Conferences and Meetings on Geometry and Topology

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers, random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

Courses and Events for Math Students and Early Career Researchers,    Algebra

The Fields Institute

This is the 17th in the sequence of annual workshops traditionally held in the month of May at Nipissing University. Among our participants, we expect to have a number of prominent mathematicians from Canada, USA and abroad. The purpose of these workshops/seminars has been mainly to provide opportunities to researchers to learn a new area as well as opportunity to collaborate. As a result of these workshops there have been numerous collaborations dealing with problems in dimension theory, geometric topology, C*-algebras, set-theoretic topology, continuum theory and complex dynamics.

CIRM – Centre International de Rencontres Mathématiques

CONFERENCE

SMCG is sponsored by the National Science Foundation and by The University of Texas at Dallas.

University of Iowa, Department of Mathematics

Some datasets are too small for standard statistical/data analysis to accurately characterize the data. Others are extremely large and data size reduction methods may be needed. One solution is to use topological data analysis to simplify and/or visualize data. This workshop will include both tutorials and research talks on topological techniques for visualizing data.

topological data analysis, TDA mapper, computational topology, persistent homology

This workshop will focus on geometric aspects of the Swampland Program, with a special emphasis on the interelation between general properties of quantum gravity and algebraic geometry. The workshop aims to bring together theoretical physicists and geometers, in order to explore the many connections between fields which have recently emerged in the study of the Swampland Conjectures. This activity is a joint initiative of the Institute of Mathematical Sciences (ICMAT) and the Institute of Theoretical Physics (IFT) in Madrid. The workshop will be held at the CFTMAT in Madrid, C/ Nicolás Cabrera, nº 13-15, Campus de Cantoblanco, UAM, 28049 Madrid SPAIN. If possible, this activity will take place on-site.

High Energy Physics, Particles and Fields,    Astronomy, Astrophysics and Cosmology

Casa Matemática Oaxaca (CMO)

CIRM – Centre International de Rencontres Mathématiques

RESEARCH SCHOOL

This conference is in the primary algebraic research areas of Michael J. Larsen: Algebraic Number Theory, Arithmetic Geometry and Group Theory. The talks will be aimed at a broad swath of algebraists at all levels. It is our hope to foster interactions across these areas in the spirit of Michael’s own body of work. There will be a contributed talks session (20-30 minutes) for young mathematicians and a professional development workshop.

Algebra,    Number Theory, Arithmetic

Greg Friedman, Texas Christian University

The 39th Annual Workshop in Geometric Topology will be held online June 6-8, 2022. The featured speaker will be Jessica Purcell of Monash University, who will give a series of three one-hour lectures on using hyperbolic geometry as a tool to study 3-manifolds and knot theory. Participants are invited to contribute talks of 20 minutes. Contributed talks need not be directly related to the topic of the principal lectures. Title and abstracts must be submitted by May 6. Talks will be selected in a way that provides a balanced collection of topics and respects the historical traditions of the workshop. Earlier responses may be given some preference. Applicants will be notified whether their talk has been accepted by May 23.

Phone: [817-257-6343];     Email: g.friedman@tcu.edu

3-manifolds, hyperbolic geometry, knot theory, geometric topology

The Fields Institute for Research in Mathematical Sciences

Algebra,    Analysis

The Langlands program has seen many exciting geometric developments recently, linking with developments in homotopy theory, p-adic geometry and derived algebraic geometry, to name a few. This conference will bring together established and junior researchers in these areas.

This workshop will focus on geometric aspects of the Swampland Program, with a special emphasis on the interelation between general properties of quantum gravity and algebraic geometry. The workshop aims to bring together theoretical physicists and geometers, in order to explore the many connections between fields which have recently emerged in the study of the Swampland Conjectures. This activity is a joint initiative of the Institute of Mathematical Sciences (ICMAT) and the Institute of Theoretical Physics (IFT) in Madrid. The workshop will be held at the CFTMAT in Madrid, C/ Nicolás Cabrera, nº 13-15, Campus de Cantoblanco, UAM, 28049 Madrid SPAIN. If possible, this activity will take place on-site.

