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# Documents  Critères de recherche : "Algebra" | enregistrements trouvés : 2 338

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## Algebraic and transcendental formulas for the smallest parts function Ahlgren, Scott | CIRM H

Post-edited

Research talks;Number Theory

We study the smallest parts function introduced by Andrews. The associated generating function forms a component of a natural mock modular form of weight 3/2 whose shadow is the Dedekind eta function. We obtain an exact formula and an algebraic formula for each value of the smallest parts function; these are analogues of the formulas of Rademacher and Bruinier-Ono for the ordinary partition function. The convergence of our expression is non-trivial; the proof relies on power savings estimates for weighted sums of generalized Kloosterman sums which follow from spectral methods. We study the smallest parts function introduced by Andrews. The associated generating function forms a component of a natural mock modular form of weight 3/2 whose shadow is the Dedekind eta function. We obtain an exact formula and an algebraic formula for each value of the smallest parts function; these are analogues of the formulas of Rademacher and Bruinier-Ono for the ordinary partition function. The convergence of our expression is ...

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## Algebraic cycles on varieties over finite fields Pirutka, Alena | CIRM H

Post-edited

Research talks;Algebraic and Complex Geometry

Let $X$ be a projective variety over a field $k$. Chow groups are defined as the quotient of a free group generated by irreducible subvarieties (of fixed dimension) by some equivalence relation (called rational equivalence). These groups carry many information on $X$ but are in general very difficult to study. On the other hand, one can associate to $X$ several cohomology groups which are "linear" objects and hence are rather simple to understand. One then construct maps called "cycle class maps" from Chow groups to several cohomological theories.
In this talk, we focus on the case of a variety $X$ over a finite field. In this case, Tate conjecture claims the surjectivity of the cycle class map with rational coefficients; this conjecture is still widely open. In case of integral coefficients, we speak about the integral version of the conjecture and we know several counterexamples for the surjectivity. In this talk, we present a survey of some well-known results on this subject and discuss other properties of algebraic cycles which are either proved or expected to be true. We also discuss several involved methods.
Let $X$ be a projective variety over a field $k$. Chow groups are defined as the quotient of a free group generated by irreducible subvarieties (of fixed dimension) by some equivalence relation (called rational equivalence). These groups carry many information on $X$ but are in general very difficult to study. On the other hand, one can associate to $X$ several cohomology groups which are "linear" objects and hence are rather simple to ...

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## Algebraicity of the metric tangent cones Wang, Xiaowei | CIRM H

Post-edited

Research talks

We proved that any K-semistable log Fano cone admits a special degeneration to a uniquely determined K-polystable log Fano cone. This confirms a conjecture of Donaldson-Sun stating that the metric tangent cone of any close point appearing on a Gromov-Hausdorff limit of Kähler-Einstein Fano manifolds depends only on the algebraic structure of the singularity. This is a joint work with Chi Li and Chenyang Xu.

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## Applications of algebra to automatic sequences and pattern avoidance - Lecture 1 Bell, Jason P. | CIRM H

Post-edited

Research schools;Algebra;Combinatorics;Computer Science;Number Theory

We will cover some of the more important results from commutative and noncommutative algebra as far as applications to automatic sequences, pattern avoidance, and related areas. Well give an overview of some applications of these areas to the study of automatic and regular sequences and combinatorics on words.

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## Cluster algebras and categorification - Lecture 1 Amiot, Claire | CIRM H

Post-edited

Research School;Algebra;Combinatorics

In this course I will first introduce cluster algebras associated with a triangulated surface. I will then focus on representation of quivers, and show the strong link between cluster combinatorics and representation theory. The aim will be to explain additive categorification of cluster algebras in this context. All the notions will be illustrated by examples.

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## Commutative algebra for Artin approximation - Part 1 Hauser, Herwig | CIRM H

