Conférences - Géométrie et topologie

Originally introduced by Martin Bartels in the early nineteenth century, and then extensively developed by Élie Cartan in the first half of the twentieth century, the method of moving frames is a powerful tool for studying the geometry of curves, surfaces, and, more generally, submanifolds under the action of a group of transformations. In 1999, a new and more general formulation of moving frame was introduced by Fels and Olver which led to a dramatic resurgence of interest in the method accompanied by a striking extension of the range of applications. The workshop will bring together a diverse group of experts with the goal of exploring existing and emerging applications of the moving frame method to differential equations and integrable systems in physics, to computer vision and object recognition, medical imaging, broken object reconstruction, discrete and differential-difference equations, geometric numerical integration, and much more.

Università di Milano-Bicocca, University of Southampton, Académie de Paris

The Workshop intends to draw together a broad range of group theory including the study of topological groups (such as profinite or more general locally compact) as well as analytical and geometrical aspects of discrete groups including random walks on Cayley graphs and coarse geometric structure. There will be 3 talks each day and participants would be free to pick and choose which ones to attend. We also plan to have space for social interaction including small splinter group discussion. If you are interested in participating, please fill out the registration form available on the webpage. Once registration is completed, you will be notified with every new update on the meeting and all the instructions.

Organizers;     Email.: ilaria.castellano@unimib.it

group theory, locally compact, profinite, geometric structures, random walks, manifolds

KTH Royal Institute of Technology and Stockholm University

The Young Topologists Meeting (YTM) is an annual event that has previously been organised by the EPFL (Switzerland), the University of Copenhagen (Denmark); and jointly by Stockholm University and the Royal Institute of Technology (Sweden). This year it will take place on July 6-10 in Stockholm. The intention of the conference is to create a setting in which young researchers in topology can meet each other and share their work.

Email.: youngtopologistsmeeting@gmail.com

CIRM – Centre International de Rencontres Mathématiques

Mathematical Sciences Research Institute (MSRI)

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

Cours et événements pour étudiants en physique,    Analyse

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.

Nesin Mathematical Village

The 5th GTSS will be held at the IMBM, İstanbul Center for Mathematical Sciences which is established in the main (South) Campus of Boğaziçi University (Bosphorus). There will be about 15 mini-courses of introductory nature, related to the Geometry-Topology research subjects. In the middle of the week there is an excursion on the Bosphorus.

Differential Geometry, Complex Differential Geometry, Topology, Algebraic Geometry

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

University of Rochester, Yerevan State University and Norwegian University of Science and Technology

University of Rochester, in collaboration with the Yerevan State University and Norwegian University of Science and Technology, is organizing a CIMPA Summer School on Finite Point Configurations and Discrete Integrable Systems, to be held at the Yerevan State University, Armenia, from July 13 until July 24. The summer school will be dedicated to finite point configurations and rigidity, Erdos problems in discrete geometry and frame theory, the Falconer distance conjecture in geometric measure theory, discrete integrable systems and connections between these topics. Participants will be introduced to various open problems and possible research projects in these very active research areas.

Finite Point Configurations, Discrete Integrable Systems, Discrete Geometry

Cours et évènements pour étudiants en mathématiques,    Analyse

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.

Systèmes, contrôle et automatisation,    Physique mathématique

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

Algèbre,    Théorie des nombres, arithmétique

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

The University of Sydney, School of Mathematics and Statistics

This workshop at the University of Sydney will bring together experts and emerging researchers from Australia, the USA and Europe to report on recent results and explore future directions in computational and algorithmic topology and related areas. There will be a focus on problems in computational geometric topology and computational algebraic topology. This workshop aims to stimulate interaction between researchers in order to bring about new collaborations on difficult problems that cannot be tackled from one viewpoint alone.

We plan to have talks by our invited speakers in the mornings, and open problem sessions, a poster session, and plenty of time for collaboration in the afternoons.

