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Documents  Critères de recherche : "Algebra" | enregistrements trouvés : 2 336

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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.

14J45 ; 32Q15 ; 32Q20 ; 53C55

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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) = ...

32J17 ; 32J27 ; 32J25 ; 32G05 ; 14D06 ; 14E30

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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.

13F60 ; 16E35 ; 16G20 ; 18E30

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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.

11B85 ; 68Q45 ; 68R15

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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 $C^m$.

26Bxx ; 46E10 ; 58A20 ; 14Qxx

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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 ...

11F37 ; 11P82

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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 ...

14C25 ; 14G15 ; 14J70 ; 14C15 ; 14H05

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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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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.

81R10 ; 81R60 ; 16T05

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ISBN 978-963-8021-01-4

Colloquia mathematica societatis Janos Bolyai , 0017

Localisation : Colloque 1er étage (SZEG)

algèbre de Boole # algèbre de Stone # algèbre de polynome # algèbre libre # algèbre régulière # algèbre universelle # automate d'arbre # homotopie # logique équationnelle # oméga-algèbre abélienne # p-algèbre modulaire complète # problème de Goralcik # puissance de Boole # suite exacte # treillis de congruence # treillis de scission # treillis de variété # treillis modulaire

06Bxx ; 06Exx ; 08C05

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ISBN 978-0-12-757150-8

Localisation : Colloque 1er étage (BIRM)

algèbre d

43A77 ; 46Bxx ; 46Fxx ; 46Jxx ; 47D30

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- 357 p.
ISBN 978-0-8218-5010-7

Contemporary mathematics , 0012

Localisation : Collection 1er étage

55-06 ; 57Rxx

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- 204 p.
ISBN 978-0-8218-5011-4

Contemporary mathematics , 0010

Localisation : Collection 1er étage

46L05 ; 55N15

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

Contemporary mathematics , 0008

Localisation : Collection 1er étage

10C04 ; 12D15 ; 12J15 ; 13J25 ; 32C05

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- 84 p.
ISBN 978-0-8218-5003-9

Contemporary mathematics , 0006

Localisation : Collection 1er étage

05-02 ; 05B20 ; 05B30 ; 16A20 ; 16A24

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- 484 p.
ISBN 978-0-8218-6002-1

C.M.S. conference proceedings , 0002

Localisation : Collection 1er étage

action de groupe # structure sur variété # topologie algébrique # transfert de groupe de classe projective # variété algébrique

55-06 ; 57-06

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- 528 p.
ISBN 978-0-387-12685-2

Lecture notes in mathematics , 1016

Localisation : Collection 1er étage

14-06

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- 308 p.
ISBN 978-0-387-12329-5

Lecture notes in mathematics , 1004

Localisation : Collection 1er étage

06C05 ; 06D05 ; 06F15 ; 08A40 ; 08B05

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- 327 p.
ISBN 978-0-8218-1118-4

Lectures in applied mathematics , 0018

Localisation : Collection 1er étage

93Bxx

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ISBN 978-0-8218-1429-1

Proceedings of symposia in pure mathematics , 0029

Localisation : Collection 1er étage

13-02 ; 13D05 ; 13F15 ; 20G05 ; 32C10

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