## Seminar information archive

Seminar information archive ～05/28｜Today's seminar 05/29 | Future seminars 05/30～

### 2009/05/12

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Discrete subgroups of the group of circle diffeomorphisms

**松田 能文**(東京大学大学院数理科学研究科)Discrete subgroups of the group of circle diffeomorphisms

[ Abstract ]

Typical examples of discrete subgroups of the group of circle diffeomorphisms

are Fuchsian groups.

In this talk, we construct discrete subgroups of the group of

orientation-preserving

real analytic cirlcle diffeomorphisms

which are not topologically conjugate to finite coverings of Fuchsian groups.

Typical examples of discrete subgroups of the group of circle diffeomorphisms

are Fuchsian groups.

In this talk, we construct discrete subgroups of the group of

orientation-preserving

real analytic cirlcle diffeomorphisms

which are not topologically conjugate to finite coverings of Fuchsian groups.

#### Seminar on Probability and Statistics

16:20-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Asymptitically efficient estimation of multiple change points in GARCH types models

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/03.html

**塩濱 敬之**(東京理科大学, 工学部)Asymptitically efficient estimation of multiple change points in GARCH types models

[ Abstract ]

Instability of volatility parameters in GARCH models in an important issue for analyzing financial time series. In this paper we investigate the asymptotic theory for multiple change point estimators of GARCH$(p,q)$ models. When the parameters of a GARCH models have changed within an observed realization, two types estimators, Maximum likelihood estimator (MLE) and Bayesian estimator (BE), are proposed. Then we derive the asymptotic distributions for these estimators. The MLE and BE have different limit laws, and the BE is asymptotically efficient. Monte Carlo studies on the finite sample behaviors are conducted. Applications to Nikkei 225 index are discussed.

[ Reference URL ]Instability of volatility parameters in GARCH models in an important issue for analyzing financial time series. In this paper we investigate the asymptotic theory for multiple change point estimators of GARCH$(p,q)$ models. When the parameters of a GARCH models have changed within an observed realization, two types estimators, Maximum likelihood estimator (MLE) and Bayesian estimator (BE), are proposed. Then we derive the asymptotic distributions for these estimators. The MLE and BE have different limit laws, and the BE is asymptotically efficient. Monte Carlo studies on the finite sample behaviors are conducted. Applications to Nikkei 225 index are discussed.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/03.html

### 2009/05/11

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

CR幾何学でのドラーム分解型定理

**林本厚志**(長野高専)CR幾何学でのドラーム分解型定理

### 2009/05/07

#### Operator Algebra Seminars

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

A fixed point property and the Kazhdan property of

$SL(n, \\mathbb{Z} [X_1, \\ldots , X_k])$ for Banach spaces

**見村万佐人**(東大数理)A fixed point property and the Kazhdan property of

$SL(n, \\mathbb{Z} [X_1, \\ldots , X_k])$ for Banach spaces

### 2009/04/30

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

ギーラー・マインハルト方程式に対するシャドウ系おける多重スポットの不安定性

**池田 幸太**(明治大 研究・知財戦略機構)ギーラー・マインハルト方程式に対するシャドウ系おける多重スポットの不安定性

[ Abstract ]

生物の形態形成に関するモデル方程式である、ギーラー・マインハルト方程式に対するシャドウ系を考える。

この系にはスポットパターンと呼ばれる定常解が存在することが知られており、この解は、その値が非常に大きい点(スポット)を持つこととその近傍の外側では急激に値が減少することにより特徴付けされる。

実は、パラメータと領域を固定しても、単一のスポットだけからなるものや、2つ以上のスポットを持つ定常解、多重スポットが同時に存在しうるが、多重スポットは常に不安定であると予想されている。

本講演では、この予想を数学的に保証するために、多重スポットが適当な条件を満たせば不安定であることを示したい。

生物の形態形成に関するモデル方程式である、ギーラー・マインハルト方程式に対するシャドウ系を考える。

この系にはスポットパターンと呼ばれる定常解が存在することが知られており、この解は、その値が非常に大きい点(スポット)を持つこととその近傍の外側では急激に値が減少することにより特徴付けされる。

実は、パラメータと領域を固定しても、単一のスポットだけからなるものや、2つ以上のスポットを持つ定常解、多重スポットが同時に存在しうるが、多重スポットは常に不安定であると予想されている。

