Séminaire et Groupes de travail
Département de Mathématiques.
Université Galatasaray

G?n: 29 Aral?k (Per?embe) 16:00 Yer: Galatasaray ?niversitesi FEF9. Konu?mac?/Speaker - Prof.Bernard Teissier - Institut Math?matique de Jussieu, Equipe G?om?trie et Dynamique. Ba?l?k /Title - On the Lojasiewicz exponent. ?zet/Abstract - The Lojasiewicz exponent measures the relative rates of vanishing of two real or complex-analytic, or subanalytic, functions which vanish on the same set. I will survey some variations on this idea in commutative algebra, including if time permits a recent result of Moret-Bailly on the Artin-Greenberg approximation theorem. G?n: 22 Aral?k (Per?embe) 16:00 Yer: Galatasaray ?niversitesi FEF9. Konu?mac?: Prof. Cemsinan Deliduman Ba?l?k : Entanglement Swapping Model of DNA Replication ?zet: Molecular biology explains function of molecules by their geometrical and electronical structures which are mainly determined by utilization of quantum effects in chemistry. However,further quantum effects are not thought to play any significant role in the essential processes of life. On the contrary, consideration of quantum circuits/protocols and organic molecules as software and hardware of living systems that are co-optimized during evolution, may be useful to pass over the dfficulties raised by biochemical complexity and to understand the physics of life. In this talk, I will describe a quantum mechanical model of DNA replication with a re- liable qubit representation of the nucleotides. In the model: 1) molecular recognition of a nucleotide is assumed to trigger an intrabase entanglement corresponding to a superposition of different tautomer forms and 2) pairing of complementary nucleotides is described by swapping intrabase entanglements with interbase entanglements. I will give some examples of quantum circuits/protocols to be used to obtain intrabase and interbase entanglements. Lastly, possible computational and experimental verification methods of the model will be discussed. G?n: 8 Aral?k (Per?embe) 16:00 Yer: Galatasaray ?niversitesi FEF9. Konu?mac?/Speaker - Arnaldo Garcia - IMPA at Rio de Janeiro. Ba?l?k /Title - Asymptotics on codes and on curves over finite fields. ?zet/Abstract- The famous bound of Hasse-Weil for the number of rational points on curves over finite fields (equivalent to the Riemann Hypothesis in this context) was shown by Ihara to be weaker as the genus of the curve grows. For a finite field with q elements, Ihara then introduced the quantity A(q) that controls the asymptotic behaviour of the number of rational points as the genus goes to infinity.To deal with A(q) one is led to consider infinite towers of algebraic curves and to study their limits for the ratios of (number of rational points) / (genus). We are going to motivate this interesting mathematical subject by its connection to the asymptotics in Coding Theory, which is a result due to Tsfasman-Vladut-Zink based on a construction of Goppa of linear codes from algebraic curves over finite fields. G?n: 3 Kas?m (Per?embe) 16:00 Yer: Galatasaray ?niversitesi FEF9. Konu?mac?: Ayberk Zeytin Ba?l?k : Polygonal decompositions of the sphere and ball quotients ?zet: After a short introduction to the subject, we will give classification of sphere quadrangulations satisfying a condition of non-negative curvature, following Thurston's classification of sphere triangulations under the same condition. If time permits, we will discuss some arithmetic applications of the classification, and its relations to Picard-Terada-Deligne-Mostow theory. (joint with M.Uludag.) Title: Polygonal decompositions of the sphere and ball quotients Abstract: After a short introduction to the subject, we will give classification of sphere quadrangulations satisfying a condition of non-negative curvature, following Thurston's classification of sphere triangulations under the same condition. If time permits, we will discuss some arithmetic applications of the classification, and its relations to Picard-Terada-Deligne-Mostow theory. (joint with M.Uludag.) Date : 13 Octobre, 16:00 Lieu :FEF9 Titre :"N=2 BPS dyons and Hessian flow" Conf?rencier: Dieter van den Bleeken (Galatasaray University) I will first review the theory of lagrangians with N=2 supersymmetry and their definition in terms of special Kahler geometry. In the second part of the talk I will discuss my forthcoming paper that analyses so called BPS solutions to the equations of motion of these theories. Below is the abstract of this paper. We revisit BPS solutions to classical N=2 effective low energy gauge theories. It is shown that the vacuum equations can be solved in full generality by the introduction of a Hessian potential, a symplectic analog of the holomorphic prepotential. We argue that the natural generalisation of the attractor equation to non-spherically symmetric solutions is a gradient flow equation with respect to this Hessian potential. Furthermore we define a complex local central charge vector that is shown to satisfy Maxwell's equations. In the last part of the paper we study the introduction of sources. We discuss the empty pole condition of Denef for spherically symmetric solutions and derive a precise set of constraint equations that restrict the location of sources in the absence of spherical symmetry.

