Conferences and Meetings on Geometry and Topology

The Illustrating Mathematics program brings together mathematicians, makers, and artists who share a common interest in illustrating mathematical ideas via computational tools. The goals of the program are to: introduce mathematicians to new computational illustration tools to guide and inform their research; spark collaborations among and between mathematicians, makers and artists; and find ways to communicate research mathematics to as wide an audience as possible.

Geometry and Topology, Algebra and Number Theory, Dynamics and Probability,

Algebra,    Number Theory, Arithmetic

The Fields Institute

With an eye towards the use and need for higher structures, this workshop will bring together experts in algebraic geometry, symplectic geometry, and theoretical physics to focus on common areas interacting with HMS. Potential topics are Bershadsky--Cecotti--Ooguri--Vafa theory, shifted symplectic structures, higher Donaldson-Thomas invariants, and symplectic duality, in relation to HMS.

Applied Mathematics (in general),    Mathematical Physics

Recent progress in the study of BPS states in string theory and in supersymmetric field theories, as well as on the theory of topological recursion, gives hints towards profound connections with the exact WKB method from the mathematical study of differential equations with a large parameter, and the abelianisation of flat connections on Riemann surfaces. The goals of our workshop are to bring together some leading experts in the field to stimulate the interactions between these lines of research, and to introduce young researchers and PhD students to attractive topics of current research with a rich potential for further developments.

BPS states, topological recursion, exact WKB and abelianisation

Algebra,    Analysis

Centre International de Rencontres Mathématiques (CIRM)

Freie Universität Berlin, Institute of Mathematics

This will be a short workshop with lectures, presentations and informal discussions on polytopes and their relations to algebraic geometry. It is funded by the Einstein Foundation Berlin. It is one of the activities in the thematic Einstein semester Varieties Polyhedra and Computations (http://ehrhart.math.fu-berlin.de/agplus/).

polytopes, algebraic geometry, toric geometry, tropical geometry, Ehrhart theory, triangulations

Graph Theory and Combinatorics,    Algebra

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

Banaras Hindu University Varanasi, University of Strasbourg

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

Cochin University of Science and technology, Kochi, Kerala, India

International conference on Semigrups and Applications will be a excellent occasion for young researchers and well established professors to assemble share and discuss their resent works related to semigroup theory and its applications. A good number of participants from around the globe will be attending the event.

Phone: [+919447663109];     Email: romeopg@cusat.ac.in

Semigroups Levitt path algebras Cross-connections

Algebra,    Group Theory

The Mathematics Research Unit, The University of Luxembourg

The conference will bring researchers across both the fields of mathematics and physics together in order to discuss recently developed topics, on-going work and speculative new ideas within supergeometry and its applications in physics. This event offers a unique opportunity to unite physicists and mathematicians who share a common interest in supermathematics. There will be enough time available for discussions between the participants and there will be a poster session.

Email: andrew.bruce@uni.lu

Supermanifolds and their generalizations (e.g., superschemes, color supermanifolds, noncommutative supergeometry...), Super Lie groups and Lie superalgebras, Supergeometric methods in physics, Geometric aspects of supersymmetric field theories, superstrings, and supergravity, Mathematical aspects of the BV-BRST formalism.

Mathematical Physics,    High Energy Physics, Particles and Fields

Instituto de Matematicas UNAM in Cuernavaca

The goal of the school is to discuss some topics in the interaction between Group Theory, Geometric Topology, and Algebraic Geometry, with particular emphasis in the theory of Cremona groups and its recent developments. It will be directed mainly toward graduate students and young postdocs.

Group Theory,    Courses and Events for Physics Students

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

Graph Theory and Combinatorics,    Group Theory

The Fields Institute

Two intensive mini-courses will be given over one week by experts on polyhedral products and toric topology. These are designed to give graduate students and early career researchers in nearby fields a better understanding of each subject by presenting multiple viewpoints from different lecturers, thus enabling the participants to better engage in the subsequent workshops and seminars.

