Conférences  >  Mathématiques  >  Géométrie et topologie

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.

CIRM – Centre International de Rencontres Mathématiques

American Mathematical Society

Diophantine equations are systems of polynomial equations solved over integers or rational numbers. Diophantine geometry is the study of Diophantine equations using ideas and techniques from algebraic geometry. It is one of the oldest subjects of mathematics and the most popular part of number theory connecting it to algebraic geometry.

The goal of this session is to explore recent developments in the theory of arithmetic geometry and with special focus on curves and Jacobian varieties. We intend to bring together mathematicians, working on this area of research, from the USA and from Europe encouraging further cooperation and discussion. We will especially encourage younger mathematicians and graduate students and newcomers in the area.

The session will focus on the following topics, but we will be open and welcoming to talks which do not fall in the list of topics below.

Tél.: [2477607447];     Email.: shaska@risat.org

algebraic curves, Abelian varieties, isogenies, torsion points, Tate modules, heights, weighted heights, height conjectures, Brauer group, K3 surfaces, Kummer varieties, Néron-Tate heights, Minimal models, minimal height, Néron models, Brauer-Siegel theorem, Mordell-Lang conjecture, Mordell-Weil, Bombieri-Lang conjecture, Vojta’s conjecture

Théorie des nombres, arithmétique,    Algèbre

In this workshop we will study surfaces in 3-manifolds from several perspectives. Each participant will be asked to give a 2-hour lecture.

Potential subtopics include but are not limited to: Virtual Haken, Character variety methods, Foliations, Minimal surfaces, Totally geodesic surfaces

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

The goal of this workshop is to create an opportunity for researchers in low-dimensional topology to encounter new research in the area, to establish new collaborations and reestablish existing ones, and to compensate for the relative isolation inflicted by the Covid-19 pandemic. One particular goal is to help researchers at earlier stages of their career to form connections, as these people were heavily affected by travel restrictions in 2020-21 and an inability to build networks. Together, ju- nior and senior researchers will exchange techniques, attack outstanding conjectures, and develop new directions of study.

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.

Geometric Group Theory

Théorie des groupes,    Algèbre

The Erdős Center semester on "Singularities and low dimensional topology" will kick off with a 2-phase winter school to introduce early stage researchers (MSc students, PhD students, postdocs) to some key concepts in singularities and low dimensional topology.

CIRM – Centre International de Rencontres Mathématiques

The conference will be the closing event of the ANR project1 ChroK, Chromatic homotopy and K-theory. A major goal is to bring together a wide range of researchers in the above fields, from advanced PhD students to leading experts, to share recent advances in research, discuss the challenges ahead, and to develop collaborations and shape long-term projects.

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

We aim to unite the study of structure and dynamics by fostering conversations between researchers who use the HHD in areas including economics, game theory, statistical physics, and machine learning. We also aim to promote collaboration between industrial and academic teams using the HHD.

University of Copenhagen

The masterclass will present spectacular recent advances in motivic filtrations and their applications. To briefly put this in context, every cohomology theory, in arithmetic geometry and elsewhere, should arise as the graded pieces of a motivic filtration of some localizing invariant, algebraic K-theory and topological cyclic homology being notable examples. The definition of the appropriate motivic filtrations, however, was long elusive. Voevodsky received the 2002 Fields medal, in part, for his definition of the motivic filtration of algebraic K-theory of schemes smooth over a field. This definition, however, was based on algebraic cycles, which are notoriously difficult to handle. In 2018, Bhatt, Morrow, and Scholze defined a motivic filtration of p-complete topological cyclic homology in an entirely different way, which is much simpler and easier to employ elsewhere, and this breakthrough has led to numerous advances.

CIRM – Centre International de Rencontres Mathématiques

The purpose of this school is to familiarise advanced Master’s students, Ph.D. students and early career researchers with the central themes of research in arithmetic geometry,and teach them both classical and state-of-the-art tools in the field. The research school is an introduction to the conference SAGA, “Symposium on Arithmetic Geometry and its Applications” and it consists of four 3-day mini-courses, taught by teams of internationally renowned researchers, who are known to be excellent teachers.

Théorie des nombres, arithmétique,    Cours et évènements pour étudiants en mathématiques

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.

CIRM – Centre International de Rencontres Mathématiques

The conference will focus on the recent developments in arithmetic geometry, its applications and explicit and computational methods in approaching the relevant problems. There will be four main axes around which all talks will be organised: Automorphic forms and moduli spaces; Galois representations: geometric and constructive, modularity; Rational points and obstructions; Effective methods in arithmetic geometry. Leading experts in the field have accepted to contribute to the conference, making it a particularly interesting event.

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.

Algèbre,    Théorie des nombres, arithmétique

The University of Sydney

This conference focuses on categorification and its applications in representation theory. Categorification is something of an art, where one mathematical object is replaced with another richer, and often categorical, one that often reveals deeper structual properties. Important examples of categorification in representation theory include the geometric categorifications of Ginzburg, Lusztig and Nakajima, which realize quantum groups and their representations in a geometric framework, and Khovanov's categorification of the Jones polynomial, and Elias and Williamson's proof of the Kazhdan-Lusztig positivity conjectures and Soergel's conjectures.

