Konferenzen  >  Mathematik  >  Algebra

MRSI – Mathematical Sciences Research Institute, Berkeley

The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes. In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and low-dimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory.

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

Kurse und Veranstaltungen für Studenten der Mathematik,    Geometrie und Topologie

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

Casa Matemática Oaxaca (CMO)

The Research Institute for Mathematical Sciences (RIMS)

The workshop Aspect'22 "Asymptotic Analysis & Spectral Theory" is expected to take place on September 26-30, 2022, in Oldenburg (Oldenburg).

CIRM – Centre International de Rencontres Mathématiques

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.

The Research Institute for Mathematical Sciences (RIMS)

ICACGA is an international conference focused on advanced computational applications of Geometric Algebra (GA) and related hypercomplex algebras such as quaternions and octonions. The reasons for investigating hypercomplex algebras for enabling advanced computational applications and, more specifically, data-centric applications range from theoretical aspects such as the unification of many mathematical systems into one easy-to-understand mathematical framework with an intuitive exploration of geometric objects and geometric operations to computational advantages such as direct integration of GA with standard programming languages, compactness and robustness of algorithms, implicit use of parallelism, and high runtime performance.

The Research Institute for Mathematical Sciences (RIMS)

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

Institut Henri Poincaré (IHP)

The Research Institute for Mathematical Sciences (RIMS)

Casa Matemática Oaxaca (CMO)

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

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

The Fields Institute

This conference is intended to provide an overview of current research in homotopy theory, which has vastly expanded since its roots in the 19th century from the study of topological spaces by algebraic and combinatorial means to other fields of mathematics, including algebraic geometry, differential topology, and mathematical physics.

The Research Institute for Mathematical Sciences (RIMS)

Motives were originally introduced by Grothendieck in the sixties to provide a universal source to various cohomology theories of algebraic, geometric and arithmetic nature. The works of Hanamura, Levine and Voevodsky in the nineties, followed by many others, have shed a new light on the subject by introducing triangulated categories of motives and relating them to a newly defined homotopy category of schemes. More recent avatars of motives include the motives with modulus of Kahn, Miyazaki, Saito and Yamazaki or the log-motives of Binda, Park and Østvær, both purposely avoiding A1-invariance.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to applications of new theoretical and computations tools in equivariant stable homotopy theory to chromatic homotopy theory and algebraic K-theory. The recent renaissance in equivariant stable homotopy theory has provided many new tools which allow us to better understand classical problems and carry out new computations.

Professor Yilmaz Simsek, (Akdeniz University, Turkey)

The aim of the conference is to bring together leading scientists of the pure and applied mathematics and related areas to present their researches, to exchange new ideas, to discuss challenging issues, to foster future collaborations and to interact with each other.

Tel.: [+90 242 310 2343];     Email: micopam2018@gmail.com

Mathematical Analysis, Algebra and Analytic Number Theory, Combinatorics and Probability, Pure & Applied Mathematics and Related Areas, Mathematical Statistics and its applications, Recent Advances in General Inequalities, Mathematical Physics, Fractional Calculus and Its Applications, Polynomials and Orthogonal systems, Special numbers and Special functions, q-analysis and its applications, Approximation Theory and Optimization, Extremal Problems and Inequalities, Integral Transformations, Equations and Operational Calculus, Differential Equations and their applications, Geometry and Its Applications, Numerical Methods and Algorithms, Scientific Computation, Mathematical Methods and Computation in Engineering, Mathematical Geosciences, p-adic numbers, p-adic analysis and their applications, Mathematical Modelling, Marketing, Business and their applications, Mathematical Methods for Engineering Applications

Analysis,    Angewandte Mathematik (allgem.)

The Research Institute for Mathematical Sciences (RIMS)

Graduate students of all levels and faculty are invited to register to give a 30 minute talk. Talks may be expository or on current research.