A complete understanding of quantum gravity, as it pertains to our universe, remains one of the biggest challenges in theoretical physics. As our observational constraints on the early universe and black hole physics improve, this theoretical challenge has become even more urgent. This conference aims to explore the latest developments in quantum gravity and string theory, ranging from ideas motivated from holographic dualities to new results developing the landscape of string theory vacua.

structure of the landscape of string theory solutions; emergence of spacetime from other degrees of freedom; quantum information aspects of quantum gravity; recent developments in AdS/CFT; QFT methods applied to gravitational problems, such as the analytic conformal bootstrap and UV deformations of QFT; perturbative amplitudes in gravity and string theory

Mathematical Physics,    Quantum Mechanics and Quantum Information Theory

This event intends to bring together international researchers from various backgrounds and interests, all of which related to geometric aspects of complex webs. The targeted audience includes, but is not restricted to, mathematicians (theoretical and applied), life scientists, computer scientists, and engineers. We intend to deepen connections between universities and universities of applied sciences (HES/FH), as well as between swiss and international researchers. A special effort will be made to allocate time for social interactions and networking.

This three-day workshop is intended to bring together young and more experienced researchers working in the fields of symplectic geometry, contact geometry, and Floer theory.

Email: cast2020.antwerpen@gmail.com

University of California, Irvine

Since 1992 UCI and UCSD have run the Southern California Geometric Analysis Seminar. The upcoming 2020 conference will be at UC Irvine. All interested participants are strongly encouraged to register via the online registration form and indicate request for financial support if needed. Financial support if available will be from the US National Science Foundation and priority will be given to graduate students, recent Ph.D.'s, and under-represented minorities.

Kyoto University

Tehran Polytechnic

The 3rd Iranian Conference on Computational Geometry (ICCG) will be held on February 16, 2020 at the Department of Mathematics and Computer Science, at Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran. Like the last two ICCGs, after the ICCG, there will be the Winter School on Computational Geometry, at the same place. ICCG is an annual, international conference whose goal is to bring together students and researchers from academia and industry, in order to promote research in the fields of combinatorial and computational geometry. Important dates: Submission deadline: November 8, 2019 Acceptance notification: December 22, 2019 Conference: February 16, 2020

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

University of Catania, Department of Mathematics and Computer Science

Our conference aims to bring together researchers and students working on set theory and its applications to a wide spectrum of areas of mathematics, and in particular to Topology, to discuss the most recent advances and main open problems in the field and foster collaboration. There will be eight invited lectures and each of the participants can contribute a 20-30 minute talk. Invited speakers: Leandro Aurichi (University of São Paulo-São Carlos, Brazil), Joan Bagaria (University of Barcelona, Spain), István Juhász (Hungarian Academy of Sciences, Hungary), Menachem Kojman (Ben Gurion University, Israel), Menachem Magidor (Hebrew University of Jerusalem, Israel), Gianluca Paolini (University of Turin, Italy), Stevo Todorcevic (University of Toronto, Canada and CNRS, Paris), Lyubomyr Zdomskyy (Kurt Gödel Research Center, Vienna, Austria).

Email: CataniaSetTheory@gmail.com

set theoretic topology, forcing, large cardinals, descriptive set theory, PCF theory, cardinal invariants.

The winter school will present two incarnations of the implicit function theorem to master and PhD students: the implicit function theorem of Nash and Moser, and the implicit function theorem in scale calculus and polyfold-theory as developed by Hofer, Wysocki and Zehnder. There will be two mini-courses on the theoretical framework of each incarnation which will be complemented by talks on classical and current applications to analysis and geometry.

Courses and Events for Physics Students,    Algebra

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

Algebra,    Numerical Analysis and Computational Mathematics

University of Arkansas, Fayetteville

The Redbud Topology Conference is a regional conference in topology and related areas, with participants from the University of Arkansas, the University of Oklahoma, Oklahoma State University, and elsewhere. The conference this year will focus on algorithmic and effectiveness in 3-manifold topology. The conference will run all day Saturday and all morning on Sunday, ending by 2 PM. There will also be a session on Friday afternoon as a warm-up for graduate students. There will be dinner outing on Saturday evening.

