CAAGTUS aims to improve contacts and foster collaborations among researchers in Commutative Algebra and Algebraic Geometry located in Arizona and its neighboring states. Its main purposes are to stimulate new directions of research, to provide opportunities to junior researchers to share their work, and to provide a venue for networking and collaboration in the southwest.

Please contact [email protected] if you have any questions.

This conference is devoted to the areas of L-functions and autmorphic forms. In particular, it focusses on the interactions between both fields, which have a long and fruitful history since the fundamental work by Hecke about 90 years ago. The topics will focus on new developments around the areas indicated in the title, as well as establishing and furthering dialogue on new developments at the boundary of these areas. Given the ubiquity of automorphic forms throughout number theory as well as their strong interaction with the field of L-functions, it is very reasonable to expect that both areas will benefit from each other in the future as well. It is likely that this would lead to ideas more broadly useful in other areas of pure mathematics as well as to new types of objects to inspect and new structural questions within both fields.

The relative Langlands program is a generalization of the classical Langlands program from reductive groups to certain homogeneous spaces. The recent work of Ben-Zvi, Sakellaridis, and Venkatesh on relative Langlands duality reveals new connections of the program to algebraic geometry and physics. The summer school and workshop will cover several aspects of the relative Langlands program and explore those new connections.

The conferences will feature a variety of events focusing on recent developments in algebraic topology and their applications to geometry, physics, and data science.

The summer school is dedicated to graduate students and young researchers, and aims to give an introduction to recent techniques and topics of additive combinatorics. The lectures of the summer school will concentrate on recent developments of the polynomial method, some combinatorial methods of additive combinatorics, and the introduction of Fourier analytic techniques connected to them. The main topics will be presented by top researchers of the area.

The lecturers will be Julia Wolf, Christian Elsholtz, Peter Pal Pach, Sean Prendiville.

Lie algebras and superalgebras are among the most important algebraic structures with ample applications in modern mathematics like geometry, harmonic analysis, algebra and representation theory, and number theory. Number Theory is one of the oldest and classical branch of mathematics. This conference aims to bring together researchers working in various areas of algebra and number theory to exchange knowledge and further possible collaborations. The key topics of the conference are as follows:

• Structure and representation theory of finite and infinite dimensional Lie algebras/Lie superalgebras
• Number Theory (Algebraic Number Theory/ Modular Forms/ Automorphic Forms/ Diophantine Equations/ Partition Theory)
• Applications of Lie Theory to Number Theory.

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 Ninth Pacific Rim Conference on Mathematics (PRCM) will be held from Mon, Jun 17 2024 to Fri, Jun 21 2024 at the Darwin Convention Centre, in Darwin (Northern Territory, Australia), hosted by the Mathematical Sciences Institute (MSI), Australian National University (ANU). The PRCM is a broad mathematical event held every few years that covers a wide range of exciting research in contemporary mathematics. Its objectives are to offer a venue for the presentation to and discussion among a wide audience of the latest trends in mathematical research, and to strengthen ties between mathematicians working in the Pacific Rim region. The conference will provide mathematicians with opportunities to engage with international research leaders, established colleagues, and junior researchers.

Algebraic geometry is the field of mathematics which concerns the study of spaces cut out by polynomial equations. This workshop concern the interaction of two important objects in algebraic geometry - the K-groups and the Brauer group. In algebraic geometry, we study spaces via invariants - the procedure of attaching simpler, more "linear" objects to these spaces in the hope of extracting information about them. Both the K-groups and Brauer group are such examples which have had an excellent track record in being both powerful and accessible at the same time. Roughly speaking, the K-groups are built out from \emph{vector bundles} on such a space - a continuous assignment of vector spaces on each point of the space. On the other hand the Brauer groups are built from "twisted" vector bundles.

Both invariants have had a history of interaction and cross-pollination and the goal of the workshop is to bring together researchers in both areas to share their research and pave the way for even more fruitful interaction in the future. We are particularly excited about the prospect of new, field-driving questions to come out from this workshop.

This conference focuses on new and emerging connections between solvable lattice models and special functions on p-adic groups and covering groups, uses of quantum groups, Hecke algebras and other methods to study representations of p-adic groups and their covers, and advances in algebraic combinatorics and algebraic geometry.

The common denominator of the entire opus of Marko Tadić, and his motivating credo according to his own words, is the seek for simplicity in mathematics, in particular in noncommutative harmonic analysis and representation theory. This inspired the title of the conference, and its topic covers different research areas touched by Tadić on his wonderful mathematical journey. These include the representation theory, unitarizability, Arthur packets, automorphic forms, and applications in arithmetic and geometry. The main goal of the conference is to consider the new developments at the cutting edge of the current research in the field, with emphasis on the discussions of the possible new research directions and innovative approaches to the important problems.

The IAS/Park City Mathematics Institute is a three-week residential summer session with a graduate summer school, a research program, an undergraduate summer school, and an undergraduate faculty program. More information can be found on the conference website. PCMI encourages applications from all those with interest in the program, both from the US and internationally. This year it is organized by Benjamin Antieau (Northwestern University), Marc Levine (Universität Duisburg-Essen), Oliver Röndigs (Universität Osnabrück), Alexander Vishik (University of Nottingham), and Kirsten Wickelgren (Duke University).

