## 過去の記録

#### 博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 122号室

On the generalized suspension theorem for directed Fukaya categories (有向深谷圏の懸垂定理の一般化について)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 122号室

On the Runge theorem for instantons (インスタントンに対するRungeの近似定理について)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 126号室

Solvability and irreducibility of difference equations (差分方程式の可解性と既約性)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 126号室

Weak Amenability for a Group Acting on a Finite Dimensional CAT(0) Cube Complex (有限次元CAT(0)方体複体に作用する群の弱従順性)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 126号室

Stone-Čech boundaries of discrete groups and measure equivalence theory (離散群のストーン-チェック境界と測度同値理論)

#### 博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 128号室

CONSTRUCTION OF ISOTROPIC CELLULAR AUTOMATON AND ITS APPLICATION (等方セル・オートマトンの構成とその応用)

### 2010年02月04日(木)

#### 博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 122号室

The Meyer functions for projective varieties and their applications to local signatures for fibered 4-manifolds (射影多様体に対するMeyer函数と,その局所符号数への応用)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 122号室

On hyperkähler manifolds of type A∞ (A∞型超ケーラー多様体について)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 122号室

On the index problem for C1-generic wild homoclinic classes (C1通有的に野性的なホモクリニック類の指数問題について)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 122号室

The abelianization of the level d mapping class group (レベルd写像類群のアーベル化)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 126号室

Singularities for Solutions to Schrödinger Equations (シュレーディンガー方程式の解の特異性)

#### 博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 126号室
Si, Duc Quang 氏 (東京大学大学院数理科学研究科)
Nevanlinna theory for holomorphic mappings and related problems (正則写像のネヴァンリンナ理論と関連する問題)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 128号室

On existence of models for the logical system MPCL (単相格論理系におけるモデルの存在について)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 128号室

Exact Solutions of Ultradiscrete Integrable Systems (超離散可積分系の厳密解)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 128号室

Vertex operators and background solutions for ultradiscrete soliton equations (超離散ソリトン方程式における頂点作用素と背景解)

### 2010年02月02日(火)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーとの合同で行います。いつもと場所が違います。
Fanny Kassel 氏 (Orsay)
Deformation of compact quotients of homogeneous spaces
[ 講演概要 ]
Let G/H be a reductive homogeneous space. In all known examples, if
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting properly discontinuously.

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Lie群論・表現論セミナーと合同, Tea: 16:00 - 16:30 コモンルーム
Fanny Kassel 氏 (Univ. Paris-Sud, Orsay)
Deformation of compact quotients of homogeneous spaces
[ 講演概要 ]
Let G/H be a reductive homogeneous space. In all known examples, if
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of
SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting
properly discontinuously.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100202kassel

### 2010年02月01日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室

Extensions of two Chow stability criteria to positive characteristics
[ 講演概要 ]
I will talk about two results on Chow (semi-)stability of cycles in positive characteristics, which were originally known in characteristic 0. One is on the stability of non-singular projective hypersurfaces of degree greater than 2, and the other is the criterion by Y. Lee in terms of the log canonical threshold of Chow divisor. A couple of examples will be discussed in detail.

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Timur Sadykov 氏 (Siberian Federal University)
Bases in the solution space of the Mellin system
[ 講演概要 ]
I will present a joint work with Alicia Dickenstein.
We consider algebraic functions $z$ satisfying equations of the
form
\
a_0 z^m + a_1z^{m_1} + a_2 z^{m_2} + \\ldots + a_n z^{m_n} +
a_{n+1} =0.
\
Here $m > m_1 > \\ldots > m_n>0,$ $m,m_i \\in \\N,$ and
$z=z(a_0,\\ldots,a_{n+1})$ is a function of the complex variables
$a_0, \\ldots, a_{n+1}.$ Solutions to such equations are
classically known to satisfy holonomic systems of linear partial
differential equations with polynomial coefficients. In the talk
I will investigate one of such systems of differential equations which
was introduced by Mellin. We compute the holonomic rank of the
Mellin system as well as the dimension of the space of its
algebraic solutions. Moreover, we construct explicit bases of
solutions in terms of the roots of initial algebraic equation and their
logarithms. We show that the monodromy of the Mellin system is
always reducible and give some factorization results in the
univariate case.