Centre International de Rencontres Mathématiques (CIRM)

This Spring School will gather together PhD students and junior researchers who use category-theoretic ideas or techniques in their research. It will provide a forum to learn about important themes in contemporary category theory, both from experts and from each other. Three invited speakers will each present a three-hour mini-course, accessible to non-specialists, introducing an area of active research. There will also be short talks contributed by PhD students and postdocs, and a poster session. The focus of the Spring School is on aspects of pure category theory as they interact with research in other areas of algebra, geometry, topology and logic. Any "categorical thinker" - that is, any mathematician whose work makes use of categorical ideas - is welcome to participate.

Email: jct.uk.2020@gmail.com

Category Theory, Grothendieck Toposes, Topos Theory, Higher Category Theory, Model Categories, Derived and Triangulated Categories

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

This workshop, sponsored by AIM, the Simons Foundation, and the NSF, will consider the role of topology in characterizing materials and in the prediction of their physical properties, particularly for two-dimensional material such as graphene. The focus will be on important mathematical questions at the interface of the analysis and topology in the context of the governing fundamental partial differential equations and other models. Two such questions are the bulk edge correspondence and the existence and robustness of edge states in aperiodic settings.

Condensed Matter Physics and Materials,    Clusters, Nanomaterials, Graphene and Fullerenes

Johns Hopkins University

Spring Topology and Dynamical Systems Conferences are a long-running series of annual conferences focusing on several actively researched areas in topology and dynamical systems. Sessions will be held in Continuum Theory, Dynamical Systems, Geometric Topology, Geometric Group Theory, Set-Theoretic Topology, and Topology in Data Science.

The Fields Institute

The workshop will introduce and explore new themes of research in toric topology. It will provide an opportunity for interaction between people who work on different aspects of torus actions, such as topological, combinatorial, symplectic and algebro-geometric.

University of Hagen

Arithmetic groups provide a fruitful link between various areas, such as geometry, topology, representation theory and number theory. Methods from geometry and topology hinge on the fact that arithmetic groups are lattices in Lie groups, whereas the theory of automorphic forms establishes a connection to representation theory and number theory. This interplay is especially intriguing in the setting of hyperbolic 3-manifolds. Indeed many conjectures in 3-manifold theory tend to be much more accessible for hyperbolic 3-manifolds whose fundamental groups are arithmetic, and conversely such manifolds provide the simplest set-up in which some of the most exciting new phenomena in the Langlands program can be studied. This conference will bring together researchers with various backgrounds around links between number theory and 3-manifolds. Central topics of the conference are the cohomology of arithmetic groups, the relation between torsion and L²-torsion, profinite invariants of 3-manifolds, and number theoretic ramifications.

Group Theory,    Number Theory, Arithmetic

Ulm University

The aim of the conference is to bring together a range of researchers working on geometric variational problems and related topics. There will be also a poster session.

Calculus, Differential Equations and Integration,    Analysis

Knots are fundamental objects of study in low dimensional topology and geometry, and the subject has seen tremendous progress in the recent years. The aim of this program is to familiarise and enthuse younger researchers in India about the latest advances in the subject with a particular emphasis on computational aspects of (co)homological, combinatorial and polynomial invariants of knots. The program will also discuss some important aspects of knot theory from physics point of view. The program will have two components, an advanced workshop (23 - 28 March 2020) followed by a discussion meeting (30 March - 03 April 2020). The advanced workshop will consist of mini courses on current aspects of knot theory by renowned experts. These topics will cover some of the latest advances in the subject, and will also prepare the participants for the discussion meeting which will consist of talks by well-known researchers in the field.

Knots, quandles, Khovanov Homology, Jones Polynomial

Cambridge University

Purdue University - AMS, American Mathematical Society

Purdue University - AMS, American Mathematical Society

University of Nantes

Mathematical Physics,    Quantum Mechanics and Quantum Information Theory

Institut Henri Poincaré, Paris

Les périodes apparaissent dans différentes branches des mathématiques, comme l’indique le titre de notre colloque : leur étude mêle arithmétique, analyse diophantienne, équations différentielles et géométrie algébrique. De nombreux résultats intéressants sur les périodes ont été prouvés ces dernières années et beaucoup de questions difficiles restent ouvertes. Le but de cette rencontre est de réunir les spécialistes de ces différents aspects des périodes et de leurs ramifications, en portant une attention particulière à d’éventuelles nouvelles applications des techniques jusqu’ici confinées à l’étude des périodes et de leurs réalisations.