This conference brings some of the top experts in this field to discuss recent advances. The conference consists of:

A workshop, February 6-10, with three lecture series on different aspects of categorification

The main conference, February 13-17.

Email.: asilata.bapat@anu.edu.au, andrew.mathas@sydney.edu.au, dtubbenhauer@gmail.com, oded.Yacobi@sydney.edu.au

Categorification, representation theory, categorical algebra, knot homologies, categorified quantum groups, Soergel bimodules

The workshop focuses on four main speakers, each giving a 4-hour mini-course on a topic in Geometric Group Theory. Their lectures present a panoramic overview over some important developments in their field with the goal to enable the participants to actively participate in the new directions of research emerging from these developments.

Théorie des groupes,    Cours et évènements pour étudiants en mathématiques

CIRM – Centre International de Rencontres Mathématiques

The conference will be devoted to the study of algebraic varieties over finite fields from an algebraic geometry point of view as a combinatorial one and their applications to coding theory.

Featured topics will include theoretical, effective and algorithmic aspects of point counting as well as algebraic geometry codes constructed from curves and higher dimensional varieties.

ICERM

Discrete periodic Schrodinger operators describe the behavior of individual electrons in "ideal" crystals in the tight-binding model of solid state physics. Spectra of such operators have the usual band-gap structure, and the corresponding dispersion relations are algebraic varieties. In the 1990's Gieseker, Knorrer, and Trubowitz used toroidal compactifications to solve questions such as irreducibility of Bloch and Fermi varieties and the density of states, for a class of mono-atomic models. Their work showed that while spectral theory is focused on the real part of the Bloch variety, the study of complex singularities and compactifications is crucial for describing formation of bands and gaps. After a gap of 30 years, spectral theory is again interacting with algebraic geometry. Recently, W. Liu gave an algebraic method to obtain more general proofs of irreducibility for Fermi surfaces, Kravaris used free resolutions to study density of states, and Kuchment and coauthors used toric varieties and numerical nonlinear algebra to study spectral edges. These and other developments have led to the realization that many open questions in spectral theory may be studied using modern tools in algebraic geometry. These include the relation of reducibility/irreducibility with physical symmetries of the crystals, the structure of spectral band edges, and Dirac cones. These methods can also be applied to quantum graphs, such as graphene-type structures, and to obtain existence and non-existence theorems for embedded eigenvalues. The goal of this workshop is to bring together experts from spectral theory, mathematical physics, and algebraic geometry to understand, apply, and advance these new methods and interactions. A significant aspect of these reemerging interactions involves computation. A key recent development in algebraic geometry is computation, both symbolic and numerical. Computation and experimentation using tools from algebraic geometry have already been important in two recent papers by Sottile on this subject, and we expect it to become a useful tool for studying periodic operators. Speakers in this workshop are firmly rooted in the uses of computation and experimentation in applications of Algebraic Geometry, and many are familiar with exploiting the atmosphere and facilities of the ICERM to initiate collaboration.

Program Staff;     Tél.: [1-401-863-5030];     Email.: programstaff@icerm.brown.edu

Algèbre,    Mathématiques appliquées (en général)

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

The central problem in algebraic geometry is to classify so-called algebraic varieties: geometric shapes cut out by algebraic equations. Algebraic varieties are parametrized by certain moduli spaces (parameter spaces whose points correspond to these different varieties) and the geometry of these moduli spaces encodes the ways of continuously deforming these shapes. Furthermore, classification questions for algebraic varieties often boil down to understanding the geometry of these moduli spaces. In the past few years, powerful new tools have been developed in moduli theory but there are still many open questions, especially in higher dimensions. This workshop will bring together a diverse group of researchers in moduli theory in order to apply these new tools to explicit examples of the classification of higher dimensional algebraic varieties and their moduli spaces and push our understanding of higher dimensional algebraic geometry to new frontiers.

ICTP

The main scientific theme of the workshop is counting BPS states in physical systems associated to 3-manifolds or links, and interpretation of these counts as old or new topological invariants.

Although the ideas behind such relations appeared already in the late 90s, the recent years have seen some dramatic new developments. The goal of this learning workshop is to bring together physicists and mathematicians who are experts in the subject and also those who would like to enter the field. In particular, the talks will be given both by senior scientists and junior ones, including PhD students who only recently began working on the subject. The talks will be supplemented by dedicated discussion sessions where experts can answer questions that will be submitted by participants to the moderator in advance, or asked directly during the session.

"Z-hat" and F_K invariants counting BPS states in 6d superconformal field theory compactified on 3- manifolds, and their relation to known invariants of 3-manifolds and links -- Knots-quivers correspondence and its generalization to knot complements -- Properties of generating functions counting BPS states, including: modularity, relation to characters of (logarithmic) Vertex Operator Algebras, GW/DT invariants

Physique mathématique,    Physique des hautes énergies, des particules et des champs

Banach Center & Polish Academy of Sciences – Institute of Mathematics

The main scope of the research group is: topological methods in estimating the minimal number of vertices which are necessary to triangulate a manifold or an action of finite group $G$ on a manifold. Another goal is the topological complexity and its computation and relation to the problem of minimal triangulation. We assume to complete two already started works in the form of publications and begin new join projects.

Mathématiques appliquées (en général),    Mathématiques numériques

University of Pennsylvania

The Geometry and Strings 2023 conference is a continuation of the series of conferences that stem from the meetings "Physics and Geometry of F-theory", established in 2012. In 2019 the conference was renamed "Geometry and Strings 2019" in order to signify the broadening of the range of topics so as to attract a broader community with an interest in the interplay between geometry and string theory.

Max Planck Institute for Mathematics, Bonn; Germany

Following a line of research culminating in the works of Weil, Eichler, Shimura and Taniyama, then further pushed by the emerging of the Langlands program, many deep and fruitful bridges between automorphic forms and algebraic geometry have been explored and led to spectacular results. During the fifty years span from the proof of Ramanujan’s conjecture on the discriminant modular form, using the validity of the Weil conjectures in algebraic geometry over finite fields, to the recent proof of the Sato-Tate conjectures for elliptic curves over CM fields, using automorphic machinery, it has been clearly established that the interaction between these two fields has amazing applications in both directions. Moreover, several guiding principles in this area have been inspired by the philosophy of motives, which has now developed into a mature theory providing not only heuristics, but concrete and sophisticated new tools to attack problems. The aim of the conference is to present the state of the art of the field by gathering leading experts at the crossroads of automorphic forms, arithmetic geometry and representation theory, and celebrating Günter Harder’s influence on these topics.

ICMS - International Centre for Mathematical Sciences

There is a history of fruitful links between low-dimensional topology and number theory, going back at least to Mazur's observation that primes in number rings can be viewed as analogues of knots in a 3-manifold. More recently, the introduction of arithmetic gauge theory by M. Kim and collaborators paves the way to further bring ideas from theoretical physics to bear on fundamental problems in number theory and arithmetic geometry. This conference aims to explore this exciting new direction, and the links between number theory, topology and physics in general, with a particular focus on the role played by gauge fields as a unifying framework.

Théorie des nombres, arithmétique,    Physique mathématique

Families of p-adic automorphic forms are well studied objects of arithmetic geometry since the pioneering work of Hida and Coleman. Their study resulted in the definition of geometric objects, called eigenvarieties, that parametrize systems of Hecke eigenvalues of p-adic automorphic forms. Conversely, the rich geometry of these varieties gives insights about p-adic (and thereby also about classical) automorphic forms. Recent techniques from perfectoid geometry, locally analytic representation theory and the point of view of the p-adic Langlands program give new insights and impulses. The spring school will give an introduction to both p-adic automorphic forms and eigenvarieties as well as the necessary background in p-adic analytic geometry. The courses will be complemented by research talks that will focus on recent developments in the area.

Algèbre,    Cours et évènements pour étudiants en mathématiques

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

The researchers participating in this workshop come from several mathematical subdisciplines, including combinatorics, algebraic geometry, and theoretical computer science. Their work and common interest here is to investigate new interactions between discrete mathematics, algebra, algebraic geometry, tropical geometry, and combinatorial algorithms. Some participants have collaborated before in smaller groups, but this meeting will provide an opportunity to work together more intensively. Several recent mathematical breakthroughs will be highlighted in the workshop, including the recent resolution of some long-standing open problems about graphs and matroids. These breakthroughs used a surprising combination of interdisciplinary techniques which the organizers expect to have exciting further applications.

Théorie des graphes et combinatoire,    Théorie de l'information, fondations de l'informatique

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

This workshop focuses on interactions between real algebraic geometry, operator theory, and optimization, with a particular emphasis on the interrelations with the Koopman operator approach to optimization and control. It is an outgrowth of three previous successful MFO workshops held in 2014, 2017, and 2020, themselves a continuation of a long series of MFO workshops on real algebraic geometry which started in 1984. The mathematical topics of interest include sum-of-squares representations of non-negative polynomials in commutative and non-commutative algebras and the dual problem of moments, including various applications, and the use of linear infinite dimensional methods in nonlinear dynamical systems.

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.

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

Northwestern University, Evanston, IL

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

The workshop will bring together some of the world's top experts and early career mathematicians working at the interface of Stochastics and Geometry, broadly understood. Through expository talks and research presentations, the workshop will give a vibrant overview of the most recent developments in the interaction between analysis, geometry and stochastic analysis. The focus of the workshop will be different approaches to random processes in geometric settings, with emphasis on problems on heat kernel analysis on finite- and infinite-dimensional manifolds, often equipped with degenerate geometries, as well as random matrices and non-commutative probability and geometric rough paths. Another objective of the workshop is to identify fundamental open problems in this area that are motivated by mathematical physics and other potential applications. We plan to maintain geographic diversity and invite many promising early career mathematicians.

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.

Physique de la matière condensée et des matériaux,    Physique mathématique

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

A shape is "convex" if for any two points in the shape, the line segment connecting them does not pass out of the shape. This fundamental notion is the beginning of a wide array of ideas in geometry and analysis, leading to much more general theories in which "line segment" is replaced by other more flexible objects, or where "convexity" is determined by properties only analogous to the classical ones. Such generalized ideas of convexity are particularly important in the mathematical fields of symplectic topology and complex geometry. While links between the symplectic and complex versions of complexity have been recognized for some time, recent years have begun to see the emergence of an even closer relationship in which techniques and tools from one field can shed light or inspire new directions in the other. This workshop will include specialists in complex analysis, symplectic geometry, contact topology, and smooth manifold theory, with the goal of introducing researchers in these fields to the techniques, ideas, and open problems in the others, united by the theme of convexity in various forms. Students and emerging researchers will be grouped with established scholars to establish new professional connections and research directions, and groups will work together to begin to bring their various tools together toward the solution of major open problems in the field.

CIRM – Centre International de Rencontres Mathématiques

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

High-quality randomness is a valuable commodity in computation, experimentation, and discovery. This workshop focuses on randomness as a resource within real and complex algebraic geometry. The program highlights three current research trends: understanding the statistical properties of fundamental geometric invariants, developing randomized algorithms for symbolic and numerical calculations in algebraic geometry, and exploring the synergies between algebraic geometry and data analysis. This workshop will, for the first time, bring together a wide range of mathematicians interested in random algebraic geometry.

Banach Center

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

Soon after Einstein postulated the General Theory of Relativity, he introduced what he called his "greatest mistake'', the so-called cosmological constant. Solutions of the Einstein equation with cosmological constant are now called Einstein manifolds, and despite Einstein's pessimistic view, play key roles both in mathematics and physics. Quasi-Einstein manifolds are generalizations of Einstein manifolds, which include not only Einstein manifolds but Ricci solitons, warped product Einstein manifolds, static Einstein manifolds, and other special manifolds. These are important in many areas of modern mathematical research, including Ricci flow, collapsed Gromov-Hausdorff limits, and general relativity. This workshop will examine progress in seemingly disparate fields which in fact share a common nexus, namely quasi-Einstein manifolds or the related notion of Bakry-Emery Ricci curvature. Problems to be discussed include the classification problem for near horizon geometries (of black holes), for Ricci solitons and for static Einstein metrics, as well as the fundamental gap problem for Laplace and Schroedinger operators, and the formulation and application of synthetic Bakry-Emery Ricci curvature.

This conference will focus on the interactions between manifolds and submanifolds of dimensions 1, 2 and 3 and their relations to topological, geometric, and group theoretic questions in a celebration of the accomplishments and influences of Yair Minsky.

Théorie des groupes,    Algèbre

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

The influence of networks in our daily life is swiftly increasing. Examples of physical networks are those that involve passenger transfers or simply the connections between different computers to send information. On the other hand, virtually, we find social networks, such as Facebook, Instagram and so on, which are widely used and known by a high percentage of the world's population. Currently, the construction of networks that optimize certain real hypotheses, is a vast area that provides mathematical problems whose answers solve real situations.

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?

Agrégats, nanomatériaux, graphène et fullerène,    Physique mathématique

The Fields Institute

The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds, begun by S. Lefschetz, and well established by the late 1950's. Many of the important Artinian graded algebras appear as cohomology rings of an algebraic variety or manifold, though recent important developments have demonstrated important cases of the Lefschetz properties beyond such geometric settings (such as Coxeter groups or matroids). This renews interest in understanding the Lefschetz property, and Artinian algebras that admit them, systematically.

Algèbre,    Théorie des graphes et combinatoire

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.

ICERM

This workshop focuses on the interplay between dynamics, rigidity, and arithmetic in hyperbolic geometry and related areas. There have been many striking developments in recent years, particularly related to totally geodesic submanifolds in both finite and infinite volume hyperbolic and even complex hyperbolic manifolds.

One aim of this workshop is to expose young researchers to these breakthroughs providing them with the necessary background from dynamics, and geometry to allow them to appreciate some of these recent advances, and prepare them to make new original contributions. For this purpose, we will have minicourses on ”Arithmeticity, Superrigidity and totally geodesic manifolds”, and ”Rigidity and geodesic planes in infinite volume hyperbolic manifolds”. These courses will be preceded by an introductory minicourse on Hyperbolic geometry. We will also have a minicourse on ”Understanding of geodesic planes in hyperbolic 3-manifolds via computations and visualization”. In addition, we wish to bring together experts in these fields to discuss the recent developments and open problems that lie at the crossroads of these different fields and to encourage more interaction among people working in these diverse areas.

Program Staff;     Tél.: [1-401-863-5030];     Email.: info@icerm.brown.edu

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

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.

Institute of Mathematics at the University of Granada (IMAG)

Soap films and bubbles have fascinated children and scientists for centuries. Mathematically, minimal surface theory -- with roots reaching back to Euler -- has been fundamental in the development of geometric analytic techniques and is presently experiencing extraordinary progress. It stands at the crossroads of several scientific disciplines including geometric analysis, algebraic geometry, dynamical systems, and mathematical physics (string theory, quantum field theories). The workshop will facilitate interactions and foster long-term collaborations between researchers in these areas who are – often unbeknownst – studying similar phenomena from different perspectives while using different techniques.

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

Hypoelliptic operators are a natural generalization of, and share similar analytic properties to, elliptic operators. These were originally studied in the PDE and microlocal analysis literature in classical works of Hörmander, Boutet de Monvel and Rothschild-Stein among others. Hypoelliptic operators have since increasingly appeared and are now pervasive in several branches of geometry. The purpose of this workshop will be to bring together researchers from different geometric fields working on hypoelliptic operators to explore common themes.