Kurse und Veranstaltungen für Studenten der Mathematik,    Graphentheorie und Kombinatorik

Nagoya University

Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates

The AUA-UAEU Workshop on Graph Theory, Combinatorics and Applications (GTCA 2022) is to be held at UAEU, Al-Ain, UAE during the three days from 13 November to 15 November 2022. It is going to be organized by Department of Mathematical Sciences, UAE University in Collaboration with University of Indonesia, Jakarta, Indonesia. This is the second workshop. The 1st Workshop on Graph Theory, Combinatorics and Applications (GTCA 2019) was held on October 9-10, 2019 face to face by UAE University which attracted around 50 researchers from different parts of the word including participants from leading Universities of Europe and Asia and was a successful event.

Graph theory and combinatorics are closely related to many mathematical subjects, such as, topology, geometry and number theory and have a lot of applications in applied sciences, engineering and optimization problems. The workshop focuses on all aspects of graph theory, combinatorics and their applications. It dedicates to creating a platform for exchanging the latest research results and ideas; sharing the advanced research methods and latest trends in these areas and to develop further collaborations.

Tel.: [0097137136389];     Email: m.imran658@uaeu.ac.ae

Graph Theory; combinatorics

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.

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

Institut Henri Poincaré (IHP)

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

The Research Institute for Mathematical Sciences (RIMS)

Graphentheorie und Kombinatorik,    Gruppentheorie

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 Research Institute for Mathematical Sciences (RIMS)

The Research Institute for Mathematical Sciences (RIMS)

The Research Institute for Mathematical Sciences (RIMS)

Operator Theory and particularly Spectral Theory are at the root of several branches in Mathematics and offer a wide range of challenging research problems. The purpose of this conference is to highlight some of the major theoretical advances in the fields of Operator Theory, Spectral Theory and Functional Analysis. The wide scope of the Conference ICOT should provide an excellent opportunity for sharing ideas and problems amongst specialists.

Analysis,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

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.

Tel.: [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

Zahlentheorie, Arithmetik,    Geometrie und Topologie

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

Graphentheorie und Kombinatorik,    Gruppentheorie

The Fields Institute

The purpose of this conference is to create a discussion between experts that work on a number of such approaches to singular spaces as well as on the broader themes that lead to these structures: Hamiltonian group actions, completely integrable systems, and geometric quantization.

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)

Watanabe's work on embedding calculus has shown us how diffeomorphisms of the 4-sphere may be studied, and Zemke's work has used the functoriality of Floer homology to derive powerful new obstructions to ribbon concordance. A common theme in these works is the emphasis on functoriality of the invariants, rather than simply computation, and a renewed interest in understanding diffeomorphism groups of a manifold rather than single isotopy groups. In this workshop, we propose to bring together experts on these interrelated topics with the aim of improving community understanding of recent developments in low-dimensional topology and promote new advances in the study of global properties of 4-manifolds.

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.

Geometric Group Theory

Gruppentheorie,    Geometrie und Topologie

Mathematical Sciences Research Institute (MSRI)

The Connections Workshop features presentations by both leading researchers and promising newcomers whose research has contact with the interrelated topics of algebraic cycles, L-values, and Euler systems. The goal is to present a variety of diverse results, so as to forge new connections, foster collaborative projects, and establish mentoring relationships. While emphasis will be placed on the work of women mathematicians, the workshop is open to all researchers.

The Research Institute for Mathematical Sciences (RIMS)

Gruppentheorie,    Mathematische Physik

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

The last several years have seen rapid development of a new language for conformal field theory(CFT), including insights from the conformal bootstrap program. This conference will bring to bear the modern arsenal of conformal field theory on the foundations of holography and quantum gravity. A theme of the conference will be the extent to which consistency conditions on quantum gravity are inherited from those of CFT, and whether they naturally lead to string/M-theory. By bringing together scientists on both sides of holographic duality, we hope to explore these issues in a broad way.Topics to be covered include large N bootstrap and the structure of holographic CFTs dual to general relativity; CFT sum rules and gravitational effective field theory; aspects of supersymmetry in holography; low-dimensional holography, modularity and quantum chaos; black holes from strongly-coupled finite temperature physics; symmetry constraints on gravitational path integrals and AdS vacua; S-matrices, their relation to CFT correlators, and holography away from AdS.

