The purpose of this lecture series is to introduce the audience to basic ideas of specific areas of contemporary pure mathematics. Each lecture shall present an area: where it comes from, where it currently is, where it goes. Lectures will be given by prominent mathematicians twice a year: in the Spring and in the Autumn. Before and after each lecture we will organize reading seminars to prepare the audience for the lecture and to dig further into the topic of the lecture. With the lecturer’s consent, lectures will be recorded, slides and/or lecture notes will be provided if available.

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

The purpose of the school is to present a self-contained proof of a famous theorem of Serre in 1972. This theorem tells us that the representation associated to the Galois action on the p-torsion points of an elliptic curve is surjective for p great enough. This theorem had a very great impact in the field of arithmetic geometry and opened the field to numerous problems that are, for some, still open today. After introducing the students to the topics needed to understand the proof, illustrating the theory through exercises and computer sessions, we will present the proof itself.

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.

This Thematic Month aims to cover topics related to singularity theory of algebraic or analytic spaces, algebraic study of differential equations, and their applications to questions of transcendence. This 5-week program covers different themes that are often not closely related. One of the main objectives is to make them interact. To encourage participants (especially the youngest ones) to attend the entire month and foster interactions outside each one’s expertise zone, the scientific program of each week of the month will consist of courses accessible to non-experts, as well as more specialized presentations. This month will consist of five successive weeks: – Logarithmic and non-archimedean methods in Singularity Theory. The first week will focus on recent results based on methods in logarithmic geometry and non-archimedean geometry in singularity theory. – Foliations, birational geometry and applications. The second week will cover topics in birational geometry, including singularity resolution, MMP (Minimal Model Program), algebraic foliation theory, and local holomorphic dynamics. – Tame Geometry. The third week will address tame geometry in various forms: o-minimality, transseries, Hardy fields, non-archimedean analogs of tame geometry, and their applications to number theory. – Galois differential Theories and transcendence. The fourth week is devoted to differential Galois theory and its applications to questions of functional transcendence and number theory, as well as the study of periods and E and G-functions. – Enumerative combinatorics and effective aspects of differential equations. The last week is dedicated to enumerative combinatorics and certain effective aspects of differential equations, especially applications in enumerative combinatorics of techniques presented in the previous week, or as effective results on topics covered in the preceding weeks.

The workshop is aimed at algebraic and arithmetic geometers curious about the potential application of model theory in their research, as well as at model theorists who are keen to learn how their tools may be extended to answer questions of geometric interest.

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.

K-stability is a central topic in modern complex geometry. It characterises Fano manifolds that admit a Kähler-Einstein metric and provides a good notion of compact moduli space for Fano varieties. The winter school will bring together experts on K-stability who will give 3 mini-courses for PhD students and young researchers with a special focus on explicit problems in dimensions two and three. Along with lecture courses, there will be exercise sessions.

The speakers for the mini-courses are: Hamid Abban (University of Nottingham), Thibaut Delcroix (Université de Montpellier), Elena Denisova (University of Edinburgh), Ruadhaí Dervan (University of Glasgow), Kristin DeVleming (University of San Diego), Erroxe Etxabarri Alberdi (University of Warwick), Kento Fujita (Osaka University), Eveline Legendre (Université de Lyon).

Organising committee: Ivan Cheltsov, Liana Heuberger, Frédéric Mangolte

Scientific committee: Carolina Araujo, Sébastien Boucksom, Simon Donaldson, Chenyang Xu

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

The goal of this workshop is to present a panorama of hot topics, and their recent progress, in arithmetic geometry (incl. p-adic Hodge theory, Shimura varieties and their cohomology, L-functions, Berkovich spaces, homotopy and anabelian geometry, Galois theory, condensed mathematics, vanishing cycles, motivic theory, birational geometry,...). Talks will include introductory presentations for graduate students and for PhD researchers.

A conference on automorphic forms and related topics. The topics include mock modular forms, Maass wave forms, elliptic curves, Siegel and Jacobi modular forms, special values of L-functions, random matrices, quadratic forms, applications of modular forms, and many others. In addition to research talks, the workshop has, in the past years, featured panel discussion sessions. We expect to have many contributed talks and a mix of students and faculty.

