## Seminar information archive

Seminar information archive ～10/21｜Today's seminar 10/22 | Future seminars 10/23～

### 2015/09/28

#### Seminar on Geometric Complex Analysis

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

Flat structures on moduli spaces of generalized complex surfaces

**Ryushi Goto**(Osaka University)Flat structures on moduli spaces of generalized complex surfaces

[ Abstract ]

The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.

The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

**Keiji Saito**(Faculty of Science and Technology, Keio University)### 2015/09/25

#### Colloquium

16:50-17:50 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

Mean curvature flow with surgery

http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken

**Gerhard Huisken**(The Mathematisches Forschungsinstitut Oberwolfach )Mean curvature flow with surgery

[ Abstract ]

We study the motion of hypersurfaces in a Riemannian manifold

with normal velocity equal to the mean curvature of the

evolving hypersurface. In general this quasilinear, parabolic

evolution system may have complicated singularities in finite time.

However, under natural assumptions such as embeddedness of the surface

and positivity of the mean curvature (case of 2-dimensional surfaces)

all singularities can be classified and developing "necks" can be

removed by a surgery procedure similar to techniques employed

by Hamilton and Perelman in the Ricci-flow of Riemannian metrics.

The lecture describes results and techniques for mean curvature flow

with surgery developed in joint work with C. