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# Documents  Critères de recherche : "Géométrie" | enregistrements trouvés : 2 879

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## Towards complex and realistic tokamaks geometries in computational plasma physics Ratnani, Ahmed | CIRM H

Post-edited

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## Autour de la géométrie stochastique : polytopes aléatoires et autres modèles Calka, Pierre | CIRM H

Post-edited

Geometry;Probability and Statistics

La géométrie stochastique est l'étude d'objets issus de la géométrie euclidienne dont le comportement relève du hasard. Si les premiers problèmes de probabilités géométriques ont été posés sous la forme de casse-têtes mathématiques, le domaine s'est considérablement développé depuis une cinquantaine d'années de part ses multiples applications, notamment en sciences expérimentales, et aussi ses liens avec l'analyse d'algorithmes géométriques. L'exposé sera centré sur la description des polytopes aléatoires qui sont construits comme enveloppes convexes d'un ensemble aléatoire de points. On s'intéressera plus particulièrement aux cas d'un nuage de points uniformes dans un corps convexe fixé ou d'un nuage de points gaussiens et on se focalisera sur l'étude asymptotique de grandeurs aléatoires associées, en particulier via des calculs de variances limites. Seront également évoqués d'autres modèles classiques de la géométrie aléatoire tels que la mosaïque de Poisson-Voronoi. La géométrie stochastique est l'étude d'objets issus de la géométrie euclidienne dont le comportement relève du hasard. Si les premiers problèmes de probabilités géométriques ont été posés sous la forme de casse-têtes mathématiques, le domaine s'est considérablement développé depuis une cinquantaine d'années de part ses multiples applications, notamment en sciences expérimentales, et aussi ses liens avec l'analyse d'algorithmes géométriques. ...

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## Geometric Langlands correspondence and topological field theory - Part 1 Ben-Zvi, David | CIRM H

Post-edited

Algebraic and Complex Geometry;Mathematical Physics

Kapustin and Witten introduced a powerful perspective on the geometric Langlands correspondence as an aspect of electric-magnetic duality in four dimensional gauge theory. While the familiar (de Rham) correspondence is best seen as a statement in conformal field theory, much of the structure can be seen in the simpler (Betti) setting of topological field theory using Lurie's proof of the Cobordism Hypothesis. In these lectures I will explain this perspective and illustrate its applications to representation theory following joint work with Nadler as well as Brochier, Gunningham, Jordan and Preygel. Kapustin and Witten introduced a powerful perspective on the geometric Langlands correspondence as an aspect of electric-magnetic duality in four dimensional gauge theory. While the familiar (de Rham) correspondence is best seen as a statement in conformal field theory, much of the structure can be seen in the simpler (Betti) setting of topological field theory using Lurie's proof of the Cobordism Hypothesis. In these lectures I will explain ...

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## The geometrical gyro-kinetic approximation Frénod, Emmanuel | CIRM H

Post-edited

Partial Differential Equations;Mathematical Physics

At the end of the 70', Littlejohn [1, 2, 3] shed new light on what is called the Gyro-Kinetic Approximation. His approach incorporated high-level mathematical concepts from Hamiltonian Mechanics, Differential Geometry and Symplectic Geometry into a physical affordable theory in order to clarify what has been done for years in the domain. This theory has been being widely used to deduce the numerical methods for Tokamak and Stellarator simulation. Yet, it was formal from the mathematical point of view and not directly accessible for mathematicians.
This talk will present a mathematically rigorous version of the theory. The way to set out this Gyro-Kinetic Approximation consists of the building of a change of coordinates that decouples the Hamiltonian dynamical system satisfied by the characteristics of charged particles submitted to a strong magnetic field into a part that concerns the fast oscillation induced by the magnetic field and a other part that describes a slower dynamics.
This building is made of two steps. The goal of the first one, so-called "Darboux Algorithm", is to give to the Poisson Matrix (associated to the Hamiltonian system) a form that would achieve the goal of decoupling if the Hamiltonian function does not depend on one given variable. Then the second change of variables (which is in fact a succession of several ones), so-called "Lie Algorithm", is to remove the given variable from the Hamiltonian function without changing the form of the Poisson Matrix.
(Notice that, beside this Geometrical Gyro-Kinetic Approximation Theory, an alternative approach, based on Asymptotic Analysis and Homogenization Methods was developed in Frenod and Sonnendrücker [5, 6, 7], Frenod, Raviart and Sonnendrücker [4], Golse and Saint-Raymond [9] and Ghendrih, Hauray and Nouri [8].)
At the end of the 70', Littlejohn [1, 2, 3] shed new light on what is called the Gyro-Kinetic Approximation. His approach incorporated high-level mathematical concepts from Hamiltonian Mechanics, Differential Geometry and Symplectic Geometry into a physical affordable theory in order to clarify what has been done for years in the domain. This theory has been being widely used to deduce the numerical methods for Tokamak and Stellarator s...