Building on the success of the four previous conferences (held in 2017, 2019, 2021 and 2023) this biennial event will aim to draw together the considerable community of researchers and practitioners who use and / or develop innovative mathematics and data driven approaches, relevant to the applications and theory of Operational Research (OR). The conference will be held at the beautiful and easily accessible Conference Centre Aston in Birmingham and will showcase activities from across all areas of OR. We welcome contributions that are empirically motivated and with a focus on application, as well as those that are theoretically driven. The conference will host plenaries from leading international experts, sessions of themed talks, as well as poster sessions, and will provide plenty of opportunities for networking. We look forward to seeing you in Birmingham in April 2025 for a terrific event and to celebrate together the successes of OR! EDI The IMA, the OR Society, and the conference committee strongly support diversity and inclusion. It is our intention to host a conference that is welcoming and inclusive for all, and we will be making active efforts to support the participation of individuals and groups who are under-represented at such academic events and in our discipline more broadly. As part of improving understanding amongst the OR community of the different barriers individuals face, we would like to invite session leaders and individual speakers to include as part of their presentation(s) their own experiences of achievement, inclusion, and exclusion. This will be complemented with a number of focused sessions with key speakers on the particular challenges faced by different groups.

Dates and Location

The conference will begin on the morning of Saturday, May 17 and finish in mid-afternoon on Sunday, May 18. All talks will take place in the ACLC Building. Please note the deadlines below.

• March 17 funding request deadline.
• April 17 abstract submission deadline.
• May 2 registration deadline.

Plenary Speakers

• Anthony Bonato, Toronto Metropolitan University
• Daniel Cranston, Virginia Commonwealth University
• Peter Nelson, University of Waterloo
• Zi-Xia Song, University of Central Florida

About

The series of Cumberland Conferences on Combinatorics, Graph Theory, and Computing began with the intention of meeting a regional need. The conferences bring together internationally known researchers, university and college professors from throughout the southeastern region, some industrial mathematicians and computer scientists, graduate students in these fields, and some undergraduate students. Particular efforts are made to include faculty and students from smaller institutions throughout the region. These conferences are typically held during the month of May, immediately after the end of the spring semester, and the location rotates among universities in the Cumberland region.

Organizing Committee

• Joe Briggs
• Jessica McDonald
• Songling Shan

• Zach Walsh

  Please contact the organizers at zww0009@auburn.edu if you have any questions.

Scientific Committee

• Mark Ellingham
• Dong Ye

The conference "Number Theory, Quantum Chaos and their Interfaces” aims at gathering distinguished researchers working in either of the disciplines to discuss recent research advances in these fields, and serve as a playground for the exchange of ideas between these, rather diverse, research communities. Another purpose of our conference is to provide a solid educational platform for more junior researchers who aspire to conduct research in the relevant fields and expose them to some of the outstanding results and open problems.

This meeting will take place on the occasion of the 60th birthday of Francesco Pappalardi. This event honours his outstanding contributions to number theory, and will also be a recognition of his exceptional activity in promoting mathematics in countries which need it the most. In particular, Francesco is a driving force for mathematical cooperation between Kurdistan Iraq and other countries, including Italy. This conference will be an opportunity to feature outstanding international mathematicians in Erbil and showcase the scientific potential of Kurdistan Iraq.

This is the 37th annual Shanks Conference, focusing on all aspects of constructive function theory and related areas, including orthogonal polynomials, special functions, potential theory, energy optimization, and various problems related to optimization and efficiency.

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.

The summer school is aimed at graduate students in low-dimensional topology. The goal is to make students familiar with the novel techniques in the field that have led to recent advances in our understanding of four-dimensional manifolds.

The program will consist of four mini-courses of 5 lectures each, all accompanied by discussion sessions:

1. Skein lasagna modules (by Mike Willis and Melissa Zhang)
2. Real Seiberg-Witten theory (by Hokuto Konno and Ian Montague)
3. Kontsevich invariants from configuration spaces (by Jianfeng Lin and Danica Kosanovic)
4. Lefschetz fibrations and closed exotic 4-manifolds (by Andras Stipsicz and Zoltan Szabo)

This is a graduate student workshop on discrete groups in topology and algebraic geometry. This includes topics like fundamental groups of varieties and mapping class groups. This is the second week of a three week long thematic program. The conference the following week may also be of interest to graduate students.

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.

The conference will consist of several research talks on topics of current interest in low dimensional topology, including four-manifolds, knot invariants, categorification, gauge theory, and connections to physics.

