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.

We are pleased to announce the fourth installment of the Upstate New York Topology Seminar (UNYTS)! Binghamton University will be hosting UNYTS 2025 from Saturday March 1st - Sunday March 2nd in Binghamton, New York. The conference is open to everyone, you do not need to be from NY to register or to apply for funding.

The registration form is on the website. Please register by 01/31 to be considered for funding. The deadline to register is 02/15.

Our plenary speakers are:

Carolyn Abbott (Brandeis University)

Christy Hazel (Grinnell College)

Thomas Koberda (University of Virginia)

J.D. Quigley (University of Virginia)

We will also have parallel sessions where individuals can give 20 minute talks. Please register if you are interested in giving one!

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.

Please join us to celebrate Stephan Stolz' retirement and topology and geometry in the Midwest! We thank the National Science Foundation (NSF) and the Department of Mathematics, School of Science, and Office of Research at Notre Dame for support.

Registration by March 1 is requested and early funding decisions will be made on February 15 (an additional round of funding decisions will be made on March 1).

Confirmed Speakers:

• Dan Berwick-Evans, UIUC
• Holt Bodish, UIUC
• Owen Gwilliam, UMass (Amherst)
• Michael Joachim, Münster
• Ralph Kaufmann, Purdue
• Martina Rovelli, UMass (Amherst)
• Maru Sarazola, Minnesota
• Laura Schaposnik, UIC

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

Women In Number theory and Geometry (WINGs) 2025 is the fifth edition of an annual retreat aimed at early-career mathematicians. Our goal is to help cultivate a sense of community among women and other under-represented genders in number theory and geometry, as well as share their research interests. This year, WINGs will be held at the Mercure Haydock Hotel from March 31st to April 3rd 2025. Accommodation and meals will be provided for all participants.

Speakers include: Sara Angela Filippini (Università del Salento) Ailsa Keating (University of Cambridge) Margarida Melo (Università Roma Tre) Eugenia Roșu (Universiteit Leiden) Rosa Winter (UniDistance Suisse) In addition, there will be two talks about opportunities beyond academia, including one by a speaker from Journal of Number Theory. There will also be social activities to encourage interaction between participants, a session of lightning talks, and 20-minute talks given by participants, in the aim of learning about each other’s research interests and practising presentation skills. You can apply here until February 9th 2025. We aim to give you a response by the end of the following week. For updates and further information, please see our website and if you have any questions, don’t hesitate to contact us at [email protected].

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

Affine Lie Algebras, Quantum Groups, and Their Representations is a workshop supported by the Croatian Science Foundation under the installation research project Quantum Current Algebras and Their Representation Theory. The workshop topics include all areas related to the representation theory of affine Lie algebras and quantum groups, such as combinatorial identities, quantum vertex algebras, etc.

The next installment of URiCA, Upcoming Researchers in Commutative Algebra (previously KUMUNU Jr), will take place on May 3rd and 4th at the University of Nebraska-Lincoln. The goal of this conference is to showcase research done by graduate students and postdocs and promote interaction among junior researchers in commutative algebra. There will be seven 50-minute invited talks as well as a poster session and a call for collaboration/open problem session. Please use the links below to register and note the registration deadline for funding is March 23rd.

List of invited speakers:

Bek Chase (Purdue University)

Caitlin Davis (University of Wisconsin-Madison)

Karthik Ganapathy (University of California, San Diego)

Nawaj KC (University of Nebraska-Lincoln)

Feiyang Lin (University of California, Berkeley)

Anastasia Nathanson (University of Minnesota Twin Cities)

Xianglong Ni (University of Notre Dame)

Please don't hesitate to contact the organizing team with any questions.

We really hope to see you at the conference!

Conference Homepage

Registration Link

09E2IhYGzxDAj5qWgthnnvYiYlTZazt3ZE4w/viewform

The 2025 Georgia International Topology Conference https://topology.franklinresearch.uga.edu/2025GITC will take place May 19 - May 30, 2025 at the University of Georgia in Athens, Georgia. This will be the ninth in a series of octennial conferences at the University of Georgia that started in 1961.

We ask all participants to register at the website.

Speakers: Mohammed Abouzaid (Stanford), Ian Agol (UC Berkeley), Daniel Alvarez-Gavela (Brandeis), John Baldwin (Boston College), Rachael Boyd* (University of Glasgow), Roger Casals (UC Davis), Julian Chaidez (University of Southern California), Dan Cristofaro-Gardiner (University of Maryland), Oliver Edtmair (ETH Zurich), Tobias Ekholm (Uppsala University), Joshua Greene (Boston College), Pazit Haim-Kislev (IAS), Jonathan Hanselman (Princeton), Kristen Hendricks (Rutgers), Amanda Hirschi (Sorbonne Université), Ko Honda (UCLA), Bruce Kleiner (NYU), Hokuto Konno (University of Tokyo), Danica Kosanović (ETH Zurich), Marc Lackenby (Oxford), Joan Licata (Australian National University), Beibei Liu (Ohio State University), Bruno Martelli (Università di Pisa), Thomas Massoni (MIT), Maggie Miller (UT Austin), Allison Miller (Swarthmore College), Jin Miyazawa (Kyoto University), Lisa Piccirillo (UT Austin), Mark Powell (University of Glasgow), Alan Reid (Rice University), Semon Rezchikov (Princeton), Laura Starkston (UC Davis), Matt Stoffregen (Michigan State University), Luya Wang (IAS), Michael Willis (Texas A&M), Ian Zemke (University of Oregon) * to be confirmed

Scientific Committee: Danny Calegari (University of Chicago), David Gabai (Princeton), Ursula Hamenstädt (University of Bonn), Robert Lipshitz (University of Oregon),Rachel Roberts (Washington University), Paul Seidel (MIT), András Stipsicz (Alfréd Rényi Institute of Mathematics), Ulrike Tillmann (Oxford)

Local Organizers: Akram Alishahi, Eduardo Fernández Fuertes, David Gay, Peter Lambert-Cole, Gordana Matic, Mike Usher

Hello everyone,

We are delighted to announce the Talbot Workshop 2025, mentored by Alexander Kupers and Nathalie Wahl! Please see below for the details of the workshop and a link to the application.