### 2010年01月29日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
Let $f$ be a given real-valued function defined on a subset of $\\mathbb{R}^n$. We explain how to decide whether $f$ extends to a function $F$ in $C^m(\\mathbb{R}^n)$. If such an $F$ exists, we show how to construct one.

### 2010年01月28日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

#### 講演会

10:40-12:10   数理科学研究科棟(駒場) 123号室
Olivier Alvarez 氏 (Head of quantitative research, IRFX options Asia, BNP Paribas)
Partial differential equations in Finance I
[ 講演概要 ]
1. Markov processes and Partial differential equations (PDE)
- Markov processes, stochastic differential equations and infinitesimal generator

- The Feynman Kac formula and the backward Kolmogorov equation

- The maximum principle

- Exit time problems and Dirichlet boundary conditions

- Optimal time problems and obstacle problems

2. Application to the pricing of exotic options
- The model equation

- The Black-Scholes equation : absence of arbitrage and dynamical hedging

- Recovering the Black-Scholes formula

- Pricing exotic options : Knock-out / knock-in, american, Asian, lookback

- Overview of affine models and semi-closed formulae

- Heston model : valuing European options

- The Hull White model for IR exotics : valuing zero-coupons, caplets and swaptions.

3. Finite difference methods in Finance
- Basic concepts for numerical schemes : consistency, stability, accuracy and

convergence; the Lax equivalence theorem

- Finite difference methods in dimension 1 : Explicit, implicit, Crank-Nicholson methods for the heat equation : overview, accuracy and convergence

Incorporating first-order derivatives : upwind derivative, stability

- Finite difference methods in dimension 2 : presentation of various schemes :explicit, implicit, alternating direction implicit (ADI), Hopscotch method

- Solving high dimensional linear systems :

LU decomposition, iterative methods

- Finite difference and Monte Carlo methods

4. Optimal control in finance
- Introduction to optimal control

- The dynamic programming principle and the Hamilton-Jacobi-Bellman equation

- The verification theorem and the determination of the optimal control policy

- Utility maximization and Merton's problem

- Pricing with uncertain parameters

- Pricing with transaction costs

- Finite difference methods for optimal control

#### 講演会

13:00-14:10   数理科学研究科棟(駒場) 122号室
Olivier Alvarez 氏 (Head of quantitative research, IRFX options Asia, BNP Paribas)
Partial differential equations in Finance II
[ 講演概要 ]
1. Markov processes and Partial differential equations (PDE)
- Markov processes, stochastic differential equations and infinitesimal generator

- The Feynman Kac formula and the backward Kolmogorov equation

- The maximum principle

- Exit time problems and Dirichlet boundary conditions

- Optimal time problems and obstacle problems

2. Application to the pricing of exotic options
- The model equation

- The Black-Scholes equation : absence of arbitrage and dynamical hedging

- Recovering the Black-Scholes formula

- Pricing exotic options : Knock-out / knock-in, american, Asian, lookback

- Overview of affine models and semi-closed formulae

- Heston model : valuing European options

- The Hull White model for IR exotics : valuing zero-coupons, caplets and swaptions.

3. Finite difference methods in Finance
- Basic concepts for numerical schemes : consistency, stability, accuracy and

convergence; the Lax equivalence theorem

- Finite difference methods in dimension 1 : Explicit, implicit, Crank-Nicholson methods for the heat equation : overview, accuracy and convergence

Incorporating first-order derivatives : upwind derivative, stability

- Finite difference methods in dimension 2 : presentation of various schemes :explicit, implicit, alternating direction implicit (ADI), Hopscotch method

- Solving high dimensional linear systems :

LU decomposition, iterative methods

- Finite difference and Monte Carlo methods

4. Optimal control in finance
- Introduction to optimal control

- The dynamic programming principle and the Hamilton-Jacobi-Bellman equation

- The verification theorem and the determination of the optimal control policy

- Utility maximization and Merton's problem

- Pricing with uncertain parameters

- Pricing with transaction costs

- Finite difference methods for optimal control

#### GCOEレクチャーズ

16:30-17:30   数理科学研究科棟(駒場) 999号室
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.

Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?

Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?

What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?