Lundi 9 mai 2011, 15h30-16h30, salle P20.
Johannes HUEBSCHMANN, université des sciences et technologies de Lille.
Singular Poisson-Kähler geometry of stratified Kähler spaces.

Abstract.

Mercredi 4 et jeudi 5 mai 2011, 16h00-18h00, salle FEF 8 (mercredi) et FEF 1 (jeudi).
Eugene HA, Galatasaray üniversitesi.
Galois Theory from Galois' Perspective.

Abstract. These lectures will cover the main theorem of the Galois theory of fields following closely the original approach of Galois. We will see how Galois theory proves the nonexistence of a general algebraic formula for the roots of rational-coefficient polynomials of degree 5 or more. We shall also illustrate the general theory in the special case of cyclotomic fields and of finite fields.

Lundi 25 avril 2011, 15h00-16h00, salle P20.
Müge KANUNI, Boğaziçi üniversitesi.
Discrete Structures in Algebra.

Abstract. Path Algebras, Leavitt Path Algebras and Incidence Algebras are algebras defined on discrete structures. We will describe these different structures and give a brief overview of their history.

Lundi 4 avril 2011, 15h00-16h00, salle P20.
Meral TOSUN, université Galatasaray.
Good slices for simple elliptic singularities.

Abstract. We will first present the relation between singularities of complex surfaces and Lie algebras. Then we will show how to generalize the Slodowy slices to simple elliptic singularities.

Jeudi 24 mars 2011, 9h00-11h00, salle FEF 5.
Athanase PAPADOPOULOS, institut de recherche mathématique avancée, Strasbourg.
Espaces métriques généralisés 2.

Mercredi 23 mars 2011, 16h00-18h00, salle FEF 10.
Athanase PAPADOPOULOS, institut de recherche mathématique avancée, Strasbourg.
Espaces métriques généralisés 1.

Lundi 21 mars 2011, 16h00-17h00, salle FEF 7.
Jiro SEKIGUCHI, Tokyo university of agriculture and technology.
A Schwarz map of Appell's F_2 whose monodoromy group is related to the reflection group of type D_4.

Abstract. The system of differential equations for Appell's hypergeometric function F_2(a,b,b',c,c';x,y) has four fundamental solutions. Let u_1,u_2,u_3,u_4 be such solutions. If the monodromy group of the system is finite, the closure of the image of the Schwarz map U(x,y)=(u_1(x,y),u_2(x,y),u_3(x,y),u_4(x,y)) is a hypersurface S of the 3-dimensional projective space {\bf P}$. Then S is defined by P(u_1,u_2,u_3,u_4)=0 for a polynomial P(t_1,t_2,t_3,t_4). It is M. Kato (Univ. Ryukyus) who determined the parameter a,b,b',c,c' such that the monodromy group of the system for F_2(a,b,b',c,c';x,y) is finite. It follows from his result that such a group is the semidirect product of an irreducible finite reflection group G of rank four by an abelian group. In this talk, we treat the system for F_2(a,b,b',c,c';x,y) with (a,b,b',c,c')=(1/2,1/6,-1/6,1/3,2/3. In this case, the monodromy group is the semidirect group of G by Z/3Z, where G is the reflection group of type D_4. The polynomial P(t_1,t_2,t_3,t_4) in this case is of degree four. There are 16 ordinary singular points in the hypersurface S. In the rest of my talk, I explain the background of the study.

Lundi 21 mars 2011, 15h00-16h00, salle FEF 7.
Athanase PAPADOPOULOS, institut de recherche mathématique avancée, Strasbourg.
La géométrie de Finsler.

Mercredi 16 mars 2011, 15h00-16h00, salle FEF 9.
Eric SOCCORSI, centre de physique théorique, Marseille.
Résolution des équations différentielles par la méthode des élements finis.

Résumé. J'expliquerai comment on résout "numériquement" une EDP en prenant pour simplifier un exemple d'EDO.

Lundi 14 mars 2011, 16h00-17h00, salle FEF 7.
Eric SOCCORSI, centre de physique théorique, Marseille.
Lipschitz stability in an inverse problem for non autonomous magnetic Schrödinger equations.

Abstract. We consider the inverse problem of determining the time dependent magnetic field of the Schrödinger equation in a bounded open subset of R^n, n>=1, from a finite number of Neumann data, when the boundary measurement is taken on an appropriate open subset of the boundary. We prove the Lispchitz stability of the magnetic potential in the Coulomb gauge class by n times changing initial value suitably.

