[Turkmath:9349] The mini-symposium (Japanese Turkish Joint Geometry Meeting) 25-26 November 2013

[Susumu Tanabe]

The mini-symposium(satellite to Japanese Turkish Joint Geometry Meeting)25-26 November 2013Galatasaray University, Istanbul, Turkey1 Schedule25 Nov:09 : 30 􀀀 10 : 20 Serge Randriambololona (Galatasaray University)10 : 20 􀀀 10 : 30 Break10 : 30 􀀀 11 : 20 ˙Ismail Sa˘glan (Koc University)11 : 20 􀀀 11 : 40 Break11 : 40 􀀀 12 : 30 Raimundas Vidunas (National Kapodistrian University of Athens)12 : 30 􀀀 14 : 00 Lunch14 : 00 􀀀 14 : 50 Kazim B¨uy¨ukb¨oduk (Koc University)14 : 50 􀀀 15 : 00 Break15 : 00 􀀀 15 : 50 Tadashi Ishibe (University of Tokyo)15 : 50 􀀀 16 : 00 Break16 : 00 􀀀 16 : 50 Jiro Sekiguchi (Tokyo University of Agriculture and Technology)16 : 50 􀀀 17 : 00 Break17 : 00 􀀀 17 : 50 Asli Deniz26 Nov:09 : 30 􀀀 10 : 20 Jiro Sekiguchi (Tokyo University of Agriculture and Technology) TBA.2 Title & Abstract(1) Speaker: Serge RandriambololonaTitle: The complex heritage of a real set (Joint work with J. Adamus and R. Shafikov)Abstract:Given a real analytic set X embeded in a complex analytic manifold Z, it is natural to try to measurehow much of the complex structure of Z is inherited, locally at a point, by the real set X. One of themeasure for the local ”complexity” of X at the point p is the maximal possible dimension of a complexanalytic germ contained in the germ of X at p. We will show that this notion of local dimension onX is well-behaved, giving rise to a filtration by closed semianalytic sets.(2) Speaker: ˙Ismail Sa˘glanTitle: Triangulations of the Sphere After ThurstonAbstract:In his paper ’Shapes of polyhedra and triangulations of the sphere’, Thurston proved that all nonnegativelycurved triangulations of the sphere can be parametrized by a quotient of positive part ofa hermitian lattice. We prove that same result is true for smaller families of non-negatively curvedtriangulations.1(3) Speaker: Raimundas VidunasTitle: Differential relations for Belyi functionsAbstract:Many Belyi functions give interesting pull-back transformations of Fuchsian differential equations.The pull-back transformations allow to compute the Belyi functions more efficiently, as they giveadditional relations for their coefficients. Genus 0 Belyi functions of degree 60 can be computedin a few minutes using the pull-back tranformations. The implied differential relations between theirpolynomial components explain appearance of Chebyshev and Jacobi polynomials with Belyi functions.Those relations allow fast computations of Klein’s pull-backs for algebraic hypergeometric or Heunfunctions.(4) Speaker: Kazim B¨uy¨ukb¨odukTitle: Beilinson-Kato elements and a conjecture of Mazur, Tate and TeitelbaumAbstract:In order to formulate a p-adic Birch and Swinnerton conjecture (BSD for short) for an elliptic curve E,Mazur, Tate and Teitelbaum (MTT) constructed a p-adic L-function attached to E. To understand itscompatibility with the usual BSD, one needs to compare the order of vanishing of the p-adic L-functionat s = 1 to that of the Hasse-Weil L-function (where the latter is called the analytic rank of E). WhenE has split multiplicative reduction mod p, MTT observed that the p-adic L-function always vanishesat s = 1 and they conjectured that its order of zero is exactly one more than the analytic rank of E.In 1992, Greenberg and Stevens proved this conjecture when the analytic rank is zero. In this talk, Iwill explain a proof of the MTT conjecture when the analytic rank is one. Statistically speaking, thiswill complete the proof of MTT conjecture in almost all cases. The main ingredients for the proof arethe Beilinson-Kato elements in the K2 of modular curves and a Gross-Zagier-style formula we provefor the p-adic height of the Beilinson-Kato elements.(5) Speaker: Tadashi IshibeTitle: On the conjugacy problem for non-Garside groupsAbstract:Through a generalization of the theory of Artin groups, I would like to understand the elliptic Artingroups, which are the fundamental groups of the complement of discriminant divisors of the semiversaldeformation of the simply elliptic singularities fE6, fE7 and fE8. Early in 70’s the braid groupsare generalized, by Brieskorn-Saito, to a wider class of groups, the fundamental groups of regular orbitspaces of finite reflection groups, which are called the Artin groups. The fundamental groups admita special presentation, by which a certain monoid structure is naturally defined, which is called theArtin monoid. By showing a certain lemma for Artin monoid, we conclude that Artin monoid injectsinto the corresponding Artin group. Due to the injectivity, some decision problems for Artin groups issuccessfully solved. At the end of 90’s, by refering to these technical framework in Artin group theory,the notion of Garside group, as a generalization of Artin groups, is defined as the group of fractionsof a Garside monoid. In my opinion, the Garside theory is still far from complete to understand theelliptic Artin groups. In this talk, we will consider another generalization of the theory Artin groups.When we attempt to do so, we find difficulty in solving the conjugacy ploblems. We will talk abouthow to overcome that difficulty.2(6) Speaker: Jiro SekiguchiTitle: A free divisor which gives an alegebraic solution of Painlev´e VI equation constructed by Hitchin.Abstract:Hitchin constructed some of algebraic solutions of Painlev´e VI equation. My talk is focused on oneof Hitchin’s algebraic solutions. There are three Icosahedral invariants constructed by F. Klein whosedegrees are 12; 20; 30. Let F(x1; x2; x3) = x33 + c2(x1; x2)x3 + c3(x1; x2) be a weighted homogeneouspolynomial of x1; x2; x3 of weight system (1; 2; 4). Assume that c2(z5=21 ; z52); c3(z5=21 ; z52) are Icosahedralinvariants of degree 20; 30 respectively, up to constant factors. Then F(x1; x2; x3) = 0 defines a freedivisor. It is possible to construct a holonomic system of rank two with singularities along F = 0.This holonomic system is regarded as a family of ordinary differential equations of x3 with parametersx1; x2, in other words, the so called an isomonodromic deformation of ordinary differential equationsand one obtains an algebraic solution of Painlev´e VI equation. This algebraic solution coincides withthat obtained by Hitchin.(7) Speaker: Asli DenizTitle: An Apllication of Hyperbolic Metric to Holomorphic DynamicsAbstract:In transcendental dynamics, dynamic rays are curves in the Julia set escaping to infinity under forwarditerates. Understanding the landing behaviors of dynamic rays is essential in the study of the topologicalstructure of the Julia set. In this talk, we present a landing theorem for periodic dynamic raysfor transcendental entire maps which have bounded post singular sets. Our main tools are contractionprinciples in hyperbolic geometry, namely, Schwarz-Pick 􀊟s Lemma. 		 	   		  
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/private/turkmath/attachments/20131120/52a4c98e/attachment.html>