High Energy Physics, Particles and Fields,    Astronomy, Astrophysics and Cosmology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

University of Milano-Bicocca

The second conference of the GABY series includes three mini-courses:

1. "An introduction to p-modular representations of p-adic groups" by Ramla Abdellatif, University of Picardie Jules Verne,

2. "Growth of groups and of group endomorphisms" by Anna Giordano Bruno, University of Udine, and

3. "Hyperbolicity and generalizations" by Davide Spriano, University of Oxford.

Some funds will be available for accommodation, and participants will have the opportunity to give a talk or present a poster. Abstracts for contributed talks and funding requests must be submitted by March 31st; the registration is open till May 1st. Additional information can be found on the conference website.

Email: gaby@unimib.it

group theory, algebra, p-modular representations, p-adic groups, growth of groups, hyperbolicity.

Algebra,    Group Theory

INdAM

The workshop will be devoted to the study of surfaces with special metrics with singularities of conical type. In particular it will focus on the case of spherical metrics, namely Riemannian metrics of curvature 1. Such metrics have been studied from many points of view, using tools coming from synthetic geometry, complex analysis and partial differential equations. The aim of the meeting is to bring together people with different backgrounds to discuss recent developments, techniques and open questions in the areas of spherical surfaces with conical points, projective structures with singularities and their monodromy, solutions of the singular Liouville equation, polyhedral spherical surfaces, polygonal linkages.

Email: mondello@mat.uniroma1.it

Special metrics with conical singularities, singular Liouville equation, complex projective structures, moduli spaces, representation spaces, monodromy

A conference on the interactions between geometry, arithmetic, and groups will be held at the University of Texas, Austin, June 20-24, 2022, celebrating the accomplishments and influences of Alan W. Reid.

Group Theory,    Number Theory, Arithmetic

Mathematical Sciences Research Institute (MRSI) and the FORTH-IACM Institute in Crete

This summer graduate school is a collaboration between MSRI and the FORTH-IACM Institute in Crete. The purpose of the school is to introduce graduate students to some of the most important geometric evolution equations. This is an area of geometric analysis that lies at the interface of differential geometry and partial differential equations. The lectures will begin with an introduction to nonlinear diffusion equations and continue with classical results on the Ricci Flow, the Mean curvature flow and other fully non-linear extrinsic flows such as the Gauss curvature flow. The lectures will also include geometric applications such as isoperimetric inequalities, topological applications such as the Poincaré onjecture, as well as recent important developments related to the study of singularities and ancient solutions.

Courses and Events for Math Students and Early Career Researchers,    Analysis

The Fields Institute

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

The Fields Institute

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

ETH Zürich, FIM - Institute for Mathematical Research

CCAAGS-22 aims to bring together researchers working in the creative mixture of combinatorial and computational ideas in applied algebraic geometry. Part of this event will celebrate Bernd Sturmfels and his contributions to the field.

Graph Theory and Combinatorics,    Algebra

Western Washington University

Join us for a five-day workshop hosted by Western Washington University. Mornings will be dedicated to talks, and in the afternoons, participants will work on open problems related to 4-manifold trisections in small groups.

Email: zupan@unl.edu

trisections, 4-manifolds, low-dimensional topology

The Fields Institute, Canada

The 2022 AGA V meeting aims to provide an exchange of ideas and techniques between young researchers and established specialists accross this field that is currently boosting with energy. Given the recent results and techniques in asymptotic geometric analysis, we hope that this meeting will be a catalyst for new directions of development. Particular encouragement to attend is given to young researchers who will be invited to give a talk or to present in the poster session.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Algebra

CIRM – Centre International de Rencontres Mathématiques

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Courses and Events for Math Students and Early Career Researchers,    Algebra

Mathematical Sciences Research Institute (MRSI)

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Courses and Events for Math Students and Early Career Researchers,    Algebra

Mathematical Sciences Research Institute (MRSI) and University of Oxford

The purpose of the summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of non-smooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.

