Seminar information archive

Seminar information archive ~05/21Today's seminar 05/22 | Future seminars 05/23~

2009/07/24

Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Carlos Simpson (CNRS, University of Nice)
Differential equations and the topology of algebraic varieties
[ Abstract ]
The study of the topology of complex algebraic varieties makes use of differential equations in several different ways. The classical notion of variation of Hodge structure contains, on the one hand, the Gauss-Manin differential equations, on the other hand Hodge metric data which satisfy harmonic bundle equations. These two aspects persist in the study of arbitrary representations of the fundamental group. Combining them leads to a notion of ``Hodge structure'' on the space of representations. This can be extended to the higher homotopical structure of a variety, by using ideas of ``shape'' and nonabelian cohomology.

Infinite Analysis Seminar Tokyo

13:00-15:30   Room #056 (Graduate School of Math. Sci. Bldg.)
武部尚志 (Faculty of Math, Higher School of Economics, Moscow) 13:00-14:00
On recursion relation of the KP hierarchy
[ Abstract ]
This talk is based on an ongoing project in collaboration with Takasaki and Tsuchiya. Our goal is to reconstruct and generalise results by Eynard et al. from the standpoint of the integrable systems. Eynard, Orantin and their collaborators found "topological recursion formulae" to describe partition functions and correlation functions of the matrix models, topological string theories etc., using simple algebro-geometric data called "spectral curves". On the other hand, it is well known that the partition functions of those theories are tau functions of integrable hierarchies.
We have found that any solution of the KP hierarchy (with an asymptotic expansion parameter h) can be recovered by recursion relations from its "dispersionless" part (which corresponds to the genus zero part in topological theories) and a quantised contact transformation (which corresponds to the string equations) specifying the solution.
高崎金久 (京大人間) 14:30-15:30
球面のフルビッツ数とKP・戸田階層の特殊解
[ Abstract ]
球面の1点を指定し、その上方で任意被覆型の分岐点
をもち、それ以外では単純分岐点のみもつような n 次分岐被覆を考える。
このような分岐被覆の位相的同型類の個数は単純フルビッツ数と呼ばれる。
1点の代わりに2点を指定して同様に定義されるものは2重フルビッツ数である。
これらのフルビッツ数にシューア函数を乗じて総和したものはそれぞれ
KP階層および戸田階層のτ函数になることが知られている。この講演では
これらの特殊解においてラックス作用素とオルロフ・シュルマン作用素が
満たす関係式 (拘束条件) を紹介し、そこから導かれる帰結を探る。

2009/07/23

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Catherine Oikonomides (慶応大理工)
Cyclic cohomology and the Novikov conjecture

2009/07/21

Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Georgi Raikov (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
[ Abstract ]
In my talk, I will consider the 3D Pauli operator with non-constant magnetic field of constant direction,
perturbed by a matrix-valued electric potential which decays fast enough at infinity. I will discuss
the low-energy asymptotics of the associated spectral shift function which is proportional to the eigenvalue
counting function at negative energies, and to the scattering phase at positive energies.

2009/07/18

Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
大石亮子 (高エネルギー加速器研究機構(KEK)) 13:30-14:30
On some algebraic properties of CM-types of CM-fileds and their reflexs
織田孝幸 (東京大学数理科学研究科) 15:00-16:00
仮題:GL(n)のWhittaker関数に関連する今後の問題
[ Abstract ]
今回は、普段から言及している、未解決の問題をできればなるべくきちんと定式化したい。「GL(n)上の保型形式論は終わった」という愚かな愚かな人たちもいるが、実は彼らにも新たな研究手法が必要であることを指摘したい。実際、現状ではカスプ形式の存在論に関しては、ほとんど何も分かっていない。

2009/07/17

Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Universite Paris-Sud)
Holomorphic dynamics in several variables: equidistribution problems and statistical properties
[ Abstract ]
The main problem in the dynamical study of a map is to understand the long term behavior of orbits. The abstract theory of non uniformly hyperbolic systems is well understood but it is very difficult to decide when a given system is non uniformly hyperbolic and to study it's sharp ergodic properties.
Holomorphic dynamics in several variables provide large classes of examples of non uniformly hyperbolic systems. One can compute the entropy, construct a measure of maximal entropy and study the sharp statistical properties: central limit theorem, large deviations and exponential decay of correlations. It is also possible to prove sharp equidistribution results for preimages of analytic sets of arbitrary dimension. The main tools are: pluripotential theory, analytic geometry, and good estimates from PDE.
These systems appear naturally if we apply Newton's method to localise the common zeros of of polynomial equations in several variables. In the study of polynomial automorphisms of complex Euclidean spaces, or automorphisms of compact K\\"ahler manifolds.