ICERM

In spite of their omnipresence and importance, a number of questions about knots remain elusive. Addressing them solicits techniques from a range of mathematical disciplines at the interface of algebra, analysis, geometry, modeling, and low-dimensional topology. Some of the most exciting recent avenues of research include optimizing geometry, quantum knot invariants, and applications in material sciences, physics, and molecular biology. This workshop emphasizes bridging the gap between theoretical, computational, and experimental approaches in knot theory and its applications, including artificial intelligence.

Program Staff;     Tél.: [1-401-863-5030];     Email.: programstaff@icerm.brown.edu

Analyse,    Algèbre

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

There exists a mysterious algebraic structure in 8-dimensional space that does not behave in the same way as the ordinary arithmetic that we all learn as children. Somewhat surprisingly, this strange algebra, called the octonions, shows up naturally in the study of certain higher dimensional geometric spaces, called manifolds, that are of importance in physics and in the study of the equations introduced by Einstein in general relativity. Geometers have been studying such spaces for a number of years, mostly using tools from calculus and differential equations. The proposed workshops intends to introduce these researchers to experts in the special octonion algebra, as well as in related special algebraic structures called spinors, to facilitate a cross-pollination of ideas, methods, and techniques. Some of these groups have never before been brought together in this way.

Casa Matemática Oaxaca (CMO)

The mathematical notion of a group encapsulates our common idea of symmetry. Groups play an important role in mathematics, and their structure has profound impact in the solution of a variety of problems in pure and applied mathematics. Groups are often studied from different perspectives, putting an emphasis on qualitatively different features of their structure, and therefore leading to the resolution of problems that tend to be different in nature. The aim of this workshop is to bring together some of the leading figures in two of these areas, so that each can learn new problems and techniques from the other. This will help open new avenues of research which will advance the current state of the art.

CIRM – Centre International de Rencontres Mathématiques

One of the most striking recent results in model theory is Johnson’s classification, in 2020, of fields of finite dp-rank : under purely combinatorial condition (the finiteness of a certain dimension) infinite non algebraically closed fields must come with a definable henselian topology. This result illustrates (and partially explains) the very strong relationship between valuation theory and model theory that has existed since the 1960’s. Valued fields are also at the center of the interaction between model theory number theory and algebraic geometry which blossomed in the past fifteen years. This conference will bring together specialists from the algebraic, arithmetic and the pure model theory communities that all study valued fields, but with very different tools. Our aim is, by ensuring a continued dialog between these communities, to further exchanges and promote new interactions. Its main focus will be on the arithmetic of valued fields, classification and geometric model theory in valued fields and non archimedean tame geometry.

Lorentz Center

Banach Center

Classical Fourier analysis uses decompositions of functions in terms of linear phases. In recent years it was discovered that for applications in ergodic theory, combinatorics, and number theory, involving patterns such as arithmetic progressions, one has to study correlations of functions with higher order polynomial phases and other more general phases, called nilsequences, which arise from natural dynamical systems on nilmanifolds. This philosophy has helped to make progress in problems that were previously considered intractable, and has resulted in new impressive applications in the above-mentioned areas. In ergodic theory this approach is used to study the limiting behavior of multiple ergodic averages and related multiple recurrence results, in topological dynamics it has led to new structural results, and in combinatorics and number theory it is used to study patterns that can be found in sets of positive density or the set of primes. Also, very recently it has played a decisive role in progress related to the Chowla and Elliott conjectures on correlations of bounded multiplicative functions and the Mobius disjointness conjecture of Sarnak. The aim of the workshop is to introduce the above topics to a wider audience, report on recent developments, and foster collaborations and new insights.

Algèbre,    Théorie des graphes et combinatoire

ICMS - International Centre for Mathematical Sciences

Algèbre,    Théorie des groupes

Isaac Newton Institute for Mathematical Sciences (INI)

The conference is part of a two week Isaac Newton Institute (INI) programme that follows up on the 2018 INI semester programme "Homotopy Harnessing Higher Structures". People interested in this conference may also consider attending the workshop at the INI in Cambridge in the following week, 12-16 June 2023, "Homotopy: Fruit of the Fertile Furrow".

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.

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

This workshop will focus on geometry, topology and their applications to control systems. Control theory deals with the problem of shaping the behavior of "systems", which can mean an engineered object, such as a robotic arm used for remote surgery, or a natural one, such as a flock of birds or even the brain. The basic driving questions are how to control or design a system which performs as desired. Geometric and topological ideas have led to technological breakthroughs throughout the years, but geometric thinking in engineering has not yet permeated the mainstream. The goal of this workshop is to bring together a diverse group of engineers and scientists working in geometry, topology and their intersection, in order to open new frontiers of research and applications.