Courses and Events for Math Students and Early Career Researchers,    Analysis

University of Vienna, Department of Mathematics

The Fields Institute

This conference is in celebration of Professor Aiden Bruen's 80th birthday, to acknowledge and honour Professor Bruen's contributions to geometry, design theory, coding theory, and combinatorics at large. Professor Bruen's research covers many areas, including geometry, error-control codes, and cryptography.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Faculty of Mathematics and Physics of the Charles University, the Institute of Mathematics of the Czech Academy of Sciences and the Faculty of Information Technology of the Czech Technical University

Algebra,    Analysis

Texas A&M University

The topic of this concentration week is metric geometry, to be held in-person at Texas A&M University in College Station, Texas. The conference will feature a variety of short research talks by participants as well as three mini-courses. Talks in any area broadly construed as metric geometry are welcome. Such areas include, but are not limited to, random geometries, metric graph theory, geometric group theory, and geometric functional analysis. The main goals of the conference are to provide a platform for participants to circulate their research achievements, expose them to new research topics, and open doors for future collaborations.

Part of the 2022 Texas A&M Workshop in Analysis and Probability

Mathematical Sciences Research Institute (MRSI)

The summer school will lead participants from appealing, simple-to-state problems at confluence of combinatorics, geometry, and topology to sophisticated topological methods that are required for their resolution. In recent years topological methods have found numerous novel applications in mathematics and beyond, such as in data science, machine learning, economics, the social sciences, and biology. The problems we will discuss are particularly well-suited to rapidly put students in a position to approach related research questions.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

ICTP

Geometry and Topology have seen spectacular recent developments, including the solution of classical problems. As a consequence, the established picture of how various parts of these areas fit together is evolving rapidly. On the topological side, among the topics that have progressed are: four-manifolds obtained as knot traces; knot concordance and homology cobordism, Stein fillings. On the Floer homology side, we have powerful new computational methods and new invariants of embedded graphs and webs. On the more analytic side, we have new compactness results and potential new invariants.

Interplay of 3-dimensional and 4-dimensional Topology, Floer homology theories and associated invariants, Khovanov homology, Geometric and analytic aspects of gauge theoretic equations

We are pleased to announce that the 20th International Conference on Random Structures and Algorithms "RS&A201/2022" will be held at the Institute of European Culture in Gniezno, 1-5 August, 2022. The conference, organized biennially since 1983, brings together probabilists, discrete mathematicians and theoretical computer scientists working in probabilistic methods, random structures and randomized algorithms.

Algorithms and Data Structures,    Probability and Statistics, Game Theory

BIRS - Banff International Research Station

The summer school will give a self-contained introduction aimed at beginning graduate students, and introduce participants to the latest developments. In addition to attending the lectures, students will meet in intensive problem and discussion sessions that will explore and extend the topics developed in the lectures.

Courses and Events for Math Students and Early Career Researchers,    Graph Theory and Combinatorics

Mathematical Sciences Research Institute (MRSI)

The goal of this summer school is to give students crash courses in tropical and logarithmic geometry, with a particular focus on the applications in enumerative geometry and moduli theory.

Courses and Events for Math Students and Early Career Researchers,    Algebra

University of California Davis

Each day will be dedicated to a specific topic. Mornings will consist of three research talks on this topic, focusing on recent developments and useful techniques for doing research. The first talk will be given by one of the leading mentors, the other two talks will be given by participants. Afternoons will consist of research working groups, where participants break into groups to do research on open problems.

ICTP

Geometry and Topology have seen spectacular recent developments, including the solution of classical problems. As a consequence, the established picture of how various parts of these areas fit together is evolving rapidly. On the topological side, among the topics that have progressed are: four-manifolds obtained as knot traces; knot concordance and homology cobordism, Stein fillings. On the Floer homology side, we have powerful new computational methods and new invariants of embedded graphs and webs. On the more analytic side, we have new compactness results and potential new invariants.