本講演では、この予想を数学的に保証するために、多重スポットが適当な条件を満たせば不安定であることを示したい。

#### Operator Algebra Seminars

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Measure Equivalence Rigidity and Bi-exactness of Groups

**酒匂宏樹**(東大数理)Measure Equivalence Rigidity and Bi-exactness of Groups

### 2009/04/28

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

The ambient metric in conformal geometry

**平地 健吾**(東京大学大学院数理科学研究科)The ambient metric in conformal geometry

[ Abstract ]

In 1985, Charles Fefferman and Robin Graham gave a method for realizing a conformal manifold of dimension n as a submanifold of a Ricci-flat Lorentz metric on a manifold of dimension n+2, which is now called the ambient space. Using this correspondence, one can construct many examples of conformal invariants and conformally invariant operators. However, if n is even, their construction of the ambient space is obstructed at the jet of order n/2 and thereby the application of the ambient space was limited. In this talk, I'll recall basic ideas of the ambient space and then explain how to avoid the difficulty and go beyond the obstruction. This is a joint work with Robin Graham.

In 1985, Charles Fefferman and Robin Graham gave a method for realizing a conformal manifold of dimension n as a submanifold of a Ricci-flat Lorentz metric on a manifold of dimension n+2, which is now called the ambient space. Using this correspondence, one can construct many examples of conformal invariants and conformally invariant operators. However, if n is even, their construction of the ambient space is obstructed at the jet of order n/2 and thereby the application of the ambient space was limited. In this talk, I'll recall basic ideas of the ambient space and then explain how to avoid the difficulty and go beyond the obstruction. This is a joint work with Robin Graham.

#### Tuesday Seminar of Analysis

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

非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)

**下村 明洋**(首都大学東京)非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)

### 2009/04/27

#### Algebraic Geometry Seminar

15:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Automorphism groups of K3 surfaces

) 17:00-18:00

The cohomological crepant resolution conjecture

**Prof. Alessandra Sarti**(Universite de Poitier) 15:30-16:30Automorphism groups of K3 surfaces

[ Abstract ]

I will present recent progress in the study of prime order automorphisms of K3 surfaces.

An automorphism is called (non-) symplectic if the induced

operation on the global nowhere vanishing holomorphic two form

is (non-) trivial. After a short survey on the topic, I will

describe the topological structure of the fixed locus, the

geometry of these K3 surfaces and their moduli spaces.

I will present recent progress in the study of prime order automorphisms of K3 surfaces.

An automorphism is called (non-) symplectic if the induced

operation on the global nowhere vanishing holomorphic two form

is (non-) trivial. After a short survey on the topic, I will

describe the topological structure of the fixed locus, the

geometry of these K3 surfaces and their moduli spaces.

**Prof. Samuel Boissier**(Universite de Nice) 17:00-18:00

The cohomological crepant resolution conjecture

[ Abstract ]

The cohomological crepant resolution conjecture is one

form of Ruan's conjecture concerning the relation between the

geometry of a quotient singularity X/G - where X is a smooth

complex variety and G a finite group of automorphisms - and the

geometry of a crepant resolution of singularities of X/G ; it

generalizes the classical McKay correspondence. Following the

examples of the Hilbert schemes of points on surfaces and the

weighted projective spaces, I will present some of the recents

developments of the subject.

The cohomological crepant resolution conjecture is one

form of Ruan's conjecture concerning the relation between the

geometry of a quotient singularity X/G - where X is a smooth

complex variety and G a finite group of automorphisms - and the

geometry of a crepant resolution of singularities of X/G ; it

generalizes the classical McKay correspondence. Following the

examples of the Hilbert schemes of points on surfaces and the

weighted projective spaces, I will present some of the recents

developments of the subject.

### 2009/04/23

#### Operator Algebra Seminars

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

Entire Cyclic Cohomology of Noncommutative 2-Tori

**内藤克利**(首都大)Entire Cyclic Cohomology of Noncommutative 2-Tori

### 2009/04/22

#### PDE Real Analysis Seminar

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

From Codazzi-Mainardi to Cauchy-Riemann

**Wilhelm Klingenberg**(University of Durham)From Codazzi-Mainardi to Cauchy-Riemann

[ Abstract ]

In joint work with Brendan Guilfoyle we established an upper bound for the winding number of the principal curvature foliation at any isolated umbilic of a surface in Euclidean three-space. In our talk, we will focus on the analytic core of the problem. Here is a model of the triaxial ellipsoid with its curvature foliation and one umbilic on the right.

