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.

Update: meanwhile this round of invitations has taken place, and the application form has been closed.

This workshop, sponsored by AIM and the NSF, will be devoted to interactions between p -adic geometry and chromatic homotopy theory. In particular, we will focus on the use of period maps and perfectoid methods to study the moduli stack of formal groups. We hope to use these methods to further our understanding of chromatic and transchromatic phenomena in stable homotopy and to see how the chromatic picture motivates and hints at possible novel results in p -adic geometry.

The main topics of the workshop are:

The p-adic geometry of the moduli stack of formal groups and its role in chromatic homotopy theory. Perfectoid methods in p-adic geometry. Period maps and generalized Rapoport--Zink spaces. This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than August 15, 2024. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.

The goal of the conference is to bring together international experts and young researchers working in foliations theory, diffeomorphism groups, 3-manifold topology, bounded cohomology, and 1-dimensional dynamics to share their insights and expertise and to foster collaborations that will lead to progress on important problems in both areas. Furthermore, to navigate the impact of the recent advances in each of these areas on the others, there will be minicourses to introduce young researchers to some of the major recent advances in these areas and there will be problem sessions and informal learning groups to come up with new problems within the scope of current techniques and long term projects between the subfields.

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 

This is a 4-day workshop that aims to explore connections between p-adic Arthur and ABV packets and geometric representation theory/the geometric Langlands program. It will feature talks from experts in both areas. The primary goal of this workshop is to foster new research directions and collaborations.

Preliminary announcement: StolzFest - a midwest topology seminar being organized by myself, Ryan Grady, and Chris Schommer-Pries honoring Stephan Stolz on the occasion of his retirement.

A list of speakers, as well as information on how to register and apply for support, will be forthcoming!

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

Calling all topologists and geometers!

We, the Topologically Allied Conference Organizers of IU Bloomington (TACOs, for short), are pleased to announce that the 2025 meeting of the Graduate Student Topology and Geometry Conference will be held at Indiana University in Bloomington, Indiana! This is the 22nd meeting of GSTGC, and it will be held from Friday, April 11 to Sunday, April 13. If you are unfamiliar, GSTGC is a conference designed by and for graduate students who are interested in topology and geometry. The conference will bring over 120 graduate students from all around the country to Bloomington, and no matter what your interests are, there will surely be both a talk that you’ll find interesting and someone else who shares those interests! There is also an opportunity for graduate students to give talks, either expositional or research (see the registration for details). If you have questions feel free to email us at [email protected]. You can find the conference website here: https://topologyandgeometry.iu.edu/gstgc25/.

Registration for the conference is now open, with a deadline of January 15, 2025. You can register at: https://topologyandgeometry.iu.edu/gstgc25/registration.html

Our plenary speakers are:

1. Sarah Koch (University of Michigan)
2. Mark Powell (University of Glasgow)
3. Inna Zakharevich (Cornell University)

In addition to our plenary speakers, we are also excited to announce the following 6 early-career speakers:

1. Agustina Czenky (University of Southern California)
2. Beibei Liu (Ohio State University)
3. Anibal M. Medina-Maradones (University of Western Ontario)
4. Maggie Miller (The University of Texas at Austin)
5. Carmen Rovi (Loyola University Chicago)
6. Roberta Shapiro (University of Michigan)

Combined, these nine speakers’ research areas cover a wide sweep of mathematics, including: topology of 4-manifolds, Bers-Teichmüller theory, scissor congruence, hyperbolic geometry, hyperbolic manifolds, topological quantum field theories, Kleinian groups, limit sets, links in 3-manifolds, applied and computational topology, homotopy theory, surgery theory, K- and L- theory, manifold theory, quantum algebra, Heegaard Floer homology, geometric group theory, and mapping class groups. There will also be at least 28 short graduate student talks to round out the weekend.

We hope to see you in Bloomington!

TACOs

During this one week summer school, Eleonora di Nezza (Paris, Sorbonne) and Siarhei Finski (Paris, CNRS) will give introductory talks on Kahler geometry to a group of non-experts, primarily composed of students and postdocs. Registration to open soon. The event is part of a special semester on complex geometry at the Renyi Insitute.