The conference is intended as an appreciation of the contributions of Tomasz Mrowka

Sabanci University, Istanbul

Finite geometry is a branch of mathematics situated within discrete mathematics and combinatorics, which is concerned with the study of discrete objects using geometric and combinatorial techniques. Typical examples are Galois geometry (the study of objects embedded in projective spaces over finite fields), and finite incidence geometry (axiomatic study of geometries). Foundational work and major contributions can be credited to Beniamino Segre (Galois geometry) and Jacques Tits (Buildings). Finite geometry has strong connections with algebraic coding theory, graph theory, finite group theory, algebraic geometry over finite fields, design theory, finite fields, algebraic combinatorics, and more. Applications are typically found in the theory of error-correcting codes (e.g. MDS codes, MRD codes), and cryptography. With the rapid development of computer algebra systems, research problems in finite geometry are often a combination of a theoretical and a computational approach, and theories/conjectures are usually motivated/supported by computational evidence. The aim of this school is to introduce some of the main concepts in finite geometry, to increase the audience's knowledge of the many results and conjectures, to introduce some techniques available in computer algebra systems to approach problems, to provide an opportunity for PhD students to discuss and share their own projects, and to enable mathematicians in this area to meet and plan scientific collaboration.

University of California Davis

Each day will be dedicated to a specific topic. Mornings will consist of three research talks on this topic, focusing on recent developments and useful techniques for doing research. The first talk will be given by one of the leading mentors, the other two talks will be given by participants. Afternoons will consist of research working groups, where participants break into groups to do research on open problems.

Texas A&M University, College Station, TX

The goal of this in-person conference is to bring together researchers studying nonsmooth spaces from different perspectives, facilitating the exchange of ideas, problems, and mathematical techniques. Perspectives coming from probability, analysis on metric spaces, and Banach space theory are of particular emphasis. Interactions among these different fields have already proven exceptionally fruitful. For example, a famous fractal space constructed by Laakso to answer a purely metric measure theoretic question inspired a similar construction (pictured above) eventually used to characterize superreflexivity in Banach spaces. Later, uniform q-convexity, a quantitative refinement of superreflexivity, was metrically characterizing using Markov convexity – a measurement of the diffusivity of Markov processes in a metric space. Together with many more examples, these show how shared geometric objects play important roles in each subject while being viewed through different lenses. More interactions of this type will be necessary to solve important open problems, such as analyst’s traveling salesman-type problems and metric characterizations of other Banach properties.

Probability and Statistics, Game Theory,    Analysis

Valdosta State University

The Department of Mathematics at the Valdosta State University is pleased to announce the VSU CBMS Conference on Topological Data Analysis and Persistence Theory which will be held from August 8 to August 12, 2022. The main goal of this conference is to provide an introduction to topological data analysis (TDA) and persistence theory (PT) to a broader audience. TDA and PT are relatively recent methods useful for finding important features in large data sets using ideas from traditionally theoretical branches of mathematics such as algebra and topology.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Graph Theory and Combinatorics

University of Copenhagen

This masterclass aims at offering an entrance door to the wide field of relative trace formulas, from different perspectives and with different applications ranging from representation theory to analytic number theory. Relative trace formulas are fundamental tools, and we bring together world-class experts to make them shine. The school will consist of three lecture series supplemented by problem sessions and further talks all related to different aspects of this area. The masterclass is mostly intended to graduate students and young researchers, but everyone interested in relative trace formulas is welcome!

Number Theory, Arithmetic,    Courses and Events for Math Students and Early Career Researchers

Mathematical Institute, University of Oxford

This summer school will feature three short courses, each comprised of five lectures. The school is aimed at a wide audience of graduate students and early career researchers; the requisite background material from model theory and o-minimality will be covered at the start of the week. Daily afternoon tutorial sessions will allow students time to work on problems and to ask questions.

Algebra,    Courses and Events for Math Students and Early Career Researchers

UiT The Arctic University of Norway

This focused workshop is intended as a meeting place for mathematicians and physicists interested in related areas of Differential Geometry, Representation Theory and Theoretical Physics motivated by Supersymmetry. The goal of the workshop is to present new results as well as create an open environment for a fruitful exchange of ideas.