Number Theory, Arithmetic,    Calculus, Differential Equations and Integration

Centre International de Rencontres Mathématiques (CIRM)

Mathematical Physics,    Courses and Events for Math Students and Early Career Researchers

University of Pennsylvania, Philadelphia

Centre International de Rencontres Mathématiques (CIRM)

California State University, Chico

Centre International de Rencontres Mathématiques (CIRM)

Simons Center for Geometry and Physics, Long Island, NY

This workshop will explore topics of current interest in the theory of Floer homology for 3-manifolds. Floer homology is a powerful tool for studying the topology of 3- and 4-dimensional manifolds, and the relations between them. The first such invariants were introduced by Floer, and arose in the context of Donaldson theory on smooth 4-manifolds.

Centre International de Rencontres Mathématiques (CIRM)

Nordic Institute for Theoretical Physics (Nordita)

Centre International de Rencontres Mathématiques (CIRM)

The workshop will review fundamental developments in several branches of anabelian geometry, as well as report on recent developments.

This workshop is one of four workshops of special RIMS year "Expanding Horizons of Inter-universal Teichmüller Theory".

Rutgers, The State University of New Jersey

geometric flows, minimal surfaces, gauge theory, symplectic geometry

University of Salerno

The aim of the Intensive Period is to bring together researchers interested in Poisson geometry in a broad sense and mathematical physics from Italy and from abroad. It also aims at presenting the foundations of the theory as well as its more recent results/ramifications to potentially interested young researchers. The Intensive Period is organized in - a Series of Seminars - a Mini-Workshop on Coisotropic Reduction - a Mini-Workshop on VB-Groupoids - a Summer School on Poisson Geometry - an International Conference on Poisson Geometry

Mathematical Physics,    Courses and Events for Math Students and Early Career Researchers

The Fields Institute

Two mini-courses will be given by experts in Geometric Group Theory. These are designed to give graduate students and early career researchers a research level perspective on how and why Polyhedral Products appear in Geometric Group Theory, thereby enabling the participants to engage fully in the workshop that immediately follows.

Courses and Events for Math Students and Early Career Researchers,    Group Theory

The Fields Institute

Two special cases of the polyhedral product construction have been immensely influential in geometric group theory, giving rise to at least three major families of examples of groups parametrized by flag simplicial complexes: right-angled Coxeter groups associated with the polyhedral product for pairs (,*); right-angled Artin groups associated with the polyhedral product for pairs (,*); and Bestvina-Brady groups associated with a covering space of the polyhedral product for pairs (,*). However, the interaction between toric topology and geometric group theory is largely unexplored. The purpose of this workshop is to significantly increase synergies between the two groups and establish a framework for approaching common problems and methods in a more global context.

Centro di Ricerca Matematica Ennio De Giorgi

The conference is the third meeting within prof. Le Donne's ERC project GeoMeG (Geometry of Metric Groups). The idea for the 2020 meeting is to focus on the following subjects: 1) large-scale geometry of nilpotent groups (and as the sub-Riemannian geometry appear as asymptotic cone) 2) Heintze groups (= homogeneous negatively curved manifolds) and their boundaries (which are nilpotent groups, possibly equipped with non-smooth distances) 3) geometry of solvable groups or, more generally, the large scale geometry of Lie groups. Tentative list of speakers: Manuel Amann, Marc Burger, Matias Carrasco Piaggio, Yves Cornulier, Moon Duchin, Tullia Dymarz, David Fisher, Misha Gromov, David Kyed, Grigoriy Margulis, Nicolas Monod, Pierre Pansu, Frederic Paulin, Roman Sauer, Yehuda Shalom, Xiangdong Xie, Robert Young.

Algebra,    Group Theory

American Matheamtical Society

The new and rapidly expanding area of Analytic Combinatorics in Several Variables (ACSV) concerns enumeration problems in such areas as lattice walks, statistical mechanical models, quantum walks and other exactly solvable models where asymptotic estimation of coefficients of a bivariate or multivariate generating function is required. The multivariate setting incorporates a wider swath of mathematics. including singularity theory, algebraic topology, and computational algebra. Participants in this MRC will be introduced to problems from these areas of mathematics whose solutions have direct applications to ACSV. These problems are not hard to state in the language of disciplines such as Morse theory, harmonic analysis, or commutative algebra, but they ask questions not typical in those fields. A long-term goal is to advance and automate this work, so that its benefits can be used by other researchers in mathematics and the natural sciences through implementations in computer algebra packages. Problems for this MRC will be arranged around five central topics: effective computer algebra methods, algorithms using computational topology, multivariate asymptotic phase transitions, singular transforms for degenerate saddle-point integrals, and applications of harmonic analysis and singularity theory. Researchers with knowledge in any one of these areas are encouraged to apply to this MRC.

Centre International de Rencontres Mathématiques (CIRM)

Algebra,    Group Theory

Institute for Mathematical Sciences/National University of Singapore

Interactions between people working in Index Theory and Complex Geometry are increasing. One of the reasons is that although researchers use different tools and techniques, their studies have profound connections and are understandable to people from both sides. Sharing experiences and techniques is an opportunity for them to accelerate collaboration works. Index Theory and Complex Geometry recently both have spectacular developments. In this program, we plan to dig out more materials on complex geometry side of global analysis led by recent development on geometric hypoelliptic Laplacians.

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

Banff International Research Station

The Banff International Research Station will host the "Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4" workshop in Banff from June 7 to June 12, 2020. This workshop will highlight new results in low-dimensional topology coming from a wide range of geometric methods. Low-dimensional topology studies the global properties of geometric spaces in dimensions 3 and 4, such as 3-dimensional space and 4-dimensional space-time.

Banff International Research Station for Mathematical Innovation and Discovery

One of the big ideas in modern mathematics is that integers (like 1, 2, 3, 4, 5, ...) in many formal ways behave similarly to polynomial equations (like y = x^2, which defines the parabola). Frequently, and perhaps surprisingly, many questions in mathematics are easier to study for polynomials than for integers. Hence intuition and results for polynomials can tell us about the integers. Commutative algebra lives at the intersection of both perspectives, and one fundamental object of study is polynomials with integer coefficients, this is called the mixed characteristic case. Recently, Yves Andre proved a long standing open conjecture in commutative algebra in this mixed characteristic setting, relying on constructions of Scholze (and then Bhatt gave a simplified proof of the same conjecture). This workshop aims to foster and discuss these and other recent tools, to study some remaining open problems in mixed characteristic. The workshop will bring together a diverse group of researchers from different fields, such as commutative algebra, algebraic geometry, and number theory.

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

Centre International de Rencontres Mathématiques (CIRM)

One of the fascinating bridges between classical mechanics and quantum physics is expressed in the fact that the length spectrum and the Laplace spectrum of a closed Riemannian manifold determine each other (at least generically). Similarly, the set of lengths of the closed orbits of a billiard table and the Laplace spectrum of that table determine each other, at least for certain billiard tables. The main goal of this school is to introduce graduate students and young researchers to basic facts on these two spectra, and to the above correspondence. The length spectrum generalizes to the action spectrum of an autonomous Hamiltonian function. Floer homology filtered by the action spectrum can be used to construct so-called action selectors, that are a principal tool in modern symplectic geometry and dynamics, yielding simple proofs of Gromov's nonsqueezing theorem, the Weinstein conjecture in R^{2n}, the existence of closed orbits in a magnetic fields, etc. The second goal is to understand this relevance of the action spectrum in symplectic geometry. A third, more hypothetical, goal is to see which parts of the two sides can be related.

Prerequisites: We expect that students have had courses in real analysis of several variables, know what an ordinary differential equation is, and have followed a course on curves and surfaces. More knowledge is useful, but not necessary to follow the lectures.

Algebra,    Courses and Events for Physics Students

Laboratoire Dieudonné, Université Côte d'Azur, Nice

On the occasion of the "Chair Montel 2020" awarded by Xiaojun Huang (Rutgers U.), we're organizing an international conference on Dynamics, Several Complex Variables and CR geometry. We expect to gather outstanding contributions in complex geometry and analytic PDEs as well.