Confirmed conference speakers: Mina Aganagić, UC Berkeley Aleksei Andreev, U. Zurich William Ballinger, Harvard Inanc Baykur, U Mass Amherst Valentina Bias, SISSA Trieste Eugene Gorsky, UC Davis Matthew Hogancamp, Northeastern Sungkyung Kang, Oxford Marc Lackenby, Oxford Jiakai Li, Harvard Cristina Palmer-Anghel, U. Leeds Qianhe Qin, Stanford Qiuyu Ren, UC Berkeley Alexander Schmidhuber, MIT Masaki Taniguchi, Kyoto University Laura Wakelin, King's College Paul Wedrich, U. Hamburg

This is a conference on discrete groups in topology and algebraic geometry, which includes topics like fundamental groups of varieties and mapping class groups. This is the third week of a thematic program on the topic.

RNT6 will be a remote collaborative research experience for the weeks of June 16 through June 27, 2025. The goal is for participants to learn new math, get to know colleagues, and have a joyful, affirming research experience. You must apply to participate! Team leaders have planned projects for participants to work on during the workshop. You can read more about the 6 projects on our website.

To ensure that all participants can share in this joyful research experience, we ask that all who apply to participate be committed to equity and justice. We will also make time to imagine a different way to do math: How can our profession be transformed to welcome and support everyone?

RNT aims to foster diversity; we particularly encourage applications from historically underrepresented people in mathematics (including Black and Indigenous people, people of color, women, LGBTQ+ members of the community, and people with disabilities), scholars at undergraduate institutions, and in general scholars at all stages of their career who believe they would benefit from this experience. Please share this announcement with any groups, students, post docs, and scholars at all points in their careers who might be interested in participating in this workshop.

The 32nd edition of Géométrie Algébrique en Liberté (GAeL) will be hosted by the Institut de Mathématiques de Toulouse from June 16-20, 2025. The deadline for applications is March 2, 2025, and the application form can be found on the website.

The GAeL conferences are a series of annual meetings organised for and by young researchers in algebraic geometry (PhD students and young postdocs). The objective is not only to introduce the participants to subjects that are likely to be of relevance in the forthcoming years, but also to encourage them to actively participate in the mathematical community at an early stage of their career. Each year we invite 3 senior lecturers to give 4 hour mini courses. The rest of the talks are chosen from among the junior participants and are often the first opportunity people get to speak in front of an international audience. We try to keep the atmosphere very friendly and inclusive.

The senior speakers in 2025 will be:

Ada Boralevi (Polytechnic University of Turin)

Talk: Spaces of matrices with rank conditions and more

Tyler Kelly (Queen Mary University of London)

Talk: A guided tour into the mirror

Daniel Loughran (University of Bath)

Talk: Stacks in birational geometry and number theory

In recent years, there has been an explosion of activity surrounding algebraic points on curves, from many different perspectives. These include the study of measures of irrationality, isolated and parametrized points, computational methods to determine algebraic points, and the arithmetic statistics of algebraic points. In this workshop, we aim to bring together researchers from these diverse perspectives, with the particular goal of developing bridges between them. The workshop will include overview talks on the various perspectives, research talks, an open problem session, and structured time for collaboration.

Flows involving solid particulates are ubiquitous in nature and industry alike. Such flows are found in pharmaceutical production, the chemical industry, the food and agricultural industries, energy production and the environment. Many unsolved problems remain, however. In order to be able to solve problems, granular flows need to be understood so that their behaviour can be controlled and predicted. We are able to describe rapid granular flows, where the particles are highly agitated and there has been some success describing static systems. The intermediate regime, where these two phases meet and coexist, is not as well understood and yet is the most commonly observed behaviour of granular flow. The objective of this meeting will be to interface the two ends of the particulate flow spectrum – those working to understand the fundamentals of granular flows and those attempting to control particulate flows in an industrial setting – to develop solutions to the complex problems presented by dense granular flows. Themes will include dense granular flow, biological systems, self-propelled particles and geological flows, exploring new developments in theoretical analysis and experimental techniques. All attendees will be provided with an opportunity to present recent work and there will be substantial time for discussion, both during the workshop and during the evening! Postgraduate and PhD students are particularly welcomed and oral presentations will reflect the breadth of the field.