Invited Speakers:

Herbert Edelsbrunner (Institute of Science and Technology Austria)

Brittany Fasy (Montana State University)

Gregory Henselman (Princeton University)

Feng Luo (Rutgers University)

Zuzana Patáková (Institute of Science and Technology Austria)

Jessica Purcell (Monash University)

Vanessa Robins (Australian National University)

Organizers:

Jonathan Spreer (The University of Sydney)

Stephan Tillmann (The University of Sydney)

Katharine Turner (Australian National University)

Email.: jonathan.spreer@sydney.edu.au

Computational topology, Low-dimensional topology, Topological Data Analysis, Computational geometry, Algebraic topology, Algorithms

Théorie des graphes et combinatoire,    Algorithmes

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.

Algèbre,    Cours et événements pour étudiants en physique

Chernivtsi National University and Lviv National University, Ukraine

The Summer School is a traditional conference for mathematicians working in diverse areas of analysis, topology, algebra and related fields. The aim of the School is to support talented students and post-graduates who are interested in fundamental mathematical research and to supply them with the newest information concerning the current status of research in these fields.

Summer School Secretariat;     Email.: maslenizza.ua@gmail.com

Analyse,    Algèbre

University of Saskatchewan

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

Mathématiques appliquées (en général),    Algorithmes

University of Nebraska-Lincoln

This conference will focus on trisections of smooth 4-manifolds and related topics. There is some space available for contributed talks, and we have funding for participant support. The deadline to apply for support or to apply to give a talk is April 15th.

Email.: zupan@unl.edu

4-manifold, trisection

Universidad de Puerto Rico

Guoliang Yu, Powell Chair in Mathematics and University Distinguished professor at Texas A&M University, will lead this series of lectures on K-theory of operator algebras and its applications to geometry and topology.

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

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

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

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

Physique des hautes énergies, des particules et des champs,    Physique de la matière condensée et des matériaux

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.

Théorie des nombres, arithmétique,    Algèbre

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

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

Mathematical Sciences Research Institute (MSRI)

The use of dynamical invariants has long been a staple of geometry and topology, from rigidity theorems, to classification theorems, to the general study of lattices and of the mapping class group. More recently, random structures in topology and notions of probabilistic geometric convergence have played a critical role in testing the robustness of conjectures in the arithmetic setting. In this introductory workshop, we will bring together junior and senior researchers in order to provide a mix of introductory lectures as well as reporting on more recent progress in topics from this diverse range of subjects.

AMS, American Mathematical Society

This workshop will discuss results and new developments in Leibniz algebras and related topics. This includes and not limited to Lie algebras, homological algebra or non-commutative geometry.

Leibniz algebras, Lie algebras, Homological algebras.

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

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

Algèbre,    Théorie des nombres, arithmétique

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

This workshop intends to be a first meeting point for specialists and young researchers active in non-commutative geometry, free probability, and topological recursion. In the two first areas, one often wants to compute expectation values of a large class of non-commutative observables in random ensembles of (several) matrices of size N, in the large N limit. The motivations come from the study of various models of 2d quantum gravity via random spectral triples, or from the problem of identifying of interesting factors via approximations by matrix models. Topological recursion and its generalizations provide a priori universal recipes to make and compactly organize such computations, not only for the leading order in N, but also to all orders of expansion in 1/N.in such a way that bridges to other domains where topological recursion has been applied (like enumerative geometry, tropical geometry, mirror symmetry, topological and more generally low-dimensional quantum field theories) become clear.

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

Algèbre,    Théorie des graphes et combinatoire

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Inspired by the success of persistent homology, the purpose of the present workshop is to replicate this success by developing robust, statistically integrated versions of other constructions from classical algebraic topology. In particular, we are interested in persistent versions of cohomology theory, that combine the robustness of persistence with the various sophisticated algebraic structures associated with cohomology.

Mathematical forum of Montenegro and Faculty of Information Studies, Novo mesto, Slovenia

MESIGMA is a symposium that brings together researchers from several fields of mathematics and computer science. As the scientific framework for MESIGMA is widely set, we consider it to be an incentive environment for finding “shared territory” of diverse scientific disciplines.

Théorie des graphes et combinatoire,    Algèbre

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

This workshop will tackle some fundamental open questions about Artin-Schelter regular algebras, in particular, elliptic algebras, and their associated Poisson structures. In particular, it will focus on the correspondence between the representations of elliptic algebras and the symplectic leaves of their semi-classical limits, as well as on the relationship between the deformation theory of Artin-Schelter regular algebras and that of the derived category or the A-infinity-category of related projective schemes. This workshop brings together leading experts in algebra and geometry from around the world to identify and attack these outstanding problems and to collaborate for future breakthroughs.