Seminar on Geometric Complex Analysis

13:45-14:45   Room #128 (Graduate School of Math. Sci. Bldg.)
Karl Oeljeklaus (University of Provence)
Logarthmic
Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)

Seminar on Geometric Complex Analysis

15:00-16:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Andrei Iordan (Univ. Paris VI)
Boundary Regularity of d-bar Operator and Non Existence of Smooth Levi Flat Hypersurfaces in Compact K¥"ahler Manifolds

Seminar on Geometric Complex Analysis

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Univ. Paris Sud)
Holomorphic Dynamics In Several
Variables: equidistribution properties and statistical behavior

2009/07/16

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ingo Runkel (King's College London)
Algebraic structures in conformal field theory
[ Abstract ]
It turned out to be fruitful to isolate questions in CFT which can be formulated in a purely categorical fashion. The way left and right moving degrees of freedom can be combined to a consistent theory is an example of this, the relevant structure being a commutative symmetric Frobenius algebra. This is true independently of whether CFT is formulated via sewing of surfaces or nets of operator algebras. Another example is modular invariance, which has a surprising alternative formulation as a certain maximality condition.

Mathematical Biology Seminar

15:00-16:20   Room #056 (Graduate School of Math. Sci. Bldg.)
Odo Diekmann (Mathematical Institute, Utrecht University)
The delay equation formulation of physiologically structured population models
[ Abstract ]
Traditionally, physiologically structured population models are formulated in terms of first order partial differential equations with non-local boundary conditions and/or transformed arguments. The stability and bifurcation theory for such equations is, in the quasi-linear case, still very immature.
The aim of this lecture is to explain that, alternatively, one can formulate such models in terms of delay equations (more precisely : renewal equations coupled to delay differential equations) without losing essential information and that for delay equations there is a well-developed local stability and bifurcation theory. As a motivating example we consider the interaction between a size-structured consumer and an unstructured resource. The lecture is based on joint work with Mats Gyllenberg and Hans Metz.

2009/07/14

Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
作間 誠 (広島大学)
The Cannon-Thurston maps and the canonical decompositions
of punctured-torus bundles over the circle.
[ Abstract ]
To each once-punctured-torus bundle over the circle
with pseudo-Anosov monodromy, there are associated two tessellations of the complex plane:
one is the triangulation of a horosphere induced by the canonical decomposition into ideal
tetrahedra, and the other is a fractal tessellation
given by the Cannon-Thurston map of the fiber group.
In this talk, I will explain the relation between these two tessellations
(joint work with Warren Dicks).
I will also explain the relation of the fractal tessellation and
the "circle chains" of double cusp groups converging to the fiber group
(joint work with Caroline Series).
If time permits, I would like to discuss possible generalization of these results
to higher-genus punctured surface bundles.

2009/07/13

Algebraic Geometry Seminar

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
佐野 太郎 (東大数理)
Seshadri constants on rational surfaces with anticanonical pencils

[ Abstract ]
射影多様体上の豊富線束の$k$-jet ample性を測る不変量として
Seshadri定数と呼ばれる正の実数がある。
この不変量を調べることでしばしば幾何的な情報が得られる。
今回、1次元以上の反標準線形系をもつ有理曲面上のSeshadri定数を計算する公式
が得られた。
その公式を使うと、対数del Pezzo曲面の特異点の情報をSeshadri定数の値から
復元できる。

2009/07/09

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数物連携宇宙研究機構)
Examples of groups of intermediate rank

2009/07/06

Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
赤堀隆夫 (兵庫県立大学)
On the CR Hamiltonian flows
[ Abstract ]
The deformation theory of CR structures was initiated by Kuranishi and the versal family of CR structures were constructed by Garfied, Lee and myself "in the sense of Kuranishi". Miyajima also discussed the versal family by the completely different method. While, our method relies on the contact geometry(this suggest that there is a deep relation between Hamiltonian geometry and CR structures). Today, I report that our family is also versal "in the sense of CR Hamiltonian flows".