Astronomie, Astrophysik und Kosmologie,    Mathematische Physik

The Research Institute for Mathematical Sciences (RIMS)

Mathematical Sciences Research Institute (MSRI)

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to the study of cluster algebras and their relation to symplectic geometry, bringing together people with expertise in these two fields. In recent years deep and intriguing connections between these two areas have been discovered, including the existence of cluster structures on moduli spaces of Lagrangian fillings, the cluster compatibility of Poisson structures on wild character varieties, the cluster algebras associated to plane curve singularities, and the cluster nature of spectral networks. This bridge between cluster algebras and symplectic geometry is proving fruitful in both directions and a central aim of the workshop is to crystalize those connections and bring forward further applications.

Mathematical Sciences Research Institute (MRSI)

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research.

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.

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

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.

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

This is a workshop in commutative algebra, broadly interpreted, with a focus on three areas, all concerned with resolutions in various forms. One is the resolution of singularities of algebraic varieties, which remains a vibrant topic of research. The second is the theory of noncommutative resolution of singularities. Introduced two decades ago, this subject has witnessed remarkable growth developing connections to algebraic geometry, commutative algebra, cluster algebras, and the representation theory of algebras, both commutative and noncommutative, among others. The third intended meaning of the word “resolution” is as in free resolutions of algebras and modules in commutative algebra.

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.

Geometrie und Topologie,    Zahlentheorie, Arithmetik

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

The Research Institute for Mathematical Sciences (RIMS)

The Research Institute for Mathematical Sciences (RIMS)

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.

The Research Institute for Mathematical Sciences (RIMS)

Amirkabir University of Technology, Department of Mathematics and Computer Science

Group theory plays an important role in different branches of Mathematics, for example, Geometry, Number Theory, and Analysis. Also, group theory is one of the most powerful mathematical tools used in applied mathematics, cryptography, coding theory, steganography, quantum chemistry, spectroscopy, robotics, computer vision, and quantum computation. It allows the user to predict, interpret, rationalize, and often simplify complex theory and data. The development in each field of group theory is getting faster and deeper. This fact makes all researchers reach for a better understanding of the current works and developments, in all fields of group theory and its applications. The aim of this conference is to exchange research ideas amongst the group theorists. In addition, specialists in the subject of group theory can present their latest research works and encourage interested students to progress and widen their knowledge in group theory.

Tel.: [+98 21 64548567];     Email: adminigtc15@aut.ac.ir

Representation and character theory, Groups and combinatorics, Geometric and combinatorial groups, Monoids, semigroups and hypergroups, Algorithmic problems in finite groups, Probabilistic methods in group theory, Permutation groups, Linear groups, Infinite groups.

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

Geometrie und Topologie,    Angewandte Mathematik (allgem.)

CRM / Université de Montréal

Measured group theory looks at groups from a probabilistic perspective, by studying their actions on probability spaces up to orbit equivalence. It turns out that the orbit equivalence relations of these actions can remember information about the group, which has yielded classification and rigidity results, as well as new invariants such as cost, |^2-Betti numbers, and ergodic dimension. Initiated by Gromov and Zimmer, the subject has become a very fruitful area of research over the last 25 years. One reason for this is that to study the orbit equivalence relation of an action, one tries to measurably equip the orbits with various combinatorial and geometric structures (graphs, trees, CW-complexes) and investigate their characteristics (colorings, matchings, ends, |^2-Betti numbers), which often requires machinery from the corresponding subjects, and also contributes back to these subjects with new results. This two-way traffic has established new connections between Measured Group Theory and various different areas, including ergodic theory, descriptive set theory, probability theory, combinatorics, geometric group theory, Lie groups, and von Neumann algebras.

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.

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

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.

ICMS - International Centre for Mathematical Sciences

Reflection arrangements appear in various areas of mathematics including algebra, combinatorics, differential geometry, integrability and singularity theory. The concrete research strands within these areas that we plan to focus on include Cherednik algebras, Coxeter-Catalan combinatorics, logarithmic vector fields, Frobenius manifolds and flat invariants. The main goals of the workshop are to bring together specialists from these diverse fields, to explore remarkable connections between these areas, to enhance viewpoints and to stimulate further research. The workshop is organised in partnership with the Clay Mathematics Institute.

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.

Mathematical Sciences Research Institute (MRSI)

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.

