HT theories lead to integrable systems and solutions of quantum Yang-Baxter equations.

3. 4d N=2 theories are linked to representation theory of K-theoretic Coulomb branches, cluster algebra categorifications, wall crossings and elliptic stable envelops.

4. New examples of chiral algebras and their dualities are derived from boundary conditions and dualities of 3d HT theories.

Moreover, many interesting TQFTs are given by deformations of holomorphic-topological theories. Examples include topological twists of 3d N=4 and 4d N=2 theories. These theories have attracted considerable attention in recent years for their connections to 3d mirror symmetry and the Langlands program. Some of these TQFTs only admit Lagrangian descriptions as HT QFTs, and therefore studying HT theories offers a possible approach for understanding these non-Lagrangian TQFTs.

This conference will focus on the representation-theoretic aspects of HT theories, particularly:

1. Chiral algebras arising from observables of HT QFT.

2. Quantum algebras, including Yangians and quantum affine algebras, and their relation to HT theories.

3. Chiral categories and OPE of line operators in HT theories.

4. Deformation of HT theories and their relation to chiral algebra deformations.

5. Relation between various HT theories under dimensional-reduction.

We aim to bring together leading mathematicians and physicists, to inform each other about the recent progress made in this area.

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Limited funding is available to support travel and lodging of early-career researchers. Due to space constraints, all participants must register and we may not be able to accept all applicants. For fullest consideration for funding and participation, please as soon as possible. For more information, please refer to the In Person Registration option on the Registration page of this website.

This workshop, sponsored by AIM and the NSF, will be devoted to non-Archimedean methods in complex geometry. The main topics for the workshop are: K-stability and canonical metrics, Degenerations of Calabi–Yau manifolds and the SYZ Conjecture, and Algebro-geometric and tropical aspects of degenerations.

The eighteenth Annual Binghamton University Graduate Combinatorics Algebra and Topology Conference (BUGCAT Conference) will meet November 15-16 at SUNY Binghamton. Graduate students at all levels, as well as faculty, are invited to give a 30-minute talk; talks may be expository or on current research. This year, we have three distinguished keynote speakers: Caroline Klivans (Brown University), Kim Ruane (Tufts University) and Matt Zaremsky (University of Albany)

For more information, visit: https://sites.google.com/binghamton.edu/bugcat-website/home

This workshop, sponsored by AIM, the NSF, the Topos Institute, and the US NSF Center for Analysis and Prediction of Pandemic Expansion, will consider how category-theoretic foundations for modeling as decision support for multidisciplinary collaboration might advance insights into pandemic science. Multidisciplinary modeling is extremely useful and also extremely difficult (for many reasons). By taking the very concept of "building a model" as itself a sort of model, and phrasing this in the formal mathematical language of (double) category theory, we can develop systems that greatly improve our capabilities for collaborative modeling.

The workshop will bring together a wide range of research communities: category theory, software engineering, dynamical systems, data science, epidemiology, infectious disease modeling, medical geography, behavioral psychology, social and urban networks, and economics.

Thematic Month on the Langlands program

The conference consists of five lectures by Professor Bjorn Poonen of the Massachusetts Institute of Technology on “Undecidability related to arithmetic geometry”. This is supported with talks by experts and structure group discussions/workshops. We have some NSF support for participants that register early.

see conference website

The conference honours the work of John F. (Rick) Jardine, a professor at the University of Western Ontario. Over his more than 40 year career, Rick has made foundational contributions to homotopy theory, K-theory, and topological data analysis, in particular shaping the current landscape of homotopical algebra.

Homotopy limits and colimits are a fundamental tool in homotopy theory, with applications to topology, geometry, and algebra. The event is aimed at graduate students, postdocs, and early-career researchers who want to learn more about this topic.

See the website for more details.

We are delighted to announce the 17th Algorithmic Number Theory Symposium (ANTS-XVII), to take place in Groningen on 6 - 10 July 2026.

The ANTS meetings, held every two years since 1994, are the premier international forum for the presentation of new research in computational number theory and its applications. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.

We have also opened a call for papers for an associated proceedings volume. We strongly encourage anyone with research related to the topics above to submit a paper by 17 January 2026. As in previous editions, for each accepted submission, at least one author must present the work at the conference.

Plenary speakers:

• Eva Bayer-Fluckiger (École Polytechnique Fédérale de Lausanne, Switzerland)
• Peter Koymans (Utrecht University, Netherlands)
• Sabrina Kunzweiler (Inria Bordeaux, France)
• Aurel Page (Inria Bordeaux, France)
• John Voight (University of Sydney, Australia)

Important dates:

• Paper submission deadline: 17 January 2026
• Conference: 6 - 10 July 2026

For more information, such as the programme committee or details on the call for papers, see the web page, https://www.antsxvii.org. In due time this web page will also contain travel and registration information, and information on our sponsors.

See conference website

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.