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.

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

This 2-day special session will be dedicated to a range of mathematical problems related to motion planning algorithms and their properties. A central role is played by the notion of topological complexity (TC), which is a homotopy invariant depending only on the configuration space of the robot that can be studied using diverse tools from a variety of fields, such as geometry, topology, algebra, combinatorics, etc. This session on theoretical and applied aspects of TC and related sectional category invariants aims to bring together scientists from all over the world working on different aspects of motion planning and TC and foster collaboration among them, expose graduate students and junior colleagues to these rich and fascinating areas of research, and identify directions for future work and interaction in these areas.

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.

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 conference aims to offer for young researchers the opportunity to discuss their research with the invited experts and to present their latest scientific contributions and achievements in Algebra, Number theory and other related topics.

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.

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.

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.