Algebraic Geometry Seminar

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
柳田 伸太郎 (神戸大学理学研究科)
アーベル曲面上の安定層とフーリエ向井変換について
[ Abstract ]
今回の講演は吉岡康太との共同研究に基づくものである. 研究の発端は, 向井茂が1980年前後(フーリエ向井変換の発見前後)に考察し, 当時の講演記録に書き残した主張や予想の解読にある.
本研究は, 大まかに言うと, 半等質層とフーリエ向井変換を用いて, アーベル曲面上の安定層のモジュライ空間の構造を調べるというものである.
アーベル曲面上には半等質層と呼ばれる半安定層があり, その分類, 構成方法やコホモロジーが完全に知られている. アーベル曲面のフーリエ向井対は半等質層のモジュライ空間であることも知られている.
今回の研究はこの半等質層をbulding blockとして一般の安定層を構成することを考える. その際に"semi-homogeneous presentation"という概念が必要になる. これはアーベル曲面上の安定層の半等質層によるある種の分解のことである. 曲面のピカール数が1の時, この種の分解の存在が安定層のチャーン指標のみを用いて判定できる.
また安定層のフーリエ変換における振舞いの記述において, 算術群や整数係数2次形式が重要な役割を果たすことも分かる. この事と先に述べた表示の存在から, 安定層のモジュライとアーベル曲面上の点のヒルベルトスキームとの間の双有理変換が明示的に構成できる.
アーベル曲面のフーリエ向井変換のフォーマリズムはK3曲面の変換と共通する部分も少なくない. 講演ではそうした点にも触れつつ, 今回の結果とその証明の概要を解説したい.

2009/07/02

Operator Algebra Seminars

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
小沢登高 (東大数理)
Dixmier's Similarity Problem ---Littlewood and Forests--- (一般の数学者向け)

2009/07/01

Lectures

15:30-17:00   Room #470 (Graduate School of Math. Sci. Bldg.)
金井 政宏 (東大数理)
ASEPおよびzero-range processの分配関数

2009/06/30

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
北山 貴裕 (東京大学大学院数理科学研究科)
Torsion volume forms and twisted Alexander functions on
character varieties of knots

[ Abstract ]
Using non-acyclic Reidemeister torsion, we can canonically
construct a complex volume form on each component of the
lowest dimension of the $SL_2(\\mathbb{C})$-character
variety of a link group.
This volume form enjoys a certain compatibility with the
following natural transformations on the variety.
Two of them are involutions which come from the algebraic
structure of $SL_2(\\mathbb{C})$ and the other is the
action by the outer automorphism group of the link group.
Moreover, in the case of knots these results deduce a kind
of symmetry of the $SU_2$-twisted Alexander functions
which are globally described via the volume form.

Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Ivana Alexandrova (東京大数理)
The Structure of the Scattering Amplitude for Schrodinger Operators with a Strong Magnetic Field
[ Abstract ]
We study the microlocal structure of the semi-classical scattering amplitude for Schrodinger operators with a strong magnetic field at non-trapping energies. We prove that, up to any order, the scattering amplitude can be approximated by a semi-classical pseudodifferential-operator-valued Fourier integral operator.

2009/06/29

Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
藤木 明 (大阪大学)
VII型曲面上の反自己双対双エルミート構造の存在について

Algebraic Geometry Seminar

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
大川 領 (東京工業大学)
Moduli on the projective plane and the wall-crossing
[ Abstract ]
射影平面上の半安定層のモジュライ空間を、Bridgeland 安定性条件
を用いることにより、ある有限次元代数の半安定表現のモジュライ空間
として構成する。階数が2以下の場合、表現の安定性条件を変化させること
により、壁越え現象としてのflip の記述を得る。
応用として、flip のBetti 数などが計算できる。

2009/06/25

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
鈴木章斗 (九州大学数理学研究院)
Infrared divergence of scalar quantum field model on pseudo Riemann manifold

2009/06/24

Number Theory Seminar

16:30-18:45   Room #056 (Graduate School of Math. Sci. Bldg.)
Vincent Maillot (Paris第7大学) 16:30-17:30
New algebraicity results for analytic torsion
Richard Hain (Duke大学) 17:45-18:45
On the Section Conjecture for the universal curve over function fields

PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Winston Ou (Scripps College / currently visiting assistant professor at Keio University)
Monge-Ampere equations, the Bellman Function Technique, and Muckenhoupt weights
[ Abstract ]
In the last few years several classical results in harmonic analysis (in particular, the study of $A_\\infty$ weights have been sharpened with the use of a version of the Bellman function method (promulgated by Nazarov, Treil, and Volberg in the 90's) that involves recognizing the Bellman function as the solution of a Monge-Ampere PDE (the method was introduced by Vasyunin in 2003). We will give a sketch of the modified technique, outline some recent work-in-progress (with Slavin and Wall) using the technique in $A_\\infty$, and then present a few related problems.

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