Centre International de Rencontres Mathématiques (CIRM)

BIRS-affiliated mathematics research centre, Casa Matemática Oaxaca (CMO)

Symplectic geometry concerns symplectic manifolds. A key modern tool is an algebraic structure called the 'Fukaya category', which is associated to a single such object. Geometric relations between the manifolds are reflected in algebraic interactions between the categories. There has been a great deal of recent progress in understanding such relations. This workshop will bring together many of the key workers in this rapidly developing field to share ideas and set further directions of exploration.

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

Birational geometry is a classical mathematic subject dating back to the late 1800s. It aims to classify geometric shapes by looking at the majority of their points and asks "if I remove some points from shape A and some other points from shape B, do they become the same shape?". This turns out to be a surprisingly difficult and fundamental mathematical question. Perhaps more surprising is that the classification of geometric shapes from birational geometry is related to the classification of abstract mathematical gadgets called derived categories, a formal language developed by prominent mathematicians in France in the 1960s. However, the relationship between derived categories and birational geometry remains unproven.

BIRS-affiliated mathematics research centre, Casa Matemática Oaxaca (CMO)

Valuation theory grew out of integral geometry, and studies such geometric quantities as volume, surface area, and their generalizations. Spaces with curvature bounds are geometric objects which are not necessarily smooth, but that retain nevertheless some of the features of smooth spaces. For example convexity/concavity properties of the distance function can be seen as a non-smooth generalization of the smooth notion of curvature of constant sign.

Centre International de Rencontres Mathématiques (CIRM)

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

Cours et évènements pour étudiants en mathématiques,    Théorie des graphes et combinatoire

The possibility of using quantum mechanics to build computers that are both faster and more secure is an exciting technological leap. One of the most promising pathways to a robust architecture, referred to as topological quantum computing, has lead to fascinating research at the frontier of mathematics and physics. Properties of new, exotic states of matter can be understood - and hence implemented in practice - using tools that were developed by pure mathematicians in connection to surfaces and their curvature. This workshop is bringing together international experts to explore the intimate connections between such topological properties of quantum matter and the key resource of quantum computing: entanglement.

Centre International de Rencontres Mathématiques (CIRM)

Mathematical Sciences Research Institute (MSRI)

The study of discrete subgroups of Lie groups and the associated locally symmetric manifolds has a long and rich history, with powerful interconnections between the geometry of the locally symmetric space, topology of towers of its finite covers, and number-theoretic aspects. More recently dynamical and probabilistic techniques have been fruitfully employed to study these groups and spaces. The workshop will take stock of recent developments in these highly active fields from a variety of backgrounds.

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

Cours et évènements pour étudiants en mathématiques,    Algèbre

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.

Théorie des groupes,    Cours et évènements pour étudiants en mathématiques

ICERM

This workshop will focus on the development of software to facilitate research in combinatorial algebraic geometry, based on the SAGE Mathematical Software System and the OSCAR Computer Algebra System. Special attention will be given to efficient computations with multi-variate polynomials, which is a critical part of many algorithms in combinatorial algebraic geometry. Aside from development of software, the workshop will feature a series of talks about polynomial computations, as well as introductory lectures about Sage and Oscar.

Email.: info@icerm.brown.edu

Algèbre,    Théorie des graphes et combinatoire

ICERM

The purpose of the workshop is to bring together a diverse group of researchers working on combinatorial and geometric aspects related to spaces with symmetries. The workshop will cover problems arising from various flavors of Schubert Calculus and enumerative geometry on flag manifolds, and problems from geometric representation theory and combinatorial Hodge theory. The topics covered include the study of Littlewood-Richardson coefficients, quantum cohomology and quantum K theory of flag manifolds, Maulik-Okounkov stable envelopes and characteristic classes, conformal blocks, and combinatorics related to moduli spaces, Macdonald theory, and quiver polynomials, Soergel bimodules, Hodge theory of matroids. These are trends in a rapidly developing area, and our aim is to facilitate interactions among researchers who work on different problems but employ similar techniques, at the intersection of algebraic geometry, combinatorics, and representation theory.