Eleonora Di Nezza: Pluripotential theory and L∞ estimates for complex Monge-Ampère equations

Abstract: In these lectures, we introduce and explore fundamental concepts in pluripotential theory, which are essential for studying (degenerate) complex Monge-Ampère equations on Kähler manifolds. We then shift our focus to a novel approach for obtaining L∞ a priori estimates for these equations. This method, which has a "local" character and relies solely on the use of envelopes, was recently developed by Guedj and Lu.

Siarhei Finski: Asymptotic study of submultiplicative filtrations

Abstract: It has long been recognized that the study of manifold degenerations plays a crucial role in addressing many questions in geometry, including the search for canonical metrics. Some degenerations can be understood on the algebraic level through the so-called submultiplicative filtrations, which are certain filtrations on rings respecting the algebraic structure. The most basic example is the filtration on the space of homogeneous polynomials given by the order of vanishing along a subvariety in the projective space.

This course is about the geometric quantization approach to these filtrations, which effectively establishes several results at the crossroads of algebraic and differential geometry. We discuss some applications towards the search of canonical metrics and cover the necessary preliminaries including the Ohsawa-Takegoshi extension theorem, Bergman kernels, and the theory of graded normed algebras.

During this one week summer school, Hans-Joachim Hein (Munster) and Daniele Angella (Firenze) will give series of talks on recent advances on Singular Kahler metrics, and Hermitian geometry respectively. We expect that the audience will consist of advanced graduate students, postdocs and junior faculty working in complex geometry. Both speakers will deliver 4 lectures of 50 minutes, with each lecture accompanied by a problem session. Registration to open soon. This event is part of a special semester on complex geometry at the Renyi Insitute

Daniele Angella: Cohomological properties and Hermitian metrics of complex non-Kähler manifolds

Abstract: the first lectures will provide a survey of the cohomological properties and topological aspects of complex manifolds, as well as canonical metrics on complex manifolds. We will then focus on some analytic problems concerning the geometry of the Chern connection on Hermitian manifolds, such as the existence of metrics with constant Chern-scalar curvature, generalizations of the Kähler-Einstein condition to the non-Kähler setting, the convergence of the Chern-Ricci flow on compact complex surfaces, and the asymptotic behavior of Monge-Ampère volumes of Hermitian metrics in the ddc-class.

Hans-Joachim Heins: TBA

The aim of this workshop is to explore recent advances in Kähler geometry, focusing on non-Archimedean aspects of the Strominger--Yau--Zaslow conjecture, potential-theoretic approaches to singular Kähler-Einstein metrics, geometric estimates for solutions to Complex Monge–Ampère equations, connections with the minimal model program, and Calabi-Yau metrics on non-compact manifolds. Registration to open soon. This event is part of a special semester on Complex Geometry at the Renyi Institute

Speakers:

Enrica Mazzon Yueqiao Wu Ye-Won Luke Cho Jian Song Bin Guo Song Sun Antonio Trusiani Christiano Spotti Chung-Ming Pan Jakob Hultgren Yuchen Liu Vincent Guedj Mihai Paun Charlie Cifarelli Yang Li (TBC) Tristan Collins Annamaria Ortu

The goal of this workshop is to bring together both senior and junior specialists in the fields of almost complex and non-Kähler geometry to present their latest achievements in research. Key topics will include cohomological properties of complex and symplectic manifolds, analytical techniques in non-Kähler geometry, special structures on complex manifolds, deformations of complex objects, topological aspects of complex and symplectic manifolds, and Hodge theory on almost Hermitian manifolds. Registration to open soon. This is event is part of a special semester on complex geometry at the Renyi Institute.

Speakers:

Yakov Eliashberg (TBC) Richard Hind Tom Holt Uros Kuzman Lorenzo Sillary Nicoletta Tardini Scott Wilson Weiyi Zhang Daniele Angella Gueo Grantcharov Nicolina Istrati Slawomir Kolodziej Alexandra Otiman Tat Dat To Valentino Tosatti Misha Verbitsky Vestislav Apostolov Gil Cavalcanti

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.