Ryerson University

The 34th Canadian Conference on Computational Geometry (CCCG 2022) will be held in Toronto, Ontario, Canada on August 25-27, 2022, at Ryerson University. The Canadian Conference on Computational Geometry (CCCG) is a forum to disseminate and discuss new theoretical and applied results in discrete and computational geometry. CCCG focuses on the design of efficient algorithms, the development of software, and the study of the mathematical foundations of computational problems whose formulations involve geometric constraints. The field of computational geometry is motivated by problems from a broad range of application areas, as diverse as computer graphics and animation, computer vision, computer-aided design and manufacturing, geographic information systems, pattern recognition, wireless communications, robotics, protein folding, urban planning, graph drawing, or statistical analysis.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will bring together experts and active researchers in geometric partial differential equations that are working on problems in conformal geometry and related topics. The goal is to to take advantage of the pattern of rich interactions between these research fields.

Asymptotic analysis on asymptotically hyperbolic manifolds, The anti-de Sitter/conformal field theory correspondences in mathematical physics correspondences in mathematical physics, Partial differential equations in conformal geometry

Calculus, Differential Equations and Integration,    Mathematical Physics

ICMAT

The Fall Workshops on Geometry and Physics have been held yearly since 1992, and bring together Spanish and Portuguese geometers and physicists, along with an ever increasing number of participants from outside the Iberian Peninsula. The meetings aim to provide a forum for the exchange of ideas between researchers of different fields in Differential Geometry, Applied Mathematics and Physics, and always include a substantial number of enthusiastic young researchers amongst the participants.

Applied Mathematics (in general),    Mathematical Physics

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Aspen Center for Physics

We plan to bring together experts in condensed matter, quantum field theory and topology to forge new advances at the interface of these subjects, with mutually reinforcing ideas from physics and mathematics in vigorous exchange and contraposition as part of an intense workshop.

Mathematical Physics,    High Energy Physics, Particles and Fields

Universität Duisburg-Essen

This event is part of the Research Training Group 2553 "Symmetries and Classifying Spaces: Analytic, Arithmetic and Derived" (funded by the German Research Foundation DFG).

Sheffield Algebraic Geometry & Mathematical Physics Group

This conference will be centred on recent progress on BPS invariants, which sit at a focal point of interaction between enumerative algebraic geometry (Donaldson-Thomas theory), quantum field and string theory (BPS spectra of N=2 theories), and the theory of complex differential equations with irregular singularities. The conference will provide a window into current topical research and it is conceived as an invitation targeted primarily at graduate students and non-specialists in the field. The meeting will feature in particular four introductory survey lectures by world-leading experts, as well as more advanced research talks. We also aim to provide ample opportunity of collaboration and discussion in a workshop-style setting, usually with no more than 4 hours of talks each day.

Jagiellonian University, Kraków, Poland

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Algebra

The Fields Institute

The study of metric spaces with upper and lower sectional curvature bounds is a rich and well developed subject that goes back some 60+ years to the work of A.D. Alexandrov. It has a wide variety of applications and connections with various areas of geometry such as geometric group theory, classical Riemannian geometry of manifolds with various sectional curvature bounds, integral geometry and the study of spaces with lower Ricci bounds.

CIRM – Centre International de Rencontres Mathématiques

Università degli Studi di Milano

Casa Matemática Oaxaca (CMO)

Spectral geometry, calculus of variations, and elliptic PDEs are a central part of modern analysis and geometric analysis. At the same time, these have important applications in other sciences, in particular mathematical physics. This workshop aims to bring together leading experts in these fields to discuss the main developments and open questions. The main research themes of the workshop include shape optimisation and sharp functional inequalities, Robin boundary value problems, Steklov eigenvalue problems, and properties of eigenfunctions and solutions to elliptic PDEs.