The 1st IMA Mathematics Anxiety International Conference will take place at the Centre for Mathematical Sciences, the University of Cambridge, in the heart of the historical city. It aims to bring together researchers, academics, teachers, publishers, policy makers and all interested in the conference theme from all over the world. We particularly welcome submissions from researchers (at any stage) in interdisciplinary fields such as education, psychological and behavioural science, and sociology and envisage a number of themes including: 1. Mathematics anxiety reported by non-specialists i.e., students studying disciplines other than mathematics 2. Gender and other dimensions to mathematics anxiety 3. Concepts linked to mathematics anxiety such as negative emotions, unfavourable attitudes, motivation, communication, self-efficacy, mathematical self-concept, resilience to failure, and autonomy 4. Precursors and impacts of mathematics anxiety 5. Communicating and teaching quantitative courses such as mathematics, statistics, research methods and operational research 6. Pedagogical interventions to support mathematics anxiety sufferers such as blended learning, mindset interventions, those designed to enhance self-efficacy, student-led education, and student-voice 7. Interventions such as brain stimulation 8. Promoting equity, inclusion and diversity (EDI), in mathematics education Proposals for Mini Symposium A mini symposium is a session on a specialist topic, consisting of three to four 20-minute relevant talks. You would be responsible for organising deadlines and contributions. If you are interested in holding a mini symposium then please fill out this form with a proposed title and abstract of less than 300 words. https://forms.gle/ZeqEyfK3FENutPHs5

SUBMISSION DEADLINE 1 August 2024

MIMAR is the premier maintenance and reliability modelling conference. It is an excellent international forum for disseminating information on the state-of-the-art research, theories and practices in maintenance and reliability modelling and offers a platform for connecting researchers and practitioners from around the world. Presentations are encouraged on theory or application of maintenance and reliability: • Maintenance and reliability modelling • Reliability and maintenance engineering • Degradation modelling and reliability assessment • Digital twin for reliability and maintenance • Predictive maintenance modelling and application • Machine learning and data analysis in reliability and maintenance engineering • Reinforcement learning for maintenance decision-making and optimization • Prognostics and health management • Awareness health control • Safety, Security and Risk and management • Fault detection and diagnosis • Expert elicitation • Operational research • Production planning and control • Quality control and management • Resilience engineering • Sustainability • Systems modelling and simulation • Life cycle/performance analysis

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 René 25 conference's purpose is to celebrate the research interests of René Schoof.

Part of a series of conferences: NTDU

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 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 Geometric and Analytic Number Theory conference will bring together world leading researchers to present talks on the latest advancements in the fields of geometric and analytic number theory with a view towards rational points on varieties and counting number fields. Attendees will have the opportunity to engage with pioneering work and connect with peers from around the world, fostering collaboration and knowledge exchange within the number theory community.

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

The 3rd IMA Conference on the Mathematics of Robotics aims to bring together researchers working on all areas of robotics which have a significant mathematical content. The idea is to highlight the mathematical depth and sophistication of techniques applicable to Robotics and to foster cooperation between researchers working in different areas of Robotics. This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM).

Areas of interest include but are not limited to: Topology. Kinematics. Algebraic topology of configuration spaces of robot mechanisms. Topological aspects of path planning and sensor networks. Differential topology and singularity theory of robot mechanism and moduli spaces. • Algebraic Geometry. Varieties generated by linkages and constraints. Geometry of stiffness and inertia matrices. Rigid-body motions. Computational approaches to algebraic geometry. • Dynamical Systems and Control. Dynamics of robots and mechanisms. Simulation of multi-body systems, e.g. swarm robots. Geometric control of robots. Optimal control, soft robotics and other optimisation problems. • Combinatorial and Stochastic Methods. Rigidity of structures. Path planning algorithms. Modular robots. • Statistics. Stochastic control. Localisation. Navigation with uncertainty. Statistical learning theory. • Cognitive Robotics. Mathematical aspects of Artificial Intelligence, Developmental Robotics and other Neuroscience based approaches.

Invited Speakers Martin Pfurner, University Innsbruck, Austria Carme Torras Genís, Institut de Robòtica i Informàtica Industrial (IRI) at the Technical University of Catalonia (UPC) Ileana Streinu, Smith College

The Algorithmic Number Theory Symposium (ANTS) is the premier international forum for the presentation of new research in computational number theory and its applications, devoted to algorithmic aspects of number theory and related fields, including elementary number theory, algebraic number theory, analytic number theory, the geometry of numbers, arithmetic geometry, finite fields, cryptography, and coding theory.

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.