Institute of Mathematics at the University of Granada (IMAG)

Mathematical developments of the last decades indicate that geometry of high dimensions, when viewed correctly, creates remarkable order and simplicity rather than untamed complexity. Its applications permeated the fields of analysis and probability, reaching far away domains as Theoretical Computer Science and Statistical Physics while, simultaneously, methods and techniques came from a variety of directions ranging from classical analysis and probability to dynamical systems and topological methods. Recent striking results such as the near resolution of the Kannan, Lov\'asz and Simonovits (KLS) conjecture and the Bourgain slicing problem, the proof of the Gaussian Correlation Conjecture and advances in concentration of measure, make ripe the timing of this workshop on the effects of convexity and probability on high-dimensional geometric phenomena. By exploiting the scientific momentum, the workshop aims to engage a new generation in exciting collaborations and research directions.

Casa Matemática Oaxaca (CMO)

A mathematical knot can be thought of as a piece of knotted string with ends attached. This knotted circle is allowed to move freely in space as long as it does not pass through itself. In recent years the study of knots has gained momentum through a series of applications, for instance in physics and in molecular biology. Such applications bring new urgency to certain classical questions pertaining to knots and how they sit inside 3-dimensional space.

Isaac Newton Institute for Mathematical Sciences (INI)

Max Planck Institute for Mathematics in the Sciences

The aim of the course is to learn how tools from algebraic geometry (in particular, from computational and real algebraic geometry) can be used to analyze standard models in molecular biology. Particularly, these models are key ingredients in the development of Systems and Synthetic biology, two active research areas focusing on understanding, modifying, and implementing the design principles of living systems. We will focus on the mathematical aspects of the methods, and exemplify and apply the theory to real networks, thereby introducing the participants to relevant problems and mechanisms in molecular biology. As a counterpart, however, the participants will also see how this field has in the past challenged current methods, mainly in the realm of real algebraic geometry, and has given rise to new general and purely theoretical results on polynomial equations. We will end our lectures with an overview of open questions in both fields.

Réseaux complexes,    Cours et évènements pour étudiants en mathématiques

Casa Matemática Oaxaca (CMO)

In addition to further developing equivariant bordism theory directly, the workshop participants will apply this theory to understand symmetries of high-dimensional objects in terms of lower-dimensional objects with similar symmetries, and, conversely, to understand when it is possible for an object with symmetry to be used to build a higher dimensional object with the same symmetry. The participants will also apply equivariant bordism theory to certain problems arising in quantum physics. Algebraic aspects of symmetry have been exploited to great effect in recent years in order to understand certain quantum mechanical systems called ``topological quantum field theories," and the workshop will push these applications further by coupling them to the geometric techniques enabled by equivariant bordism theory. The workshop activities have been carefully organized with the goal of nurturing new cosmopolitan research collaborations that unite experts and students from diverse backgrounds---both mathematical and personal.

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

Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Recent work by physicists has uncovered a conjectural relationship between the enumerative invariants of noncompact Calabi-Yau geometries and the spectra of quantum curves. In certain limits, this connection may be recast in terms of zeroes and limits of higher normal functions, which are generalized periods arising from algebraic K-theory. Other interpretations and applications abound, in contexts ranging from integrable systems to resurgence theory. This workshop will be the first time that an interdisciplinary group of researchers working on this topic from various perspectives has been convened. The organizers expect it to generate new insights and new research liaisons among the attendees.

Physique mathématique,    Algèbre

MPI f. Mathematik, Bonn

The Arbeitstagung 2023 will focus on Condensed Mathematics, a new approach to topology, and its applications throughout mathematics, from logic over algebra, analysis and K-theory to group theory and dynamical systems. As usual at an Arbeitstagung, part of the program will only be decided during the event depending on the interests of the audience.

ICMS - International Centre for Mathematical Sciences

This workshop will aim to bring together experts in the theory of C*-algebras with mathematicians who have already been inspired by C*-algebras or who work in areas where there are natural connections with C*-algebras.

In the early 1920s, Emmy Noether introduced the fundamental concept of a Noetherian ring, a notion that has had a remarkably broad impact on mathematics over the last century. In this conference, we celebrate Noether's legacy with research talks from many areas of algebra, broadly construed, including algebraic geometry, commutative algebra, number theory, and representation theory.

Algèbre,    Théorie des nombres, arithmétique

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.

Théorie des groupes,    Théorie des graphes et combinatoire

Mathematical Sciences Research Institute (MSRI)

This graduate summer school will introduce students to two important and inter-related fields of differential geometry: geometric flows and minimal surfaces.

MDPI

Casa Matemática Oaxaca (CMO)

Convexity is a branch of classical mathematics and it is located at the confluence of geometry, analysis, topology and combinatorics. Although its origins can be traced back to Archimedes and its systematic study started at the end of the nineteenth century, it was not until the mid-twentieth century that convexity became a well established branch of mathematics. Nowadays, it is an important area that is attracting young researchers and students. Why? Because of its intrinsic beauty, it’s fascinating and intriguing open questions that have an instant intuitive appeal, but also, because of its many relations with other areas of mathematics and its multiple applications, such as in economics, engineering and data science. The purpose of this workshop is to bring together key people working in this area, in order to explore recent progress and to help focus on future research directions.

Renyi Institute

Cours et évènements pour étudiants en mathématiques,    Algèbre

Mathematical Sciences Research Institute (MSRI)

The school is built around two related courses on geometric (‘derived spaces’) and categorical (‘derived categories’) aspects of the theory. Our goal is to explain the key ideas and concepts, while trying to keep technicalities to a minimum.