Please share this message with anyone you think would benefit from attending.

Best regards, The Talbot Workshop organizers (Maxine Calle, Alex Karapetyan, and Eunice Sukarto)

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2025 Talbot Workshop: Homological Stability Mentored by: Alexander Kupers and Nathalie Wahl Dates: May 26 - June 1, 2025 Location: TBA, but somewhere in the US

Application link: https://forms.gle/KaStAZurFQ5LDB1z5 Application deadline: Feb 2, 2025 More details can be found on the website: https://sites.google.com/view/talbotworkshop/home

What: The Talbot Workshop is a one week learning workshop for roughly 35 graduate students and a few postdocs. Most of the talks will be given by participants, and will be expository in nature.

Topic description: Many groups and spaces come in families depending on a parameter: configuration spaces depend on the number of points considered, mapping class groups of surfaces on the genus of the surface. For such families, it often happens that the homology stabilizes as this parameter goes to infinity. Moreover, computing the stable homology frequently turns out to be easier because other tools can be used. In recent years, combining homological stability results with stable computations has become a powerful tool in algebraic topology and robust machinery for proving homological stability theorems has been developed. In this workshop we aim to introduce the participants to this circle of ideas.

Outline: This workshop will explain how to prove homological stability results through examples, such as symmetric groups, configuration spaces, mapping class groups, and others, and how to use them in conjunction with stable computations. The homological stability machines that we will cover are Quillen’s classical inductive approach and a more recent approach using Ek-algebras. Both machines have as input connectivity results for simplicial complexes and we will also see how such results are proved.

Background: The workshop will be aimed towards graduate students with a basic understanding of algebraic topology, including spectral sequences and classifying spaces.

Talbot is meant to encourage collaboration among young researchers, with an emphasis on graduate students. We also aim 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. As we are committed to promoting diversity in mathematics, we especially encourage women, minorities, and underrepresented groups in mathematics to apply.

If you have any questions, please do not hesitate to email the organizers at talbotworkshop (at) gmail (dot) com.

Conference Quasiweekend III - Twenty years on collects together experts, from all fields of mathematics, using quasiconformal methods, especially in complex dynamics, geometric function theory, geometric group theory, analysis on metric spaces. Previous conferences in this series, Quasiweekend and Quasiweekend II – Ten years after, took place in 2005 and 2015, respectively, in Helsinki. With Quasiweekend III we celebrate mathematical legacy of Juha Heinonen -- initiator of this conference series -- in the broad field of quasiconformal analysis.

QTMART is a workshop on algebra and representation theory taken in a broad sense, run by and for queer and trans mathematicians. It aims to showcase the research done in this field by this community and bring together senior researchers, junior researchers, and graduate students to discuss topics of common interest in a non-competitive environment.

Alongside the workshop, an exploratory program on queer mathematics and inclusion will take place. The activities of the program will focus on exploring what it means to do mathematics as a queer or trans mathematician, and if there is such a thing as queer mathematics. It will also address the question of how to make the working culture and environment more welcoming and diverse, and will aim to initiate concrete actions in this regard.

This workshop welcomes talks by early-career researchers. Please indicate on the application form if you would like to give a talk and on what topic.

The event is open to everyone accepting the community agreement (which will be based upon Oberwolfach's Statement of Respect and Collegiality https://www.mfo.de/about-the-institute/guiding-principles/equality-diversity-inclusion/statement-for-respect-and-collegiality, taking suggestions from the participants into account). However, priority in assigning talks will be given to self-identifying queer and trans mathematicians, and some activities in the program will be reserved for this group.

Plenary Speakers:

• Chris Bowman (University of York)
• Ian Musson (University of Wisconsin-Milwaukee)
• J. Daisie Rock (FWO, KU Leuven, UGent)
• Beth Romano (King's College London)
• Dani Tubbenhauer (University of Sydney)

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.

We are hosting two events, each one a week long:

• A summer school on Galois Representations, Relative Langlands Duality, Beyond Endoscopy, and Relative Trace Formulae. 4-9 August 2025.
• A number theory conference. 11-15 August 2025.

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 Annual International Conference of the Georgian Mathematical Union was established in 2010 and has been held traditionally at Batumi Shota Rustaveli State University. Batumi is the city of Georgia and the capital of the Autonomous Republic of Adjara. It is located along the coast of the Black Sea in the southwest region of Georgia. In accordance with recent developments, the conference has been conducted in a hybrid format since 2021.

The purpose of the conference is to bring together mathematicians from various fields to present their original research results and provide opportunities to establish new connections within the fields of pure and applied mathematics, as well as science, engineering, and technology. The conference also provides valuable networking opportunities for you to meet great personnel in these fields.

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.