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

Centre International de Rencontres Mathématiques (CIRM)

The Computational Geometry Week (CG Week) is the premier international forum for advances in computational geometry and its many applications. The 2020 edition with the 36th International Symposium on Computational Geometry (SoCG 2020) will take place in Zürich, Switzerland, June 22-26, 2020.

The main purpose of the conference is to stimulate the exchange of new ideas in algebra, topology and geometry, and to celebrate 50 years of the Jan Kochanowski University. On the occasion of the jubilee, we plan to remind the brightest moments of mathematical research and education in Kielce. The conference will be divided int two parts - the anniversary and the scientific. The first one gives the opportunity to meet many of the former and the current elmployees of our Institute. The second, provides the space for scientific discussions at four thematic sessions, that is Topology, Analysis, Geometry and Didactics. We warmly invite all mathematicans to share our joy and scientific enthusiasm in theese special days.

Analysis,    Didactics of Scientific Disciplines

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

International Centre for Mathematical Sciences, Edinburgh; UK

Andrew Ranicki and his theory of algebraic surgery played a central role in linking manifold theory, algebraic K-theory, and its close cousin L-theory. These areas have seen great developments and advances in the last decade from distinct research communities. This workshop will bring together mathematicians working on the topology of high-dimensional manifolds and their automorphisms with those working on the algebraic K-theory (and its cousins hermitian K-theory and L-theory) of rings and ring spectra, in order to share recent progress in these areas and kindle a fresh interaction between them.

Graph Theory and Combinatorics,    Algebra

Department of Mathematics, Faculty of Information Technology, University of Pannonia in cooperation with the Regional Centre of the Hungarian Academy of Sciences, Veszprém

The conference Geometry Festival will celebrate the 65th birthday of Karoly Bezdek (University of Calgary, Canada and University of Pannonia, Hungary). The theme of the conference will be discrete geometry, related fields, aspects, recent progress. The program of the conference will consist of invited lectures and contributed talks.

Applied Mathematics (in general),    Numerical Analysis and Computational Mathematics

The purpose of the present workshop is to expose fundamental, introductory aspects of combinatorial anabelian geometry, as well as more recent developments related to the Grothendieck-Teichmüller group and the absolute Galois groups of number fields and mixed-characteristic local fields.

Graph Theory and Combinatorics,    Number Theory, Arithmetic

Department of Mathematics of the University of Salerno

Poisson 2020 is the 12nd in a series of international conferences on Poisson geometry. It will be held in the Department of Mathematics of the University of Salerno, Fisciano (SA), and the Accademia Pontaniana, Napoli, Italy. The event comprises: - a Summer School (July 6 - 10), aimed at students in their final years, PhD students and young researchers. - an International Conference (July 13 - 17), to be attended by students and researches from around the world, including some of the leading mathematicians in the field of Poisson Geometry. Links to the previous conferences in the series can be found at the Poisson Geometry Home Page: www.lpthe.jussieu.fr/~dito/poissongeometry.

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

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

This conference contains contributions that give an overview of the current research in geometric mechanics. This scientific subject is simultaneously close to mathematics, physics, and engineering and its general philosophy consists in taking advantage of fruitful interactions between geometry on the one hand and dynamics and mechanics on the other. This conference will be the occasion to celebrate the 70th birthday of Tudor Ratiu who over the years has made many fundamental contributions in the development of this field.

Systems theory, Control and Automation,    Mathematical Physics

Conference on algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Topics include: integer-valued polynomials, polynomial functions, multiplicative ideal theory, topological methods in ring theory, Zariski-Riemann spaces of valuation domains, factorization theory in rings and semigroups, module theory and linear algebra over rings, Dedekind, Pruefer and Krull domains and generalizations

Algebra,    Number Theory, Arithmetic

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

Northwestern University, Evanston, IL

The goal of this summer school is to introduce participants to tools and ideas from algebraic topology and homotopy theory that are used in the study of fixed point theory. The workshop will be centered around mini-courses, both on classical fixed-point theory and on modern techniques such as duality theory, spectra, and trace methods in algebraic K-theory.