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

CIRM – Centre International de Rencontres Mathématiques

ICMS - International Centre for Mathematical Sciences

This workshop will bring together researchers with common interests in fractals and related areas such as ergodic theory, geometric measure theory, and analysis. The aim of the workshop is to stimulate collaboration and research activity between the various groups in the UK, encourage and support the work of early career researchers in this area, and provide a platform for dissemination of work in fractal geometry.

The Department of Mathematics of University of Patras and the Department of Electrical and Computer Engineering of University of Peloponnese

Description:

All areas of Topology and its Applications are included:

General Topology, Set-Theoretic Topology,

Geometric Topology, Algebraic Topology, Applied Topology.

In particular:

Topological Groups, Dimension Theory, Dynamical Systems and

Continua Theory, Computational Topology, History of Topology.

Email.: georgiou@math.upatras.gr

Banff International Research Station (BIRS) / UBCO

Geometry is all around us. The circles and triangles of the Ancient Greeks have never left us. Film, art, and architecture ha ve all been touched by mathematics and geometry. 3D printing, robotics, and origami are a new wave of geometry. At Geometry: Education, Art, and Research, leading researchers pair up with educations and artists to push the boundaries of contemporary geometry.

Histoire et philosophie de la science,    Conférences publiques et sensibilisation

ICMS - International Centre for Mathematical Sciences

The main objective of this workshop is to bring together a range of researchers in geometry and topology, whose research interests are closely aligned to topics where geometric flows either already or are expected to play a key role, with experts in the analysis of geometric flows.

University of Bristol

Victor P. Snaith (1944 – 2021) was distinguished not just as an outstanding mathematician who made deep and lasting contributions in algebraic topology and number theory but also as a charismatic leader who enthusiastically developed research communities and generously supported young researchers.

The conference will bring together homotopy theory, cohomology of groups, algebraic K-theory and number theory, the main areas in which Vic worked. The aim is to feature important developments, paying special attention to synergies between these areas, as Vic did in much of his versatile research.

Algèbre,    Théorie des nombres, arithmétique

ICERM

This will be a one-week conference broadly focused on the topics of the LMFDB, mathematical databases, computation, number theory, and arithmetic geometry. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time set aside for research and collaboration. This workshop is an activity of the Simons Collaboration 'Arithmetic Geometry, Number Theory, and Computation' and is supported by the Simons Foundation.

Program Staff;     Tél.: [1-401-863-5030];     Email.: info@icerm.brown.edu

Théorie des nombres, arithmétique,    Mathématiques numériques

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.

Cours et évènements pour étudiants en mathématiques,    Algèbre

Banach Center

ICMS - International Centre for Mathematical Sciences

The principal objective of the workshop is to bring together researchers in the relevant areas to consolidate recent advances, present new results and encourage collaborations on extensions of recent work or new ideas.

Théorie des graphes et combinatoire,    Réseaux complexes

Galileo Galilei Institute For Theoretical Physics

Casa Matemática Oaxaca (CMO)

The workshop is designed to explore the interactions that exists between set theory, topology, and algebra. The focus of the workshop will be on the study of topological problems of set-theoretic flavor arising in topological algebra and algebraic topology, as well as the study of topological games and homogeneity.

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

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

The workshop is concerned with geometric objects arising from polynomial equations known as algebraic curves. Such curves have been studied extensively since the 19th century, but recent developments in combinatorics have led to a plethora of new techniques and solutions to major problems in the field. Bringing together experts from classical algebraic geometry and the adjacent combinatorial areas, the workshop aims to bridge the different points of views, identify key open problems in the field, and to examine how progress can be achieved via a combination of old and new tools.

Calcul infinitésimal, équations différentielles et intégrales,    Théorie des graphes et combinatoire

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

Casa Matemática Oaxaca (CMO)

This workshop will concentrate on the development on new topological tools to capture the structure of data that depends on many parameters simultaneously. The meeting will provide an welcome opportunity to bring together many parts of mathematics to support topology in this work, and to discuss a new range of potential exciting applications.

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

ICMS - International Centre for Mathematical Sciences

Some of the most exciting developments in geometric representation theory revolve around the relatively new theory of W-algebras. Broadly speaking these are obtained via the process of quantum Hamiltonian reduction from the some of the most influential structures in modern representation theory: enveloping algebras and universal affine vertex algebras. The applications of W-algebras are seemingly endless, but we list some key examples: the ordinary and modular representation theory of Lie algebras, the classification of integrable systems (especially generalisations of the KP hierarchy), a deeper understanding of smooth representations of affine Lie algebras, conformal field theories (and their associated AdS duals), modular tensor categories and the famous geometric Langlands program, once described by Edward Frenkel as “the grand unifying theory of mathematics”. The aim of this workshop is to bring the world's leading experts together to investigate recent developments in the theory of W-algebras and their representation theory, as well as interactions with other topics in geometric representation theory.

