Seminar information archive

Seminar on Mathematics for various disciplines

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Calibration problems for Black-Scholes American Options under the GMMY process
[ Abstract ]
The calibration problem is formulated as a control problem for the parabolic variational inequality. The well-posedness of the formulation is discussed and the necessary optimality is derived. A numerical approximation method is also presented.

GCOE lecture series

17:00-18:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Eric Opdam (University of Amsterdam)
The spectral category of Hecke algebras and applications

[ Abstract ]
Hecke algebras play an important role in the harmonic analysis of a p-adic reductive group. On the other hand, their representation theory and harmonic analysis can be described almost completely explicitly. This makes affine Hecke algebras an ideal tool to study the harmonic analysis of p-adic groups. We will illustrate this in this series of lectures by explaining how various components of the Bernstein center contribute to the level-0 L-packets of tempered representations, purely from the point of view of harmonic analysis.

We define a "spectral category" of (affine) Hecke algebras. The morphisms in this category are not algebra morphisms but are affine morphisms between the associated tori of unramified characters, which are compatible with respect to the so-called Harish-Chandra μ-functions. We show that such a morphism generates a Plancherel measure preserving correspondence between the tempered spectra of the two Hecke algebras involved. We will discuss typical examples of spectral morphisms.
We apply the spectral correspondences of affine Hecke algebras to level-0 representations of a quasi-split simple p-adic group. We will concentrate on the example of the special orthogonal groups $SO_{2n+1}(K)$. We show that all affine Hecke algebras which arise in this context admit a *unique* spectral morphism to the Iwahori-Matsumoto Hecke algebra, a remarkable phenomenon that is crucial for this method. We will recover in this way Lusztig's classification of "unipotent" representations.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

2009/01/06

Lectures

16:00-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第3回)
[ Abstract ]

・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播

Lectures

14:00-15:30   Room #123 (Graduate School of Math. Sci. Bldg.)

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第2回)
[ Abstract ]

・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導

2009/01/05

Lectures

16:00-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第1回)
[ Abstract ]

・ 膜電位とイオンチャネル
・ 細胞の体積調節
・ チャネルの開閉
・ Hodgkin-Huxley モデルと興奮性

・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導

・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播

2008/12/26

Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)

On Siegel Eisenstein series of degree two and weight 2
[ Abstract ]
Cups singularities の組み合わせ論的な解析を援用して、あるレベルのモジュラー群に対する表題の空間の次元を決定する。

2008/12/19

Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

2008/12/18

Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Benoit Collins (東大数理/Ottawa 大学)
Some geometric and probabilistic properties of the free quantum group $A_o(n)$

2008/12/17

Seminar on Probability and Statistics

13:40-14:50   Room #002 (Graduate School of Math. Sci. Bldg.)
Ilia Negri (University of Bergamo, Italy)
Goodness of fit tests for ergodic diffusions by discrete sampling schemes
[ Abstract ]
We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional ergodic diffusions, where the diffusion coefficient is a nuisance function which is estimated in some sense. Using a theory for the continuous observation case, we construct two kinds of tests based on different types of discrete observations, namely, the data observed discretely in time or in space. We prove that the limit distribution of our tests is the supremum of the standard Brownian motion, and thus our tests are asymptotically distribution free. We also show that our tests are consistent under any fixed alternatives.

joint with Yoichi Nishiyama (Inst. Statist. Math.)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/09.html

Seminar on Probability and Statistics

15:00-16:10   Room #002 (Graduate School of Math. Sci. Bldg.)
Stefano Maria Iacus (Universita degli Studi di Milano, Italy)
Divergences Test Statistics for Discretely Observed Diffusion Processes
[ Abstract ]
In this paper we propose the use of $\\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt = b(Xt, theta)dt + sigma(Xt, theta) dWt, from discrete observations at times ti = i*Dn, i=0, 1, ..., n, under the asymptotic scheme Dn - 0, n*Dn - +oo and n*Dn^2 - 0. The class of phi-divergences is wide and includes several special members like Kullback-Leibler, Renyi, power and alpha-divergences. We derive the asymptotic distribution of the test statistics based on phi- divergences. The limiting law takes different forms depending on the regularity of phi. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.

joint work with A. De Gregorio
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/10.html

Seminar on Probability and Statistics

16:20-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Nicolas Privault (City University of Hong Kong)
Stein estimation of Poisson process intensities
[ Abstract ]
In this talk we will construct superefficient estimators of Stein type for the intensity parameter lambda > 0 of a Poisson process, using integration by parts and superharmonic functionals on the Poisson space.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/11.html

2008/12/12

Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

ガスタービン翼の伝熱について

2008/12/11

Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Certain aperiodic automorphisms of unital simple projectionless $C^*$-algebras