Tropical geometry is a piece-wise linear geometry which merges ideas from algebraic, symplectic and non-archimedean geometry with tools from combinatorics and convex geometry. Via the process of tropicalization, classical varieties and geometric problems can be connected to the tropical world and, in some cases, solved there. In non-archimedean geometry, the valuation on the underlying field makes the idea of tropicalization particularly natural and powerful. In recent years, this connection has received much attention and exhibited links to diverse topics such as Hodge theory, mirror symmetry and the study of zeta functions. The main goal of this event is to introduce students and young mathematicians to these exciting topics and to foster and strengthen the connections between local researchers and the international mathematical community.

The school will introduce the participants to tropical and non-archimedean geometry via two minicourses given by Ilia Itenberg (Sorbonne Université) and Marco Maculan (Sorbonne Université). Additionally, in the research talks we will explore the latest developments in the field. We hope that this school can serve as the starting point for a local network of researchers and students and therefore can be continued in the coming years by follow-up events of a similar type.

The Young Topologists Meeting is an annual international conference aimed at early-career researchers in topology - both pure and applied - covering the whole breadth of the subject. It serves as a platform for graduate, PhD students, and early postdocs to present their research, exchange ideas, and build international connections.

Previous editions of the conference have been organized by the EPFL, Switzerland, the University of Copenhagen, Denmark, and jointly by the University of Stockholm and the Royal Institute of Technology, Sweden. Next up: Münster, Germany.

A celebration of the mathematics of Eric Friedlander on the occasion of his 80th birthday

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).

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.

The research school is an introductory meeting to the thematic program “Representation Theory and Noncommutative Geometry” to be held at IHP from January to March 2025. The trimester is part of an ongoing effort to bridge two fiels of Mathematics : the representation theory of locally compact groups and the theory of operator algebras. These research domains share origins in harmonic analysis, spectral theory and quantum mechanics but grew in separate directions. Recent progress in representation theory, involving especially non-Riemannian symmetric spaces and spherical varieties, and new tools developed in operator algebras, especially those involving K-theory and the other methods of non-commutative geometry, offer exciting prospects for new work at the interface between the two fields.

Mini-course are:

• Erik P. van den Ban (Universiteit Utrecht): Harmonic analysis of non-Riemannian symmetric spaces
• Tyrone Crisp (University of Maine): Tempered representations from the point of view of Langlands, and from the point of view of operator algebras
• Omar Mohsen (Université de Paris-Saclay): Introduction to hypoelliptic operators and their index theory
• Hang Wang (East China Normal University): Groups C*-algebras and their K-theory

Intertwining operators are ubiquitous in representation theory. Their construction typically requires a considerable amount of analysis, and they often assume an interesting form. For instance, they are frequently pseudodifferential operators associated with pseudodifferential calculi of intense current study in noncommutative geometry. Conversely, in all multiplicity-one decompositions of representations (e.g. the theta correspondence), the essentially unique intertwining operator, or its symbol, should encode important information on the representation-theoretic decomposition.

However, those operators have received little attention from within operator algebra theory. This meeting will be the occasion to present classical and recent aspects of the theory of intertwining operators and explore the connections between operator algebras and representation theory.

Topics of special interest will include:

• Symmetry breaking operators: special families of intertwining operators between representations of a group and a subgroup. These operators, for Lie groups and algebraic groups over local fields, are the subject of intense study in various settings via analytic, algebraic and geometric methods.
• Concrete study of the intertwining operators appearing in the theta-correspondence over local fields, including interpretations coming from operator algebras and noncommutative geometry.
• Applications of intertwining operators in equivariant index theory and noncommutative geometry, such as K-theoretic constructions based on the BGG complex.

The classification of tempered irreducible representations for real reductive groups was completed in the 1970s by Knapp and Zuckerman, following Harish-Chandra's work on the Plancherel formula. But some aspects of the subject are now undergoing a re-examination, following the discovery of new perspectives. C*-algebras and K-theory are valuable tools in Representation Theory, as shown, for instance, by the Mackey bijection. Indeed, it was the Connes-Kasparov isomorphism in K-theory that motivated the search for a natural bijection between the tempered dual of a real reductive group and the unitary dual of its Cartan motion group, as initially suggested by Mackey in the 1970s.

The meeting will focus on recent developments in which K-theoretic ideas have offered new perspectives on the tempered dual for reductive groups or symmetric spaces, and conversely on new approaches to operator-algebraic problems using contemporary tools in representation theory.

Topics will include:

• New approaches to the Mackey bijection through pseudodifferential operator theory, which has itself undergone an extensive conceptual redesign in the past decade, thanks again to C*-algebra and K-theory connections;
• New perspectives on the the Connes-Kasparov isomorphism using Dirac cohomology and cohomological induction;
• Higher orbital intergrals, which make it possible to go beyond the "noncommutative topology of the tempered dual'', hinting at something like the "differential geometry'' of this noncommutative space;
• Study of the Casselman-Schwartz algebras and their K-theory via Paley-Wiener theorems, and connections with the Connes-Kasparov isomorphism;
• C*-algebraic analysis of the tempered dual from the point of view of G as a symmetric space for GxG, and more generally of the tempered spectrum of symmetric spaces.

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