In joint work with Brendan Guilfoyle we established an upper bound for the winding number of the principal curvature foliation at any isolated umbilic of a surface in Euclidean three-space. In our talk, we will focus on the analytic core of the problem. Here is a model of the triaxial ellipsoid with its curvature foliation and one umbilic on the right.

#### Geometry Seminar

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

Einstein-Weyl structures on 3-dimensional Severi varieties

Toric non-Abelian Hodge theory

**中田文憲**(東京工業大学理工学研究科) 14:45-16:15Einstein-Weyl structures on 3-dimensional Severi varieties

[ Abstract ]

The space of nodal curves on a projective surface is called a Severi variety.In this talk, we show that any Severi variety of nodal rational curves on a non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N. Hitchin in the context of twistor theory. We will explain some properties of the Einstein-Weyl spaces given by this method, and we will also show some examples of such Einstein-Weyl spaces. (This is a joint work with Nobuhiro Honda.)

The space of nodal curves on a projective surface is called a Severi variety.In this talk, we show that any Severi variety of nodal rational curves on a non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N. Hitchin in the context of twistor theory. We will explain some properties of the Einstein-Weyl spaces given by this method, and we will also show some examples of such Einstein-Weyl spaces. (This is a joint work with Nobuhiro Honda.)

**Tamas Hausel**(Oxford University) 16:30-18:00Toric non-Abelian Hodge theory

[ Abstract ]

First we give an overview of the geometrical and topological aspects of the spaces in the non-Abelian Hodge theory of a curve and their connection with quiver varieties. Then by concentrating on toric hyperkaehler varieties in place of quiver varieties we construct the toric Betti, De Rham and Dolbeault spaces and prove several of the expected properties of the geometry and topology of these varieties. This is joint work with Nick Proudfoot.

First we give an overview of the geometrical and topological aspects of the spaces in the non-Abelian Hodge theory of a curve and their connection with quiver varieties. Then by concentrating on toric hyperkaehler varieties in place of quiver varieties we construct the toric Betti, De Rham and Dolbeault spaces and prove several of the expected properties of the geometry and topology of these varieties. This is joint work with Nick Proudfoot.

#### Seminar on Probability and Statistics

15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)

Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html

**Arnaud DOUCET**(統計数理研究所)Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations

[ Abstract ]

We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.

(this is joint work with Professor Pierre Del Moral)

[ Reference URL ]We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.

(this is joint work with Professor Pierre Del Moral)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html

### 2009/04/21

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Some algebraic aspects of KZ systems

**Ivan Marin**(Univ. Paris VII)Some algebraic aspects of KZ systems

[ Abstract ]

Knizhnik-Zamolodchikov (KZ) systems enables one

to construct representations of (generalized)

braid groups. While this geometric construction is

now very well understood, it still brings to

attention, or helps constructing, new algebraic objects.

In this talk, we will present some of them, including an

infinitesimal version of Iwahori-Hecke algebras and a

generalization of the Krammer representations of the usual

braid groups.

Knizhnik-Zamolodchikov (KZ) systems enables one

to construct representations of (generalized)

braid groups. While this geometric construction is

now very well understood, it still brings to

attention, or helps constructing, new algebraic objects.

In this talk, we will present some of them, including an

infinitesimal version of Iwahori-Hecke algebras and a

generalization of the Krammer representations of the usual

braid groups.

### 2009/04/20

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Indefinite Kähler surfaces of constant scalar curvature

**鎌田博行**(宮城教育大学)Indefinite Kähler surfaces of constant scalar curvature

### 2009/04/18

#### Infinite Analysis Seminar Tokyo

11:00-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Invariant Differential Operators for Non-Compact Lie Groups

TBA

**Vladimir Dobrev**(Institute for Nuclear Reserch and Nuclear Energy, Sofia, Bulgaria) 11:00-12:00Invariant Differential Operators for Non-Compact Lie Groups

[ Abstract ]

We present a canonical procedure for the explicit construction of

invariant differential operators. The exposition is for semi-simple

Lie algebras, but is easily generalized to the supersymmetric and

quantum group settings. Especially important is a narrow class of

algebras, which we call 'conformal Lie algebras', which have very

similar properties to the conformal algebras of n-dimensional

Minkowski space-time. Examples are given in detail, including diagrams of

intertwining operators, or equivalently, multiplets of elementary

representations (generalized Verma modules).