Post-edited

Research talks;Algebra;Algebraic and Complex Geometry

In this series of four lectures we develop the necessary background from commutative algebra to study solution sets of algebraic equations in power series rings. A good comprehension of the geometry of such sets should then yield in particular a "geometric" proof of the Artin approximation theorem.
In the first lecture, we review various power series rings (formal, convergent, algebraic), their topology ($m$-adic, resp. inductive limit of Banach spaces), and give a conceptual proof of the Weierstrass division theorem.
Lecture two covers smooth, unramified and étale morphisms between noetherian rings. The relation of these notions with the concepts of submersion, immersion and diffeomorphism from differential geometry is given.
In the third lecture, we investigate ring extensions between the three power series rings and describe the respective flatness properties. This allows us to prove approximation in the linear case.
The last lecture is devoted to the geometry of solution sets in power series spaces. We construct in the case of one $x$-variable an isomorphism of an $m$-adic neighborhood of a solution with the cartesian product of a (singular) scheme of finite type with an (infinite dimensional) smooth space, thus extending the factorization theorem of Grinberg-Kazhdan-Drinfeld.
CIRM - Chaire Jean-Morlet 2015 - Aix-Marseille Université
In this series of four lectures we develop the necessary background from commutative algebra to study solution sets of algebraic equations in power series rings. A good comprehension of the geometry of such sets should then yield in particular a "geometric" proof of the Artin approximation theorem.
In the first lecture, we review various power series rings (formal, convergent, algebraic), their topology ($m$-adic, resp. inductive limit of Banach ...

13J05

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Post-edited

Research talks

Let $X$ be a compact Kähler manifold. The so-called Kodaira problem asks whether $X$ has arbitrarily small deformations to some projective varieties. While Kodaira proved that such deformations always exist for surfaces. Starting from dimension 4, there are examples constructed by Voisin which answer the Kodaira problem in the negative. In this talk, we will focus on threefolds, as well as compact Kähler manifolds of algebraic dimension $a(X) = dim(X) -1$. We will explain our positive solution to the Kodaira problem for these manifolds. Let $X$ be a compact Kähler manifold. The so-called Kodaira problem asks whether $X$ has arbitrarily small deformations to some projective varieties. While Kodaira proved that such deformations always exist for surfaces. Starting from dimension 4, there are examples constructed by Voisin which answer the Kodaira problem in the negative. In this talk, we will focus on threefolds, as well as compact Kähler manifolds of algebraic dimension $a(X) = ... Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## The Weil algebra of a Hopf algebra Dubois-Violette, Michel | CIRM Post-edited Research talks;Algebra;Algebraic and Complex Geometry;Mathematical Physics We give a summary of a joint work with Giovanni Landi (Trieste University) on a non commutative generalization of Henri Cartan's theory of operations, algebraic connections and Weil algebra. Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Whitney problems and real algebraic geometry Fefferman, Charles | CIRM H Post-edited Research talks;Analysis and its Applications;Algebraic and Complex Geometry This talk sketches connections between Whitney problems and e.g. the problem of deciding whether a given rational function on$\mathbb{R}^n$belongs to$C^m\$.

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## Adams memorial symposium on algebraic topology. Vol. 1 :international symposium on ... #July Ray N. ; Walker, G. | Cambridge University Press 1992

Congrès

- 292 p.
ISBN 978-0-521-42074-7

London mathematical society lecture note series , 0175

Localisation : Collection 1er étage

axe de couplage # calcul d"homotopie # ensemble d"homotopie # espace fibré # extension des groupes nilpotents # groupe métacyclique # retracte des espaces classifiants # sous-groupe de Swan # séquence spectrale de Grothendieck # théorie de dimension # théorie des espaces # topologie algébrique

55-06

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## Adams memorial symposium on algebraic topology. Vol. 2 :international symposium on... #July Ray N. ; Walker, G. | Cambridge University Press 1992

Congrès

- 305 p.
ISBN 978-0-521-42153-9

London mathematical society lecture note series , 0176

Localisation : Collection 1er étage

groupe d

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## Advances in algebra and model theoryselected surveys presented at two conferencesJune 9-11 1994and June 8-10 1995 Droste, Manfred ; Gobel, Rudiger | Gordon and Breach Sciences Publishers 1997

Congrès

ISBN 978-90-5699-101-2

Algebra, logic and applications series , 0009

Localisation : Colloque 1er étage (DRES)

algèbre # algèbre booléen # domaine de valuation # groupe abélien # groupe d'automorphisme # groupe de permutation infinie # groupe p-adique abélien # module # structure de catégorie # théorie de modèle # théorie des groupes

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## Advances in algebraic geometry motivated by physics :AMS special session on enumerative geometry in physics held at the University of Massachusetts#April 1-2 Previato, Emma | American Mathematical Society 2001

Congrès

- 294 p.
ISBN 978-0-8218-2810-6

Contemporary mathematics , 0276

Localisation : Collection 1er étage

géométrie algbrique # physique # géométrie énumérative # courbe de module # classe de Schubert # variété torique # variation des structures de Hodge # théorie quantique # symétrie miroir # invariant de Gromov-Witten # cohomologie quantique # arrangement d'hyperplan

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## Advances in combinatorics.In part based on the 3rd Waterloo workshop on computer algebra (WWCA, W80) 2011.Dedicated to Herbert Saul Wilf on the occasion of his 80th birthdayWaterloo # may 26-29, 2011 Kotsireas, Ilias S. ; Zima, Eugene V. | Springer 2013

Congrès

- xx; 293 p.
ISBN 978-3-642-30978-6

Localisation : Colloque 1er étage (WATE)

combinatoires # Wilf Herbert S.

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## Advances in operator algebras and mathematical physics.Proceedings of the 2nd conference on operator algebras and mathematical physicsSinaia # June 26 - July 4, 2003 Boca, Florin-Petre ; Bratteli, Ola ; Longo, Roberto ; Siedentop, Heinz | Theta Foundation 2005

Congrès

- xvi; 285 p.
ISBN 978-973-85432-7-0

Theta series in advanced mathematics , 0005

Localisation : Colloque 1er étage (SINA)

algèbre d'opérateurs # C*-algèbre # physique mathématique

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## Advances in representation theory of algebras.Selected papers of the 15th international conference on representations of algebras and workshop (ICRA XV)Bielefeld # August 8-17, 2012 Benson, David J. ; Krause, Henning ; Skowronski, Andrzej | European Mathematical Society 2013

Congrès

- vii; 367 p.
ISBN 978-3-03719-125-5

EMS series of congress reports

Localisation : Colloque 1er étage (BIEL)

algèbre commutative # représentation d'algèbres # catégorie abélienne # représentation de groupes # théorie de la représentation # algèbre de dimension finie # algèbre de Lie # algèbres à grappes # algèbre homologique # catégorie dérivée # catégorie triangulée # anneau et module

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## Affine algebraic geometry :special session on affine algebraic geometry at the first joint AMS-RSME meeting#June 18-21 Gutierrez, Jaime ; Shpilrain, Vladimir ; Yu, Jie-Tai | American Mathematical Society 2005

Congrès

- 276 p.
ISBN 978-0-8218-3476-3

Contemporary mathematics , 0369

Localisation : Collection 1er étage

géométrie algébrique # géométrie affine # conjecture jacobienne # automorphisme de surface # application rationnelle # idéal polynomial

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## Affine algebraic geometry:the Russell festschrift.Outgrow of an international conference held in honour of professor Peter Russell on the occasion of his 70th birthdayMontréal # june 1-5, 2009 Daigle, Daniel ; Ganong, Richard ; Koras, Mariusz | American Mathematical Society 2011

Congrès

- xvii; 334 p.
ISBN 978-0-8218-7283-3

CRM proceedings & lecture notes , 0054

Localisation : Collection 1er étage

géométrie algébrique # géométrie affine # action de groupe # théorie des invariant # conjecture du jacobien # algèbre avec identité polynomiale # variété algébrique # automorphisme

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## Agebraic analysis and related topics :workshop on Lie groups and Lie algebras held at the Mathematical Conference Center#Sept. 4-15 Strasburger, Aleksander ; Hilgert, Joachim ; Neeb, Karl-Hermann ; Wojtynski, Wojciech | Institute Of Mathematics;Polish Academy of Sciences 2002

Congrès

- 357 p.
ISBN

Banach center publications , 0055

Localisation : Salle des périodiques 1er étage

géométrie # analyse # groupe de Lie fini # groupe de Lie infini # groupe topologique # algèbre de Lie # théorie de la représentation # groupe d'homotopie # opérateur de Toeplitz # espace de Hardy # structure de Jordan # noyau de Berezin

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## Algebra and analysisproceedings of the international centennial Chebotarev conferenceJune 5-11 Arslanov, M. M. ; Parshin A. N. ; Shafarevich, I. R. | Walter De Gruyter 1996

Congrès

ISBN 978-3-11-014803-9

Localisation : Colloque 1er étage (KAZA)

algèbre et anneau commutatifs # aspect spécial # bi-module # fondement # groupe abélien # groupe fini # groupe infini # idéal # logique mathématique # module # théorie de recursion # théorie de représentation d'anneau et d'algèbre # théorie général d'anneau commutatif

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