Lundi 14 mars 2011, 15h00-16h00, salle FEF 7.
Oleg BELEGRADEK, İstanbul Bilgi Üniversitesi.
How similar can non-isomorphic algebraic structures be?

Abstract. In this talk (oriented to a general mathematical audience not necessarily familiar with model theory) I will discuss the notion of elementary equivalence, one of the basic notions of model theory, illustrating it with various algebraic examples, both classical and more recent. In particular, some author's results on model-theoretic properties of unitriangular groups will be discussed.

Mercredi 9 mars 2011, 15h00-16h00, salle FEF 10.
Jawad SNOUSSI, universidad nacional autónoma de méxico.
Modifiactions des singularités.

Résumé. Nous expliquerons les concepts d'éclatement, de normalisation, de modification de Nash et leur relations avec la résolution des singularités .

Lundi 7 mars 2011, 15h00-16h00, salle FEF 4.
Jawad SNOUSSI, universidad nacional autónoma de méxico.
Equisingularity in complex surfaces.

Abstract. We explain the equivalence for complex surfaces between Whitney regularity and Zariski equisingularity criterion. We will give some applications such as the fact that any surface Whitney regular along its singular locus has a smooth normalisation .

Lundi 28 février 2011, 15h00-16h00, salle P 23.
Eugene HA, université Galatasaray & Fields Institute, Toronto.
The problem of cohomology for an Arakelov divisor.

Abstract. We shall discuss Tate's Riemann-Roch theorem for number fields and the peculiar nature that it implies for the cohomology of an Arakelov divisor (that is, a divisor for the spectrum of a number field formally completed at archimedean infinity).

Vendredi 7 janvier 2011, 15h00-16h00, salle FEF 1.
Gülay KAYA, université Galatasaray.
The Groebner fan of a polynomial ideal.

Lundi 20 décembre 2010, 15h00-16h00, salle FEF 9.
Muhammed ULUDAĞ, université Galatasaray.
Hypergeometric Galois Actions.

Lundi 6 décembre 2010, 15h00-16h00, salle FEF 9.
Cédric MILLIET, université Galatasaray.
Quelques mots de théorie des modèles.

Résumé. Le but de l'exposé est de faire voir un peu de théorie des modèles. J'ai choisi de présenter un théorème de Macintyre (de 1971) disant qu'un corps omega-stable est soit fini, soit algébriquement clos. Après avoir dit ce qu'est une théorie, ou un modèle, et énoncé quelques questions typiques que se posent habituellement les logiciens, je rappelerai deux invariants des espaces topologiques compacts dénombrables qui permettent de les classifier à homéomorphisme près, avant de donner une preuve du théorème de Macintyre, allégée grâce à des arguments de Poizat. L'exposé devrait être accessible à tous.

Mercredi 24 novembre 2010, 17h15-18h15, salle FEF 9.
Susumu TANABE, université Galatasaray.
Invariants of hy pergeometric groups for Calabi--Yau complete intersections in weighted projective spaces

Abstract. Let Y be a smooth Calabi--Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the mirror manifold of Y in the sense of Batyrev and Borisov is one-dimensional and spanned by the Gram matrix of a classical generator of the derived category of coherent sheaves on Y with respect to the Euler form. This is a confirmation of an expected consequence of the homological mirror symmetry conjecture by Kontsevitch.

Vendredi 5 novembre 2010, 10h-12h, salle P 19.
Xavier BRESSAUD, institut de mathématiques de Toulouse.
Introduction à la dynamique symbolique. (2/2)

Jeudi 4 novembre 2010, 10h-11h, salle FEF 9.
Xavier BRESSAUD, institut de mathématiques de Toulouse.
Introduction à la dynamique symbolique. (1/2)

Mercredi 27 octobre 2010, 16h00, salle FEF 10. Affiche
Hervé GAUSSIER, institut Joseph Fourier, Grenoble
Pseudoholomorphic curves and applications

Abstract. Pseudoholomorphic curves are important objects by their role in different subjects such as symplectic or contact geometry. I will present recent results on the study of almost complex manifolds, concerning the (non)existence of pseudoholomorphic curves and more generally of pseudoholomorphic maps.

Mardi 26 octobre 2010, 15h00, salle FEF 1. Affiche
Hervé GAUSSIER, institut Joseph Fourier, Grenoble
Géométrie et calcul infinitésimal. Séminaire introductif à destination des étudiants

Résumé. J'essaierai de montrer les liens entre la géométrie classique, notamment la construction à la règle et au compas, et les premières études sur le calcul différentiel. Je montrerai aussi l'évolution de la géométrie euclidienne vers d'autres géométries.

Date de dernière mise à jour : 9 février 2011.