Mathematical Physics,    Analysis

The Simons SCGP-Workshops---21_webCenter for Geometry and Physics, Stony Brook University

Over the past ten years tremendous progress has been achieved in quantum field theory thanks to the realization that symmetries can be interpreted in terms of the action of topological defects on the space of operators. This gives a generalization of the notion of symmetries, explicitly realized in many instances exploiting Lagrangian field theory techniques, uncovering a rich and unexpected landscape of physical effects. The product rules for symmetry defects are organized by higher structures, and moreover examples of non-invertible symmetry defects have been found, indicating that global symmetries are categorical. Thanks to geometric field theory methods in string theory, an understanding of generalized global symmetries for field theories without a conventional Lagrangian formulation is at reach in terms of appropriate defect groups, determined exploiting the dynamics of membranes in the string theory realization.

High Energy Physics, Particles and Fields,    Mathematical Physics

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Algebra

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

University of Regensburg

The aim of this workshop is to bring together researchers in bounded cohomology theory and related fields and discuss recent developments. In addition to the invited talks, there will be opportunities for researchers to give contributed talks and ample time for discussions and collaboration.

bounded cohomology, simplicial volume

Research Group Metric Geometry, Karlsruhe Institute for Technology

The main aim of this workshop is to bring together experts in Complex Geometry, Geometric Group Theory, Low dimensional topology, and their interactions. Historically, interactions between these field have proven very fruitful and have lead to an array of interesting research an results. We expect that this workshop will deepen existing and foster new interactions. To achieve this there will be an attractive selection of talks by experts in the different areas, as well as ample time for discussions.

The conference is aimed at exchanging on the latest results in the research areas of Diophantine Geometry and L-functions. This will be the opportunity to celebrate the accomplishments of Marc Hindry in these fields, in the occasion of his 65th birthday.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to exploring and solidifying connections between the mathematical study of higher categories and the exotic physics of topologically ordered systems.

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

Algebra,    Courses and Events for Math Students and Early Career Researchers

Institut Henri Poincaré (IHP)

Probability and Statistics, Game Theory,    Scientific Computing and Data Science

CIRM – Centre International de Rencontres Mathématiques

High Energy Physics, Particles and Fields,    Analysis

Casa Matemática Oaxaca (CMO)

CIRM – Centre International de Rencontres Mathématiques

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

The Fields Institute

Structures having Ricci curvature bounded either from below and/or from above in some sense have been at the center of intense investigations in the last ten years, the reason being the deep effect at the geometric, analytic and probabilistic level that this sort of assumption carries. The study of such bounds and their geometric and analytic effects therefore attracts a constellation of mathematicians with a diverse set of skills and backgrounds. The conference aims at gathering specialists from different sectors to foster communication between various (sub)fields of research. We aim at covering the synthetic side of the story, the non-commutative one, the regularity of Ricci-limit spaces and geometric evolution problems.

Mathematical Sciences Research Institute (MRSI)

The workshop will focus on the interaction between homotopy theory and symplectic topology and low dimensional topology that is mediated by Floer theory. Among the topics covered are foundational questions, applications to concrete geometric questions, and the relationship with finite dimensional approaches.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to recent developments in the study of Lagrangian Floer theory of symmetric products of Riemann surfaces and Hilbert schemes of symplectic 4-manifolds, and their applications both to symplectic topology and the low dimensional topology.

The Fields Institute

This workshop will further explore interactions between set theory, Ramsey theory, and the geometry and dynamics of Polish groups. An emphasis will be placed on the large scale geometry and dynamics of homeomorphism groups, mapping class groups of spaces of infinite type, and of automorphism groups of countable structures. It will also include work on automatic continuity in the context of transformation groups.

Mathematical Sciences Research Institute (MSRI)

This workshop will highlight talks on various aspects of Diophantine Geometry. The goal of the workshop is to bring together researchers at different career stages and of various backgrounds in order to establish new collaborations and mentoring relationships.

Mathematical Sciences Research Institute (MSRI)

This workshop will feature expository lectures about current developments in Diophantine geometry. This includes the uniform Mordell—Lang for rational points on curves, the Andre—Oort conjecture for special points on Shimura varieties, and effective results via Chabauty method, and related topics in Arakelov theory, unlikely intersections, arithmetic statistics, arithmetic dynamics, and p-adic Hodge theory.