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## Galois codes for arithmetic and geometry via the power of valuation theory Koenigsmann, Jochen | CIRM H

Post-edited

Algebra;Number Theory

We give a survey on recent advances in Grothendiek's program of anabelian geometry to characterize arithmetic and geometric objects in Galois theoretic terms. Valuation theory plays a key role in these developments, thus confirming its well deserved place in mainstream mathematics.
The talk notes are available in the PDF file at the bottom of the page.

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## Whitney problems and real algebraic geometry Fefferman, Charles | CIRM H

Post-edited

This talk sketches connections between Whitney problems and e.g. the problem of deciding whether a given rational function on $\mathbb{R}^n$ belongs to $C^m$.

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## Stability and applications to birational and hyperkaehler geometry - Lecture 1 Bayer, Arend | CIRM H

Post-edited

Algebra;Algebraic and Complex Geometry

This lecture series will be an introduction to stability conditions on derived categories, wall-crossing, and its applications to birational geometry of moduli spaces of sheaves. I will assume a passing familiarity with derived categories.

- Introduction to stability conditions. I will start with a gentle review of aspects of derived categories. Then an informal introduction to Bridgeland’s notion of stability conditions on derived categories [2, 5, 6]. I will then proceed to explain the concept of wall-crossing, both in theory, and in examples [1, 2, 4, 6].

- Wall-crossing and birational geometry. Every moduli space of Bridgeland-stable objects comes equipped with a canonically defined nef line bundle. This systematically explains the connection between wall-crossing and birational geometry of moduli spaces. I will explain and illustrate the underlying construction [7].

- Applications : Moduli spaces of sheaves on $K3$ surfaces. I will explain how one can use the theory explained in the previous talk in order to systematically study the birational geometry of moduli spaces of sheaves, focussing on $K3$ surfaces [1, 8].
This lecture series will be an introduction to stability conditions on derived categories, wall-crossing, and its applications to birational geometry of moduli spaces of sheaves. I will assume a passing familiarity with derived categories.

- Introduction to stability conditions. I will start with a gentle review of aspects of derived categories. Then an informal introduction to Bridgeland’s notion of stability conditions on derived categories ...

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## Statistical inverse problems and geometric "wavelet" construction Kerkyacharian, Gérard | CIRM H

Post-edited

Probability and Statistics

In the fist part of the talk, we will look to some statistical inverse problems for which the natural framework is no more an Euclidian one.
In the second part we will try to give the initial construction of (not orthogonal) wavelets -of the 80 - by Frazier, Jawerth,Weiss, before the Yves Meyer ORTHOGONAL wavelets theory.
In the third part we will propose a construction of a geometric wavelet theory. In the Euclidian case, Fourier transform plays a fundamental role. In the geometric situation this role is given to some "Laplacian operator" with some properties.
In the last part we will show that the previous theory could help to revisit the topic of regularity of Gaussian processes, and to give a criterium only based on the regularity of the covariance operator.
In the fist part of the talk, we will look to some statistical inverse problems for which the natural framework is no more an Euclidian one.
In the second part we will try to give the initial construction of (not orthogonal) wavelets -of the 80 - by Frazier, Jawerth,Weiss, before the Yves Meyer ORTHOGONAL wavelets theory.
In the third part we will propose a construction of a geometric wavelet theory. In the Euclidian case, Fourier transform ...

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## Ancient solutions of geometric flows Daskalopoulos, Panagiota | CIRM H

Post-edited

Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Geometry

We will give a survey of recent research progress on ancient or eternal solutions to geometric flows such as the Ricci flow, the Mean Curvature flow and the Yamabe flow.
We will address the classification of ancient solutions to parabolic equations as well as the construction of new ancient solutions from the gluing of two or more solitons.

53C44

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## Condition: the geometry of numerical algorithms - Lecture 1 Bürgisser, Peter | CIRM H

Post-edited

The performance of numerical algorithms, both regarding stability and complexity, can be understood in a unified way in terms of condition numbers. This requires to identify the appropriate geometric settings and to characterize condition in geometric ways.
A probabilistic analysis of numerical algorithms can be reduced to a corresponding analysis of condition numbers, which leads to fascinating problems of geometric probability and integral geometry. The most well known example is Smale's 17th problem, which asks to find a solution of a given system of n complex homogeneous polynomial equations in $n$ + 1 unknowns. This problem can be solved in average (and even smoothed) polynomial time.
In the course we will explain the concepts necessary to state and solve Smale's 17th problem. We also show how these ideas lead to new numerical algorithms for computing eigenpairs of matrices that provably run in average polynomial time. Making these algorithms more efficient or adapting them to structured settings are challenging and rewarding research problems. We intend to address some of these issues at the end of the course.
The performance of numerical algorithms, both regarding stability and complexity, can be understood in a unified way in terms of condition numbers. This requires to identify the appropriate geometric settings and to characterize condition in geometric ways.
A probabilistic analysis of numerical algorithms can be reduced to a corresponding analysis of condition numbers, which leads to fascinating problems of geometric probability and integral ...

