Manual Global Aspects of Complex Geometry

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Any "categorical thinker" - that is, any mathematician whose work makes use of categorical ideas - is welcome to participate. AIM Workshop: Mathematics of topological insulators. 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. Shokurov's 70th Birthday. 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. Systems theory, Control and Automation. Workshop on Torus Actions in Topology. 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. 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.

Conferences and Meetings on Geometry and Topology

The program will have two components, an advanced workshop 23 - 28 March followed by a discussion meeting 30 March - 03 April 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.


  1. Complex Geometry and Dynamics - The Abel Symposium | John Erik Fornaess | Springer.
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Knots, quandles, Khovanov Homology, Jones Polynomial. Arithmetic geometry, cycles, Hodge theory, regulators, periods and heights. Number Theory, Arithmetic. Periods, Motives and Differential equations: between Arithmetic and Geometry. Real Algebraic Geometry.

Facets of Real Algebraic Geometry. Quantum Topology and Geometry. Foundations and Perspectives of Anabelian Geometry. The workshop will review fundamental developments in several branches of anabelian geometry, as well as report on recent developments. 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.

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.

Group Theory. Index Theory and Complex Geometry. 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. One of the big ideas in modern mathematics is that integers like 1, 2, 3, 4, 5, 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.

Workshop — Geometrie. Classical Elegance: the Geometry of Algebraic Varieties. Workshop — Geometric Structures in Group Theory. Multimedia, Computer Graphics and Visualization. Contemporary Mathematics in Kielce 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.

Workshop — Arithmetic Geometry. Geometry, Mechanics, and Dynamics.

Chebyshev Approximation and the Global Geometry of Model Predictions.

Conference in Honor of the 70th Birthday of Tudor Ratiu. 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.


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  • 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. Conference on Rings and Polynomials. 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.

    Workshop — Topologie. Workshop — Topological properties of gauge theories and their applications to high-energy and condensed-matter physics. 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.

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    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. Workshop — Topological and Smooth Dynamics on Surfaces. Topological Matter and Duality. 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. Workshop — Discrete Geometry. Focus Week — Topological Phases of Matter. 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.

    Stability, Boundedness and Fano Varieties. Chinese J. Math 4 , B UTTG Daskalopoulos and R. Classification of Weil-Petersson isometries. Papadopoulos ed. The Geometry and Topology of Coxeter Groups. Princeton Univ.

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    Press, Princeton NJ, Douady and C. Conformally natural extension of homeomorphisms of the circle. Earle and J. Eells and L. Deformation of metrics and associated harmonic maps. Bombay , World Scientific. Two reports on harmonic maps Publishing Co. Eells and J. Harmonic Mappings of Riemannian Manifolds Am.

    Fischer and J. Deformations of the scalar curvature. Duke Math. Fischer and A.

    Complex geometry - Wikipedia

    S 42 , Riemannian - On a purely proof of the structure and dimension of the unramified moduli space of a compact Riemann surface. Gromov and R. Harmonic mappings into singular spaces and p-adic super-rigidity for lattices in groups of rank one. Hautes Etudes Sci. Gilbarg and N. On homotopic harmonic maps. Jost and R. On the existence of harmonic diffeomorphisms. The inverse function theorem of Nash and Moser.


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      Hokkaido Math. Automorphisms of complex of curves on punctured spheres and on punctured tori. Topology Appl. Korevaar and R. Sobolev spaces and harmonic maps for metric target spaces. Global existence theorems for harmonic maps to non-locally compact spaces. Global existence theorems for harmonic maps: finite rank spaces and an approach to rigidity for smooth actions. Preprint Harmonic maps between flat surfaces with conical singularities.

      Harmonic mappings of surfaces with respect to degenerate metrics. Lins, A Denjoy-Wolff. Cambridge Phil. Li and L. Uniqueness and regularity of proper harmonic maps. Annals Math. Automorphisms of the complex of curves. On the solutions of quasi-linear elliptic partial differential equations. S 43 , Peter and D.

      An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Masur and M. The Weil-Petersson isometry group.