Banach Center

This conference is a celebration of the mathematical career of Szymon Dolecki, representing advances in the various fields he contributed to: Control Theory and observability (main speaker: Enrique Zuazua), Optimization (main speaker: Jean Paul Penot), Topology (main speakers: Alexander V. Arhangel’skii, Ahmed Bouziad, Jean Goubault-Larrecq, Steve Watson), as often as possible from the point of view of the unifying theme of convergence space theory (workshop leader: Frédéric Mynard), a domain of which he is one of the most prominent world specialist and that centrally occupied the later part of his career.

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

The geometry of Hyperkahler varieties is certainly one of the most studied topics in Algebraic Geometry, with many connections to Representation Theory and Arithmetic Geometry. The aim of this workshop is to survey the recent developments in this area and to investigate the open problems and conjectures, by creating new collaborations between participants from different research fields. In addition to the research talks provided by selected participants, there will be four mini-courses delivered by some of the main experts in this area.

Young postdoctoral researchers and graduate students are very welcome to attend the workshop and to contribute with a junior talk.

Cours et évènements pour étudiants en mathématiques,    Algèbre

Casa Matemática Oaxaca (CMO)

The proposed Workshop aims to study bridges between representations of algebras on one side and algebraic geometry and singularity theory on the other. One such bridge is provided by a process called `silting', allowing for example the transfer of combinatorial or homological structure in either direction. It is expected that the joint efforts of a group of internationally leading experts from many different areas of mathematics is yielding new insight in the difficult nature of these objects of study.

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

CIRM – Centre International de Rencontres Mathématiques

The conference is about recent developments in Arithmetic Algebraic Geometry. Its central theme is the geometry of Shimura varieties and related spaces in all its facets. Topics to be covered include: Integral models of Shimura varieties and the geometry of their reductions, p-adic and perfectoid geometry, special cycles on Shimura varieties, moduli spaces of Galois representations and (φ, Γ)-modules.

CIRM – Centre International de Rencontres Mathématiques

ICMS - International Centre for Mathematical Sciences

Topology is likely to be featured prominently in any truly useful quantum computation scheme. The hurdle of scalable fault-tolerance is insurmountable with the current incremental progress -- while it is possible to engineer systems supporting hundreds of physical qubits, applications beyond academic interest require millions of qubits to implement robust error correction. Topological quantum computation (TQC) relies upon the preparation of topological phases of matter supporting non-abelian anyons to perform inherently fault-tolerant operations. As errors are corrected at the hardware level through the topological nature of anyons, the problem of scalability is simultaneously overcome. On the other hand, despite years of effort we still don't have unassailable confirmation that non-abelian anyons exist. This workshop will bring together researchers in a diversity of fields in and around TQC for the purpose of broadening and deepening the subject, with an eye towards accelerating the realization of scalable technology.

Matériaux quantiques, basses températures,    Mécanique quantique et l'information quantique

Banach Center

The conference concerns the broadly understood mathematical analysis, in particular, the so-called geometric analysis (including calculus of variation and partial differential equations of geometric origin, Sobolev spaces theory on manifolds and on metric spaces, and knot theory issues related to curvature energies).

Analyse,    Calcul infinitésimal, équations différentielles et intégrales

CIRM – Centre International de Rencontres Mathématiques

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

The Banff International Research Station will host a diverse, international group of mathematicians in 2023 to study geometric approaches to fluids and optimal transport. The ideas of geodesic settings for fluids have been circulating since the late 1960s, but received a strong surge lately, in the last 5-10 years, with the development of new techniques in infinite-dimensional geometry and group theory. The original idea is that the particles in an ideal liquid or gas move in a curved infinite-dimensional space, in the same way as an airplane flying around the earth: along the shortest path. Properties of the fluid, such as how well it can be predicted in the future, how well it mixes together, and how extreme the speed can be, can all be related to how curved this infinite-dimensional space is, which helps us understand features of the weather and climate geometrically. More recently similar ideas have been used to understand solids as well, for example when a pile of rocks are transported from one place to another at the optimal cost.

Physique de la matière condensée et des matériaux,    Thermodynamique, dynamique des fluides et physique statistique

CIRM – Centre International de Rencontres Mathématiques

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

Many important questions in convex geometry are related to the study of sections and projections of convex bodies. For example, can convex bodies be uniquely determined by the size of their sections or projections? What are the largest and smallest sections of the cube? Do convex bodies with smaller sections have smaller volume? A common feature of all these problems is that they are solved with the help of harmonic analysis. The aim of the proposed workshop is to bring together leading experts and young researchers to discuss recent progress in applications of harmonic analysis to convex geometry.

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

The concept of manifold in mathematics corresponds approximately to the everyday idea of a smooth surface --- think of soap bubbles or sheets of fabric --- except that it can have any number of dimensions. A question that lies at the origin of topology, the mathematics of shape, is: can we write down a list of all manifolds? At first, such a classification was attempted through numerical invariants. Over time, the focus of algebraic topology has shifted from using numerical invariants to the algebraic objects underlying them, and then ascended further to studying moduli spaces. This workshop concerns recent breakthroughs in this philosophy for studying of manifolds, combining higher-algebraic methods with novel geometric techniques.

CIRM – Centre International de Rencontres Mathématiques

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

CIRM – Centre International de Rencontres Mathématiques

Algèbre,    Théorie des nombres, arithmétique

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

Algèbre,    Théorie des graphes et combinatoire