2008/12/10

Geometry Seminar

14:45-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)

Acyclic polarizations and localization of Riemann-Roch numbers
[ Abstract ]

Megumi Harada (McMaster University) 16:30-18:00
The topology of symplectic and hyperkahler quotients
[ Abstract ]
Symplectic geometry lies at the crossroads of many exciting areas of research due to its relationship to geometric representation theory, combinatorics, and algebraic geometry, among others. As often happens in mathematics, the presence of symmetry in these geometric structures -- in this context, a Hamiltonian G-action for a Lie group G, i.e. an action with an associated moment map -- turns out to be crucial in the computation of topological invariants, such as the Betti numbers, the cohomology ring, or the K-theory, of symplectic manifolds which arise as Hamiltonian quotients. In the first part of the talk, I will give a bird's-eye, motivating overview of this subject, and in particular will introduce one of the main technical tools of the field, which is the Morse theory associated to the moment map. In the second part, I will give a more detailed account of recent joint work with Graeme Wilkin, which deals with Nakajima quiver varieties, a special case of hyperkahler Hamiltonian quotients. In particular, we develop a Morse theory for the hyperkahler moment map analogous to the case of the moduli space of Higgs bundles. In particular, we show that the Harder-Narasimhan stratification of spaces of representations of quivers coincide with the Morse-theoretic stratification associated to the norm-square of the real moment map. Our approach also provides insight into the topology of specific examples of small-rank quiver varieties, including hyperpolygon spaces and some ADHM quivers.

2008/12/09

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Bertrand Deroin (CNRS, Orsay, Universit\'e Paris-Sud 11)
Tits alternative in $Diff^1(S^1)$
[ Abstract ]
The following form of Tits alternative for subgroups of
homeomorphisms of the circle has been proved by Margulis: or the group
preserve a probability measure on the circle, or it contains a free
subgroup on two generators. We will prove that if the group acts by diffeomorphisms of
class $C^1$ and does not preserve a probability measure on the circle, then
in fact it contains a subgroup topologically conjugated to a Schottky group.
This is a joint work with V. Kleptsyn and A. Navas.

2008/12/08

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Critically finite holomorphic maps on projective spaces

2008/12/05

Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

2008/12/04

Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

カッツ環の作用の分類

Lie Groups and Representation Theory

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Genkai Zhang (Chalmers and Gothenburg University)
Realization of quanternionic discrete series as spaces of H-holomorphic
functions
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2008/12/03

Mathematical Finance

17:30-19:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Freddy Delaben (ETH)
The structure of dynamic utility functions in a Brownian Filtration

[ Abstract ]
The penalty function for monetary dynamic utility functions
has a special form. They can be seen as potentials. In the Brownian Filtration Rao's theorem permits to give a complete description.

Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Mean-periodicity and analytic properties of zeta-functions
[ Abstract ]
Mean-periodicityというのは周期性の概念のひとつの一般化である。最近、I. Fesenko, G. Ricottaとの共同研究により、数論的スキームのゼータ関数を含むある複素関数のクラスと、mean-periodicityとの関連性が新しく見出された。
これはHecke-Weilによる, 解析接続と関数等式を持つDirichlet級数と保型形式との対応の一つの拡張ともみなせる. この背景には, I. Fesenkoの高次元アデール上のゼータ積分の理論があり、数論的スキームのHasseゼータ関数の解析接続を高次元アデール上の調和解析から導こうというプログラムの一環となっている。
この講演ではそのような背景にも若干触れた上、ゼータ関数の解析的性質とmean-periodicityの関連、特に解析接続と関数等式との関連について解説する。

2008/12/02

Lie Groups and Representation Theory

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
The aim of my talk is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank noncompact Lie group, on the other.

The connection is established via "transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1- form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

Vanishing and Rigidity
[ Abstract ]
The aim of my talk is to reveal an unforeseen link between
the classical vanishing theorems of Matsushima and Weil, on the one hand,
andrigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank
noncompact Lie group, on the other. The connection is established via
"transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the
orbit foliation of the Weyl chamber flow that is tangentially closed
(and satisfies a certain mild additional condition) can be extended to a closed 1- form on the
whole space in a canonical manner. In particular, infinitesimal
rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.

2008/12/01

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Kentaro Hori (University of Toronto / IPMU)
A pair of non-birational but derived equivalent Calabi-Yau
manifolds from non-Abelian gauge theories
[ Abstract ]
We construct a family of (2,2) supersymmetric gauge theories
in 2-dimensions that flows to a family of (2,2) superconformal fields theories with \\hat{c}=3. The family has two limits and three singular points. The two limits correspond to two Calabi-Yau manifolds which are not birationally equivalent. The two are, however, derived equivalent
by general principle of supersymmetric quantum field theory.