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## Local acyclicity in $p$-adic geometry Scholze, Peter | CIRM H

Post-edited

Algebraic and Complex Geometry;Number Theory

Motivated by applications to the geometric Satake equivalence and in particular the construction of the fusion product, we define a notion of universally locally acyclic for rigid spaces and diamonds, and prove that it has the expected properties.

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## Interactions of analytic number theory and geometry - lecture 1 Schindler, Damaris | CIRM H

Post-edited

Algebraic and Complex Geometry;Number Theory

A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer-Manin obstruction.

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## Geometry,von Staudt's point of viewproceedings of the NATO advanced study institute held at Bad Windsheim,West Germany,july 21 - aug. 1,1980 Plaumann, Peter ; Strambach, Karl | D. Reidel Publishing Company 1981

Congrès

ISBN 978-90-277-1283-7

Nato a.s.i. series

Localisation : Colloque 1er étage (BAD)

Staudt # conique # géométrie # géométrie spéciale # plan projectif # point fixe # projectivité # quadrique # topologie

51Axx

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## Symplectic geometrycolloque symplectique 4èeme journéees Ffermat qui a eu lieu à la Faculté des SciencesMars 5-7 Crumeyrolle, A. ; Grifone, J. | Pitman Advanced Publisher Program 1983

Congrès

ISBN 978-0-273-08575-1

Research notes in mathematics , 0080

Localisation : Colloque 1er étage (TOUL)

*-produit invariant # action de groupe de Lie # action hamiltonienne # analyse lagrangienne # asymptotique géométrique # classe de Maslov-Arnold # déformation # feuilletage symplectiquement régulier # foliation # forme différentielle # groupe de symétrie # géométrie différentielle # géométrie symplectique # immersion de Lagrange # intégrale exponentielle # intéraction gravitationnelle # le tour de Yang-Mills # presque-point # problème de Kepler # quotient de sous-variété invariante # relation symplectique linéaire # relativité générale # représentation du moment d'énergie # singularité # sous-variété # stabilité en mécanique céleste # structure symplectique # structure transverse symplectique ou de contact # système hamiltonien contraint # théorie de Galois différentielle # variété canonique # variété de Poisson # variété graduée *-produit invariant # action de groupe de Lie # action hamiltonienne # analyse lagrangienne # asymptotique géométrique # classe de Maslov-Arnold # déformation # feuilletage symplectiquement régulier # foliation # forme différentielle # groupe de symétrie # géométrie différentielle # géométrie symplectique # immersion de Lagrange # intégrale exponentielle # intéraction gravitationnelle # le tour de Yang-Mills # presque-point # problème de Kepler ...

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## Ordered fields and real algebraic geometryproceedings of the special session on... held in san francisco#Jan. 7-11 Dubois, D. W. ; Recio, T. | American Mathematical Society 1982

Congrès

- 360 p.
ISBN 978-0-8218-5007-7

Contemporary mathematics , 0008

Localisation : Collection 1er étage

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## Geometry of the laplace operatorproceedings of the symposium in pure mathematics held at the university of hawaii,honolulu,hawaii,march 27-30, 1979 Osserman, Robert ; Weinstein, Alain | American Mathematical Society 1980

Congrès

ISBN 978-0-8218-1439-0

Proceedings of symposia in pure mathematics , 0036

Localisation : Collection 1er étage

58-06

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## Surveys in differential geometry 2017. Vol. XXII:celebrating the 50th anniversary of the journal of differential geometry: lectures given at the geometry and topology conference at Harvard University in 2017 Cao, Huai-Dong ; Li, Jun ; Schoen, Richard M. ; Yau, Shing-Tung | International Press 2018

Congrès

- viii; 406 p.
ISBN 978-1-57146-361-6

Surveys in differential geometry , 0022

Localisation : Colloque 1er étage (CAMB)

géométrie différentielle # physique mathématique # courbure

53-XX

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## Combinatorics' 81 in honour of beniamino segreproceedings of the international conference on combinatorial geometries and their application rome,june 7-12, 1981 Barlotti, A. ; Ceccherini, P. V. ; Tallini, G. | North-Holland Publishing Co. 1983

Congrès

ISBN 978-0-444-86546-5

North-holland mathematics studies , 0078

Localisation : Colloque 1er étage (ROME)

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## Conference on differential geometric methods in theoretical physicsinternational centre for theoretical physicsJune 30 - July 3 Denardo, G. ; Doebner, H. D. | Pt Ltd.;World Scientific Publisher Co. 1983

Congrès

ISBN 978-9971-950-58-3

Localisation : Colloque 1er étage (TRIE)

gravité # géométrie de l'espace-temps # méthode de géométrie différentielle # méthode de quantification # opérateur différentiel sur variété # physique des particules # physique théorique # supergravité # théorie de jauge # théorie du champ quantique

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## Algebriac geometry :proceedings of the 3rd midwest conference on... held at the university of michigan#Nov. 14-15 Dolgachev, I. | Springer-Verlag 1983

Congrès

- 138 p.
ISBN 978-0-387-12337-0

Lecture notes in mathematics , 1008

Localisation : Collection 1er étage

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