Yves Benoist, Toshihisa Kubo #1, Eric Opdam, Toshihisa Kubo #2, Takayuki Okuda, Oskar Hamlet #1, Oskar Hamlet #2, Ali Baklouti #1, Ali Baklouti #2, Toshihisa Kubo #3, Hiroshi Konno, Masaki Watanabe, Tatsuyuki Hikita,

GCOE Lectures | |

Date: | May 29 (Tue), 2012, 16:30-18:00 |

June 5 (Tue), 2012, 16:30-18:00 | |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Yves Benoist (CNRS, Orsay) |

Title: | Random walk on reductive groups I, II |

Abstract: [ pdf ] |
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks. |

Date: | June 12 (Tue), 2012, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Toshihisa Kubo (久保利久) (the University of Tokyo) |

Title: | Conformally invariant systems of differential operators of non-Heisenberg parabolic type |

Abstract: [ pdf ] |
Minkowski space上のwave operatorはconformally invariant operatorの典型的な例である。 近年、Barchini-Kable-Zierauによって1つのdifferential operatorの conformal invarianceがそのsystemに一般化された (conformally invariant systems)。 このセミナーではmaximal non-Heisenberg parabolicを使って、 その様なsecond order differential operatorのsystemを作りたい。 またconformally invariant systemは、あるgeneralized Verma module間の homomorphismを誘導するが、もし時間が許せばそれについても述べたい。 |

Date: | July 17 (Tue), 2012, 17:00-18:30 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Eric Opdam (University of Amsterdam) |

Title: | Dirac induction for graded affine Hecke algebras |

Abstract: [ pdf ] |
In recent joint work with Dan Ciubotaru and Peter Trapa we constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator. We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover. |

Date: | July 24 (Tue), 2012, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Toshihisa Kubo (久保利久) (the University of Tokyo) |

Title: | The Dynkin index and conformally invariant systems of Heisenberg parabolic type |

Abstract: [ pdf ] |
Heisenberg parabolic subalgebraから構築されたconformally invariant systemに関する二つの定数について考察する。それらの定数はそのconformally invariant systemを構築する際に重要な役割を果たしたが、ある二つの式の比率 として定義されただけで具体的な式などは表されなかった。本講演ではそれらの 具体的かつ一様な式をDynkin indexを交えて紹介する。 |

Date: | November 6 (Tue), 2012, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Takayuki Okuda (奥田隆幸) (the University of Tokyo) |

Title: | An explicit construction of spherical designs on S^{3} |

Abstract: [ pdf ] |
The existence of spherical t-designs on S^d for any t and d are proved
by Seymour-Zaslavsky in 1984.
However, explicit constructions of spherical designs were not known
for d > 2 and large t. In this talk, for a given spherical t-design Y on S^2, we give an algorithm to make a spherical 2t-design X on S^3 which maps Y by a Hopf map. In particular, by combining with the results of Kuperberg in 2005, we have an explicit construction of spherical t-designs on S^3 for any t. |

Date: | November 13 (Tue), 2012, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Oskar Hamlet (Chalmers University) |

Title: | Tight maps, a classification |

Abstract: [ pdf ] |
Tight maps/homomorphisms were introduced during the study of rigidity properties of surface groups in Hermitian Lie groups. In this talk I'll discuss the properties of tight maps, their connection to rigidity theory and my work classifying them. |

(Talk) | |

Date: | November 16 (Fri), 2012, 14:50-16:50 |

Place: | Room 123, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Oskar Hamlet (Chalmers University) |

Title: | Kaehler area of triangles in Hermitian symmetric spaces |

Abstract: [ pdf ] |
In this talk I will follow the paper "The Gromov norm of the Kaehler class of symmetric domains" by Domic & Toledo. In the paper a very concrete formula for calculating triangle areas is given and using this one shows that the Kaehler class is a bounded class. |

(Talk) | |

Date: | November 20 (Tue), 2012, 14:50-16:00 |

Place: | Room 123, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Ali Baklouti (Sfax University) |