Algebraic Cycles, L-Values, and Euler Systems

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

The Fields Institute

This workshop will bring together those working in pure Borel combinatorics with those studying the ergodic theory, dynamics, and geometry of countable groups. Featured topics will include Gaboriau's theory of cost, Borel and measurable chromatic numbers, Borel matchings, and amenable and hyperfinite equivalence relations.

ICMS - International Centre for Mathematical Sciences

The past several years have seen landmark progress in the interplay between representation theory, geometry and mathematical physics. Particularly notable have been Braverman, Finkelberg and Nakajima's definition of the Coulomb branch of an N=4 supersymmetric (SUSY) 3d gauge theory, and Mellit's proof of the Hausel-Letellier-Rodriguez-Villegas conjecture on the Poincar\'e polynomials of character varieties. The area has also seen exciting connections to other fields, such as significant progress on the conjectures of Gorsky, Negut and Rasmussen relating coherent sheaves on Hilbert schemes to Khovanov-Rozansky homology. The goal of this conference is to push forward research in areas at the nexus between these results: affine Springer theory, double affine Hecke algebras and Coulomb branches, creating new connections between experts, and exposing young mathematicians to this fast-progressing and exciting research area.

Northwestern University, Evanston, IL

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

The Arbeitsgemeinschaft (study group) mainly addresses to non-specialists who want to broaden their outlook on mathematics and to junior mathematicians who wish to enter a field for future research. Experts are also welcome. The idea is “learning by doing” – similar to the Seminaire Bourbaki. Participants have to volunteer for one of the lectures described in the program of the Arbeitsgemeinschaft. After the deadline for application the organizers choose the actual speakers to give them enough time to understand the subject and to prepare for their lectures.

CIRM – Centre International de Rencontres Mathématiques

ln this workshop, we will consider variants of Artin's primitive root conjecture leading to the study of the Galois groups of various radical extensions. Beyond the case of the multiplicative group studied by Lenstra and others, there are now also interesting results for elliptic radicals, and for division points in more general abelian varieties. ln this context, the elliptic analogue of Artin's conjecture is the Lang-Trotter conjecture, which is still open after more than 40 years.

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

CIRM – Centre International de Rencontres Mathématiques

ICMS, The Bayes Centre, Edinburgh

This workshop will bring together leading, as well as early career, researchers on arithmetic statistics and on algorithmic aspects of algebra and number theory, with the aim of fostering collaborations within and between these communities, and to offer early career researchers the opportunity to get a broad overview of the most recent achievements and of the most pressing problems in these fields. The workshop will also celebrate the mathematics of Hendrik W Lenstra Jr.

CIRM - Jean-Morlet Chair

In recent years, a number of techniques have led to outstanding progress on Lang-Vojta conjectures, such as the Subspace Theorem, p-adic approaches to finiteness, and modular methods. Similarly, spectacular progress has been achieved on unlikely intersection conjectures thanks to new methods and tools, such as height formulas for special points, connections to model theory, refined counting results, and new theorems of Ax-Shanuel type (bi-algebraic geometry). The goal of this workshop is to create the opportunity for these two groups to interact, to share their techniques, to update on the most recent progress, and to attack the outstanding open questions in the field.

Mathematical Sciences Research Institute (MRSI)

A central topic in Diophantine Geometry is to understand how the geometry of a variety influences the arithmetic of its algebraic points, and conversely. Conjectures of Bombieri, Lang, and Vojta suggest that rational points of algebraic varieties satisfying suitable approximation conditions, are algebraically degenerate. On the other hand, conjectures on unlikely intersections suggest that algebraic points of special type —e.g. torsion points in semi-abelian varieties, special points in Shimura varieties— avoid subvarieties, unless the subvariety itself is also special (in a technical sense). In recent years, a number of techniques have led to outstanding progress on Lang-Vojta conjectures, such as the Subspace Theorem, p-adic approaches to finiteness, and modular methods. Similarly, spectacular progress has been achieved on unlikely intersection conjectures thanks to new methods and tools, such as height formulas for special points, connections to model theory, refined counting results, and new theorems of Ax-Shanuel type (bi-algebraic geometry). The goal of this workshop is to create the opportunity for these two groups to interact, to share their techniques, to update on the most recent progress, and to attack the outstanding open questions in the field.