We present a canonical procedure for the explicit construction of

invariant differential operators. The exposition is for semi-simple

Lie algebras, but is easily generalized to the supersymmetric and

quantum group settings. Especially important is a narrow class of

algebras, which we call 'conformal Lie algebras', which have very

similar properties to the conformal algebras of n-dimensional

Minkowski space-time. Examples are given in detail, including diagrams of

intertwining operators, or equivalently, multiplets of elementary

representations (generalized Verma modules).

**笠谷昌弘**(東大数理) 13:30-14:30TBA

[ Abstract ]

TBA

TBA

### 2009/04/16

#### Operator Algebra Seminars

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

Large Deviations in Quantum Spin Chains

**緒方芳子**(東大数理)Large Deviations in Quantum Spin Chains

### 2009/04/15

#### Lectures

15:30-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Invariant measures for stochastic partial differential equations: new a priori estimates and applications

**Wilhelm Stannat**(Darmstadt 工科大学)Invariant measures for stochastic partial differential equations: new a priori estimates and applications

#### Seminar on Probability and Statistics

16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Estimating the successive Blumenthal-Getoor indices for a discretely observed process

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html

**Jean JACOD**(Universite Paris VI)Estimating the successive Blumenthal-Getoor indices for a discretely observed process

[ Abstract ]

Letting F be a Levy measure whose "tail" $F ([-x, x])$ admits an expansion $\\sigma_{i\\ge 1} a_i/x^\\beta$ as $x \\rightarrow 0$, we call $\\beta_1 > \\beta_2 >...$ the successive Blumenthal-Getoor indices, since $\\beta_1$ is in this case the usual Blumenthal-Getoor index. This notion may be extended to more general semimartingale. We propose here a method to estimate the $\\beta_i$'s and the coefficients $a_i$'s, or rather their extension for semimartingales, when the underlying semimartingale $X$ is observed at discrete times, on fixed time interval. The asymptotic is when the time-lag goes to $0$. It is then possible to construct consistent estimators for $\\beta_i$ and $a_i$ for those $i$'s such that $\\beta_i > \\beta_1 /2$, whereas it is impossible to do so (even when $X$ is a Levy process) for those $i$'s such that $\\beta_i < \\beta_1 /2$. On the other hand, a central limit theorem for $\\beta_1$ is available only when $\\beta_i < \\beta_1 /2$: consequently, when we can actually consistently estimate some $\\beta_i$'s besides $\\beta_1$ , then no central limit theorem can hold, and correlatively the rates of convergence become quite slow (although one know them explicitly): so the results have some theoretical interest in the sense that they set up bounds on what is actually possible to achieve, but the practical applications are probably quite thin.

(joint with Yacine Ait-Sahalia)

[ Reference URL ]Letting F be a Levy measure whose "tail" $F ([-x, x])$ admits an expansion $\\sigma_{i\\ge 1} a_i/x^\\beta$ as $x \\rightarrow 0$, we call $\\beta_1 > \\beta_2 >...$ the successive Blumenthal-Getoor indices, since $\\beta_1$ is in this case the usual Blumenthal-Getoor index. This notion may be extended to more general semimartingale. We propose here a method to estimate the $\\beta_i$'s and the coefficients $a_i$'s, or rather their extension for semimartingales, when the underlying semimartingale $X$ is observed at discrete times, on fixed time interval. The asymptotic is when the time-lag goes to $0$. It is then possible to construct consistent estimators for $\\beta_i$ and $a_i$ for those $i$'s such that $\\beta_i > \\beta_1 /2$, whereas it is impossible to do so (even when $X$ is a Levy process) for those $i$'s such that $\\beta_i < \\beta_1 /2$. On the other hand, a central limit theorem for $\\beta_1$ is available only when $\\beta_i < \\beta_1 /2$: consequently, when we can actually consistently estimate some $\\beta_i$'s besides $\\beta_1$ , then no central limit theorem can hold, and correlatively the rates of convergence become quite slow (although one know them explicitly): so the results have some theoretical interest in the sense that they set up bounds on what is actually possible to achieve, but the practical applications are probably quite thin.