Algebra,    Number Theory, Arithmetic

Mathematical Sciences Research Institute (MSRI)

The topical workshop will be dedicated to Shouwu Zhang, to mark the occasion of his 60th birthday, and to honour his numerous beautiful contributions to the theory of Shimura varieties and special values of L-functions. It will highlight cutting edge work on topics such as the construction of Euler systems; relations between special cycles on Shimura varieties and L-functions, such as generalized Gross-Zagier formulas and the Tate conjecture; the construction of Galois representations in cohomology; and related aspects of the theory of automorphic forms.

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

Recent developments in several disparate areas make it a pressing and opportune time to confront the interplay between topology, symmetry and interactions. This conference will catalyze the discussion on this broad topic by highlighting a burst of recent advancements, both theoretical and experimental, along this direction. An important goal is to enhance cross-talk between the weakly and strongly correlated communities interested in topology that have not yet had adequate interactions with each other. The conference will bring participants up to speed in this rapidly growing field and sharpen the central questions that will be discussed in the remainder of the associated program.

Condensed Matter Physics and Materials,    Mathematical Physics

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

Nanoparticle assembly is a hierarchical approach to functional materials. It operates at the mesoscale where elementary building blocks still feel their atomic nature and can profit from quantum function but at the same time are flexible enough in shape and interaction to permit high structural complexity. The realization of nanoparticle assemblies requires the convergence of and communication among several scientific disciplines: chemistry for synthesis, materials science for characterization, chemical engineering for up-scaling, and physics for a theoretical description and quantum phenomena. The goal of the conference will be to provide a coherent view of the current state of the field, bringing together researchers with different expertise and background. It should catalyze the development of new methods, both theoretical, computational and experimental, and define the basic science in this field. A focus will be recent developments but also a look forward: What should be the focus for the next decade and beyond? What are they key physics concepts that need to be developed and from where will the new game-changing technological advances emerge?

Clusters, Nanomaterials, Graphene and Fullerenes,    Mathematical Physics

CRM / Université de Montréal

Understanding the geometry of the finitely generated subgroups of a group informs our understanding of that group significantly. For example, some hyperbolic groups enjoy the property that every finitely generated subgroup is quasi-convex. Groups which are incoherent and groups which are algebraically fibered do not have this property. This conference aims to explore some of the many directions in this field, including quasi-convexity in other contexts.

CRM / Université de Montréal

This workshop focuses on several themes related to the fundamental groups of 3-manifolds. The themes include: the theory character varieties, Thurston norm polytopes and fibrations, orderability, profinite rigidity, and variations on the Cannon conjecture. The first week of the workshop will feature mini-courses by Ian Biringer (Boston College), Michelle Chu (Minnesota), Nathan Dunfield (Illinois-Urbana), and Daniel Groves (Illinois-Chicago). The second week will be devoted to research talks.

CRM / Université de Montréal

The mini-courses and research talks will address several themes, including: nonpositively-curved cube complexes, median spaces, (coarsely) Helly spaces and groups, and various combinatorial notions of nonpositive curvature. The first week of the workshop involves mini-courses by Elia Fioravanti (MPI Bonn), Thomas Haettel (Université de Montpellier), Nima Hoda (ENS Paris), Nir Lazarovich (Technion). The second week will be devoted to research talks.

Group Theory,    Graph Theory and Combinatorics

Renyi Institute

Affine algebraic geometry studies algebraic subvarieties of complex affine space C^n. A major contributor to this field in the following generation is Shulim Kaliman, whose work this conference is intended to honor on the occasion of his 70th birthday. The conference will feature 10-12 prominent plenary speakers from among Kaliman's research colleagues, such as Mikhail Zaidenberg, with additional talks that include younger researchers. Kaliman's work draws from an impressive range of tools, not only in algebra and geometry but also in topology and analysis. The title of the conference reflects this: the embeddings, automorphisms, structure and topology of affine varieties are themes running throughout Kaliman's work. The talks will focus on current trends within these themes, and will not only bring together active researchers in the field but will also seek to engage students and early career researchers in the study of affine algebraic geometry.