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.

Gruppentheorie,    Geometrie und Topologie

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.

Geometrie und Topologie,    Graphentheorie und Kombinatorik

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)

Eduard Helly proved in 1913 one of the most celebrated results in geometry that gives conditions for the members of a family of convex objects (with convex boundary and without holes) to have a common point. Helly's theorem gives rise to numerous generalizations and variants, and is very close related with the classical theorems of Radon, Caratheodory and Tverberg, which is the r-partite version of Radon's theorem. All this theorems have a deep connection with many other areas in mathematics such as algebraic topology, discrete geometry, combinatorial geometry, and analysis and could be seen as a multidisciplinary area since it uses tools from, topology, geometry, computer sciences, probability etc. and, in resent years have been useful tool for applications to model problems in real life. The proposed workshop will assemble the key people senior and students working in this area, in order to explore recent progress and to help focus on future directions of research.

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.

Geometrie und Topologie,    Graphentheorie und Kombinatorik

CIRM – Centre International de Rencontres Mathématiques

Our goal is to organise a conference devoted to interactions between pure mathematics (in particular arithmetic and algebraic geometry) and information theory (especially cryptography and coding theory). This conference will be the eighteenth edition, with the first one held in 1987, in a series that has traditionally brought together some of the top specialists in the domains of arithmetic, geometry, and information theory. The corresponding international community is very active and all of the concerned research domains are developing and expanding rapidly.

Algebraic and arithmetic geometry over finite fields and global fields. Number theory, especially explicit and algorithmic. Algebro-geometric codes constructed from curves and higher-dimensional algebraic varieties over finite fields and global fields. -Arithmetic and geometric aspects of cryptography (symmetric, public key, and post-quantum) and cryptanalysis.

Kryptographie, Blockchain und Informationssicherheit,    Informationstheorie und Grundlagen der Informatik

ICMS - International Centre for Mathematical Sciences

Gruppentheorie,    Geometrie und Topologie

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.

Queen's University, Kingston, Ontario

Structure of finite dimensional algebras Structure of module categories Auslander--Reiten components Homological methods in representation theory Homological conjectures Algebras of finite global dimension Self-injective algebras Tame algebras Combinatorial aspects of representation theory Geometry of algebras and modules Homological invariants of algebras and modules Triangulated categories and tilting theory Relations of the above topics with Lie theory, Singularity theory, Cohen--Macaulay modules, quantum groups and other algebraic structures.

Hausdorff Center for Mathematic

This conference will be on various aspects of the local Langlands correspondence over p-adic fields and methods from p-adic Hodge theory. Topics will include the usual local Langlands correspondence, the p-adic local Langlands correspondence and the relation to coherent sheaves on spaces of Galois representations, and the geometry and cohomology of local Shimura varieties.

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)

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.

Geometrie und Topologie,    Zahlentheorie, Arithmetik

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

Banach Center

LOOPS'23 conference will belong to the LOOPS conferences, a series of conferences held every 4 years since 1999. The LOOPS conferences cover all aspects of nonassociative mathematics, including quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, quandles and their applications. The conference intends not only to highlight new relevant results in algebra and geometry, but also to foster connections to combinatorics, group theory, knot theory, cryptography and physics. The previous LOOPS conferences have been held in Prague, in Trest, Czech Republic, Ohrid, North Macedonia, and Budapest, Hungary.

quasigroups and loops • quantum Latin squares • applications in cryptography • automated deduction • algebraic structures derived from the Yang-Baxter equation • connections to low-dimensional topology

Interest in specialization of polynomials and Galois groups goes back at least to the work of Hilbert on the inverse Galois problem. This theory has found an abundance of applications in Algebra, Number Theory, Group Theory, and Arithmetic Geometry. In recent years, the area is blooming and we see striking results that open completely new horizons: The discovery of Hilbert irreducibility properties of algebraic groups, its connection with expanders and random walks, the interrelation with arithmetic-geometric properties of parametrizing varieties, and the exciting progress on the Cohen-Lenstra heuristics. The conference aims to bring together leading experts and young researchers interested in the area. We plan to leave an abundance of free time, dedicated to informal discussions. We believe that this will encourage the transfer of ideas, techniques, and will foster new collaborations and new research directions.