Email.: info@icerm.brown.edu

CIRM – Centre International de Rencontres Mathématiques

The conference will bring together leading experts and research scholars to exchange and share their experience and research results on all aspects of mathematical physics and to promote transference of knowledge at the crossroads of mathematics and physics. There will be plenary sessions (30 to 40min), short talks and posters for student presentations. The scope of the conference will be quite broad, including in particular the following topics: polyanalytic function theory, harmonic analysis, representation theory and quantization, Clifford analysis and applications, coherent states, time-frequency analysis and wavelets, orthogonal polynomials, special functions and q-analogues, Hopf algebras and quantum groups, geometric mechanics and symmetry, exact solvable systems, spectral theory and quantum systems, topological methods. With the goal of encouraging communication and collaborative research between the participants, a feature of ICMMP2021 will be the inclusion of specific time-slots for scientific discussion.

Tél.: [(212) (0) 663564850];     Email.: mouayn@gmail.com

Harmonic analysis, representation theory and quantization, Clifford algebras, Clifford analysis and applications, Coherent states & wavelets, q-deformation, Hopf algebras and quantum groups, Geometric mechanics and symmetry, Orthogonal Polynomials, special functions and exact solvable systems, Spectral theory and quantum systems, Topological Methods

Physique mathématique,    Théorie des groupes

CIRM – Centre International de Rencontres Mathématiques

ICERM

The workshop will revolve around the interplay between algebraic geometry and combinatorial structures such as graphs, polytopes, and polyhedral complexes. In particular, the workshop will foster dialogue among groups of researchers who use similar combinatorial geometric tools for different purposes within algebraic geometry and adjacent fields. The topics covered will include Newton-Okounkov bodies, Ehrhart theory, toric geometry, tropical geometry, matroids, and interactions with mirror symmetry.

Email.: Info@icerm.brown.edu

CIRM – Centre International de Rencontres Mathématiques

CIRM IHP PROGRAM

Mathematical Sciences Research Institute (MSRI)

The talks in this workshop will present a wide array of current applications of topology in neuroscience, including classification and synthesis of neuron morphologies, analysis of synaptic plasticity, algebraic analysis of the neural code, topological analysis of neural networks and their dynamics, topological decoding of neural activity, diagnosis of traumatic brain injuries, and topological biomarkers for psychiatric disease. Some of the talks will be devoted to promising new directions in algebraic topology that have been inspired by neuroscience.

CIRM – Centre International de Rencontres Mathématiques

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

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

Cours et évènements pour étudiants en mathématiques,    Algèbre

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

Cours et évènements pour étudiants en mathématiques,    Analyse

Applied and computational topology, one of the most rapidly growing branches of mathematics, is becoming a key tool in applied sciences. It is making impact not only in mathematics, but on the wide interdisciplinary environment including material and medical sciences, data science, robotics.

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

University of Portsmouth, School of Mathematics and Physics

Tél.: [02392846358];     Email.: ittay.weiss@port.ac.uk

Clay Mathematics Institute (CMI)

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

Algèbre,    Calcul infinitésimal, équations différentielles et intégrales

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

The focus of this meeting is the connections between lattices and number theory and geometry. Number theory, one of the oldest branches of pure mathematics, is devoted to the study properties of the integers and more sophisticated number systems. Lattices and number theory have many deep connections. For instance using number theory it was recently demonstrated that certain packings of balls in high dimensions are optimally efficient. Lattices also appear naturally when one studies certain spaces that play an important role in number theory; one of the main focuses of this meeting is to investigate computational and theoretical methods to understand such spaces and to expand the frontier of our algorithmic knowledge in working with them.

CIRM – Centre International de Rencontres Mathématiques

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

The cohomology of arithmetic groups is the study of the properties of ``holes'' in geometric spaces that contain information about number theory. The workshop will bring together mathematicians with expertise in number theory, topology, and geometric group theory to tackle these problems and explore recent developments.

Théorie des groupes,    Théorie des nombres, arithmétique

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

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