(joint with Yacine Ait-Sahalia)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html

#### Seminar on Probability and Statistics

15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)

A survey on realized p-variations for semimartingales

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html

**Jean JACOD**(Universite Paris VI)A survey on realized p-variations for semimartingales

[ Abstract ]

Let $X$ be a process which is observed at the times $i\\Delta_n$ for $i=0,1,\\ldots,$. If $p>0$ the realized $p$-variation over the time interval $[0, t]$ is

V^n(p)_t=\\sum_{i=1}^{[t/\\Delta_n]}|X_{i\\Delta_n}-X_{(i-1)\\Delta_n}|^p.

The behavior of these $p$-variations when $\\Delta_n ightarrow 0$ (and t is fixed) is now well understood, from the point of view of limits in probability (these are basically old results due to Lepingle) and also for the associated central limit theorem.

The aim of this talk is to review those results, as well as a few extensions (multipower variations, truncated variations). We will put some emphasis on the assumptions on $X$ which are needed, depending on the value of $p$.

[ Reference URL ]Let $X$ be a process which is observed at the times $i\\Delta_n$ for $i=0,1,\\ldots,$. If $p>0$ the realized $p$-variation over the time interval $[0, t]$ is

V^n(p)_t=\\sum_{i=1}^{[t/\\Delta_n]}|X_{i\\Delta_n}-X_{(i-1)\\Delta_n}|^p.

The behavior of these $p$-variations when $\\Delta_n ightarrow 0$ (and t is fixed) is now well understood, from the point of view of limits in probability (these are basically old results due to Lepingle) and also for the associated central limit theorem.

The aim of this talk is to review those results, as well as a few extensions (multipower variations, truncated variations). We will put some emphasis on the assumptions on $X$ which are needed, depending on the value of $p$.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html

### 2009/04/14

#### Lectures

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Resolution of symplectic orbifolds obtained from reduction

**Klaus Niederkruger**(Ecole normale superieure de Lyon)Resolution of symplectic orbifolds obtained from reduction

[ Abstract ]

We present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a symplectic orbifold admit a resolution and that pre-quantizations of symplectic orbifolds are symplectically fillable by a smooth manifold.

We present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a symplectic orbifold admit a resolution and that pre-quantizations of symplectic orbifolds are symplectically fillable by a smooth manifold.

### 2009/04/13

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

A new method to generalize the Nevanlinna theory to several complex variables

**千葉優作**(東大数理)A new method to generalize the Nevanlinna theory to several complex variables

### 2009/04/09

#### Operator Algebra Seminars

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

Bimodules, planarity and freeness

**Dietmar Bisch**(Vanderbilt University)Bimodules, planarity and freeness

### 2009/04/08

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station

**横山悦郎**(学習院大学)Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station

[ Abstract ]

We present a model of the time evolution of a disk crystal of ice with radius $R$ and thickness $h$ growing from supercooled water and discuss its morphological stability. Disk thickening, {\\it i.e.}, growth along the $c$ axis of ice, is governed by slow molecular rearrangements on the basal faces. Growth of the radius, {\\it i.e.}, growth parallel to the basal plane, is controlled by transport of latent heat. Our analysis is used to understand the symmetry breaking obtained experimentally by Shimada and Furukawa under the one-G condition. We also introduce that the space experiment of the morphological instability on the ice growing in supercooled water, which was carried out on the Japanese Experiment Module "Kibo" of International Space Station from December 2008 and February 2009.

http://kibo.jaxa.jp/experiment/theme/first/ice_crystal_end.html

We show the experimental results under the micro-G condition and discuss the feature on the "Kibo" experoments.

We present a model of the time evolution of a disk crystal of ice with radius $R$ and thickness $h$ growing from supercooled water and discuss its morphological stability. Disk thickening, {\\it i.e.}, growth along the $c$ axis of ice, is governed by slow molecular rearrangements on the basal faces. Growth of the radius, {\\it i.e.}, growth parallel to the basal plane, is controlled by transport of latent heat. Our analysis is used to understand the symmetry breaking obtained experimentally by Shimada and Furukawa under the one-G condition. We also introduce that the space experiment of the morphological instability on the ice growing in supercooled water, which was carried out on the Japanese Experiment Module "Kibo" of International Space Station from December 2008 and February 2009.

http://kibo.jaxa.jp/experiment/theme/first/ice_crystal_end.html

We show the experimental results under the micro-G condition and discuss the feature on the "Kibo" experoments.

### 2009/03/25

#### GCOE lecture series

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II

**Mark Gross**(University of California, San Diego)The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II

[ Abstract ]

The second half of the lecture.

The second half of the lecture.

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