Zahlentheorie, Arithmetik,    Gruppentheorie

ICMS - International Centre for Mathematical Sciences

The workshop will focus on recent new trends connecting different classical as well as quantum integrable systems through dualities and symmetries. We are inviting world leading researchers from a diverse range of the integrable systems community in order to disseminate these new important developments and techniques; strengthen and explore new and existing connections between different aspects of integrable systems; identify future perspectives and aims; and provide a networking opportunity for established and early career researchers.

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.

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.

This is the ninth Iwasawa conference following conferences in Besancon, Limoges, Irsee, Toronto, Heidelberg, London, Tokyo and Bordeaux. The conference is dedicated to the memory of John Henry Coates

In the tradition of the earlier events, this workshop aims at bringing together the leading experts in the field, covering a broad spectrum reaching from the more theoretically-oriented over the explicit to the algorithmic aspects. The fundamental problem motivating the workshop asks for a description of the set of rational points X(Q) for a given algebraic variety X defined over Q. When X is a curve, the structure of this set is known, and the most interesting question is how to determine it explicitly for a given curve. When X is higher-dimensional, much less is known about the structure of X(Q), even when X is a surface. So here the open questions are much more basic for our understanding of the situation, and on the algorithmic side, the focus is on trying to decide if a given variety does have any rational point at all.

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

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

Hausdorff Center for Mathematic

This conference will be on various aspects of the global Langlands correspondence. Topics will include in particular the geometry and cohomology of Shimura varieties and more general locally symmetric spaces, or moduli spaces of shtukas.

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

This workshop focuses on addressing general theoretical problems that underpin cutting-edge applications of linear algebra, including low-rank approximation and tensor decomposition, optimization, machine learning, nonlocal network dynamics, and uncertainty quantification. By bringing together experts from these different communities at a BIRS workshop, new insights in applied linear algebra will be brought to these challenging problems, which we expect to generate significant advances to state-of-the-art computational algorithms in the next decade.

Neuronale Netze und Künstliche Intelligenz, Maschinelles Lernen,    Komplexe Netzwerke

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

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

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.

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.

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

CIRM – Centre International de Rencontres Mathématiques

CIRM – Centre International de Rencontres Mathématiques

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

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

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

The workshop is conceived in response to recent breakthroughs in physics and mathematics. One is the real quantization of Hitchin moduli spaces due to Gaiotto and Witten, and the other is a deformation quantization theory of Kontsevich and Soibelman that has achieved a vast mathematical foundation and generalization of topological recursion of Eynard and Orantin in random matrix theory. The vision of the organizers is that these two theories should be related through mirror symmetry. The workshop is organized to test this vision, and to explore its mathematical consequences.

CIRM – Centre International de Rencontres Mathématiques

ICMS - International Centre for Mathematical Sciences

This event will be a twinned transatlantic conference on “C*-algebras and tensor categories”, promoting new connections between C*-algebra theory and tensor categories/subfactors - an interface with tremendous, yet barely explored, potential. The two locations of the conference will be the Fields Institute in Canada and ICMS in Edinburgh.

Many major breakthroughs in the classification of C*-algebras of finite topological dimension have been underpinned by the large-scale transfer of von Neumann techniques on multiple levels. The overarching objective of this conference is to bring together researchers at the interface of the rapidly developing areas of the structure and classification of C*-algebras and subfactor theory/tensor categories.

ICMS - International Centre for Mathematical Sciences

This event will be a twinned transatlantic conference on “C*-algebras and tensor categories”, promoting new connections between C*-algebra theory and tensor categories/subfactors - an interface with tremendous, yet barely explored, potential. The two locations of the conference will be the Fields Institute in Canada and ICMS in Edinburgh.

Many major breakthroughs in the classification of C*-algebras of finite topological dimension have been underpinned by the large-scale transfer of von Neumann techniques on multiple levels. The overarching objective of this conference is to bring together researchers at the interface of the rapidly developing areas of the structure and classification of C*-algebras and subfactor theory/tensor categories.

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

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

Geometrie und Topologie,    Zahlentheorie, Arithmetik

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

Geometrie und Topologie,    Graphentheorie und Kombinatorik