The intended audience for this summer school should be familiar with the material in Hatcher (except the appendices). This reflects our goal that the school be accessible to second and third year students with an interest in algebraic topology from any PhD granting institution. The school will be structured around a few mini-courses, which will run in an active-learning style.

Algebra,    Courses and Events for Physics Students

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

The Galileo Galilei Institute for Theoretical Physics

Many remarkable properties of gauge theories rely on the topology of field configurations and/or ambient spacetime and are connected with quantum anomalies and nonperturbative excitations. These properties, often exact, have many implications in the physics of fundamental interactions, condensed matter systems and statistical mechanics models. They also account for a large part of the investigations in string theory, and combined with supersymmetry have led to exact solutions of low-energy theories and the discovery of duality relations between supersymmetric gauge theories. Meanwhile, a renewed interest in topological aspects has emerged from condensed matter physics, through the study of topological phases of quantum matter. The effective field theories for these systems are not of the usual Landau-Ginzburg-Higgs type, rather, they are described by topological gauge theories. The goal of this GGI activity is to bring together theoreticians of different backgrounds, in condensed matter, high energy and mathematical physics, with the belief that interdisciplinary approaches can lead to substantial progress in many directions.

Anomalies of quantum field theories * Generalized symmetries * Topological aspects of quantum states in condensed matter * (Supersymmetric) dualities in (2+1)-dimensions * Time-reversal symmetry and 4d theta-terms

High Energy Physics, Particles and Fields,    Condensed Matter Physics and Materials

Regensburg University, Dep. of Mathematics, SFB1085 (U. Bunke, D.C. Cisinski, G. Kings )

Homotopical and higher categorical methods have seen increasing importance in mathematics, both as foundations and as computational tools. In fact, such methods merge two apparently distinct goals: understanding geometrical forms and classifying mathematical structures. This conference aims at gathering together under this perspective geometers in a rather broad sense. It seeks to foster the applications of these higher methods in the interplay between homotopy theory, arithmetic, and algebraic geometry.

Number Theory, Arithmetic,    Algebra

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

The Galileo Galilei Institute for Theoretical Physics

Topological properties of gauge theories find application in the characterization of novel phases of matter and in establishing nonperturbative phenomena such as the duality relations between quantum field theories in three and four spacetime dimensions. This conference is meant to expose the current status of research in several domains dealing with topology and duality

Anomalies of quantum field theories * Generalized symmetries * Topological aspects of quantum states in condensed matter * (Supersymmetric) dualities in (2+1)-dimensions * Time-reversal symmetry and 4d theta-terms

High Energy Physics, Particles and Fields,    Mathematical Physics

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

The Galileo Galilei Institute for Theoretical Physics

Anomalies of quantum field theories * Generalized symmetries * Topological aspects of quantum states in condensed matter * (Supersymmetric) dualities in (2+1)-dimensions * Time-reversal symmetry and 4d theta-terms

High Energy Physics, Particles and Fields,    Mathematical Physics

Algebra,    Number Theory, Arithmetic

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

Algebra,    Graph Theory and Combinatorics

Centre International de Rencontres Mathématiques (CIRM)

Centre International de Rencontres Mathématiques (CIRM)

Centre International de Rencontres Mathématiques (CIRM)

Institute for Mathematical Sciences/National University of Singapore

In this two-week program, we explore the interactions between geometric group theory, geometric structures and Anosov representations. Geometric group theory, in the broadest sense, seeks to understand the structure of groups through their actions on objects with geometric meaning. Conversely, one can take a known group and attempt to understand all its geometrically meaningful actions. One natural notion that arises in this setting is an Anosov representation, which came about as an attempt to describe what it means for the action of a discrete group on a homogeneous space to be geometrically well behaved. Also, in his Erlangen program, Felix Klein viewed geometry as a space which is invariant under a group of transformations. This gave rise to the notion of a geometric structure, which gives yet another notion of a geometrically meaningful action of a group on a homogeneous space.

Group Theory,    Courses and Events for Math Students and Early Career Researchers

Stability, Boundedness and Fano Varieties at the Beijing International Center for Mathematical Research.