Title: | On some aspects of deformation theory of discontinuous subgroups acting on exponential homogeneous spaces |

Abstract: [ pdf ] |
In this lecture, I will introduce the Kobayashi's new framework of deformation theory for general non-Riemannian homogeneous spaces, putting the focus on the context of exponential solvable settings. |

Date: | November 20 (Tue), 2012, 16:30-17:30 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Ali Baklouti (Sfax University) |

Title: | On the geometry of discontinuous subgroups acting on some homogeneous spaces |

Abstract: [ pdf ] |
Let $G$ be a Lie group, $H$ a closed subgroup of $G$ and $\ Gamma$ a discontinuous subgroup for the homogeneous space $G/H$. I first introduce the deformation space ${\mathcal{T}}^{K_o}(\Gamma, G, H) $ of the action of $\Gamma$ on $G/H$ in the sense of Kobayashi and some of its refined versions, namely the Clifford--Klein space of deformations of the form ${\mathcal{X}}=\Gamma \backslash G/H$. The deformation space ${\mathcal{T}}^{G_o}(\Gamma, G,H)$ of marked $(G,H)$- structures on ${\mathcal{X}}$ in the sense of Goldman is also introduced. As an important motivation, I will explain the connection between the spaces ${\mathcal{T}}^{K_o}(\Gamma, G, H)$ and ${\mathcal{T}}^{G_o}(\ Gamma, G, H)$ and study some of their topological features, namely the rigidity in the sense of Selberg--Weil--Kobayashi and the stability in the sense of Kobayashi--Nasrin. The latter appears to be of major interest to write down the connection explicitly. |

(Talk) | |

Date: | November 21 (Wed), 2012, 14:50-16:50 |

Place: | Room 123, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Kubo Toshihisa (久保利久) (the University of Tokyo) |

Title: | The Heisenberg ultrahyperbolic equation and the associated Kelvin transform |

Abstract: [ pdf ] |
In this talk we study the paper "The Heisenberg ultrahyperbolic equation: K-finite and polynomial solutions" by Anthony C. Kable. We mainly focus on the conformal invariance property of the Heisenberg ultra hyperbolic operator. If time permits then we are also going to discuss a result on the polynomial solutions of the operator. |

Date: | November 27 (Tue), 2012, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Hiroshi Konno (今野宏) (the University of Tokyo) |

Title: | Convergence of Kahler to real polarizations on flag manifolds (旗多様体のケーラー偏極の実偏極への収束) |

Abstract: [ pdf ] |
In this talk we will discuss geometric quantization of a flag manifold. In particular, we construct a family of complex structures on a flag manifold that converge 'at the quantum level' to the real polarization coming from the Gelfand-Cetlin integrable system. Our construction is based on a toric degeneration of flag varieties and a deformation of Kähler structure on toric varieties by symplectic potentials. This is a joint work with Mark Hamilton. |

Date: | November 29 (Thu), 2012, 16:30-17:30 |

Place: | Room 122, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Masaki Watanabe (渡部正樹) (the University of Tokyo) |

Title: | On a relation between certain character values of symmetric groups |

Abstract: [ pdf ] |
We present a relation of new kind between character values of symmetric groups which explains a curious phenomenon in character tables of symmetric groups. Similar relations for characters of Brauer and walled Brauer algebras and projective characters of symmetric groups are also presented. |

Date: | December 11 (Tue), 2012, 17:00-17:30 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Tatsuyuki Hikita (疋田辰之) (Kyoto University) |

Title: | Affine Springer fibers of type A and combinatorics of diagonal coinvariants |

Abstract: [ pdf ] |
We introduce certain filtrations on the homology of affine Springer fibers of type A and give combinatorial formulas for the bigraded Frobenius series of the associated graded modules. The results are essentially given by generalizations of the symmetric function introduced by Haglund, Haiman, Loehr, Remmel, and Ulyanov which is conjectured to coincide with the bigraded Frobenius series of the ring of diagonal coinvariants. |

© Toshiyuki Kobayashi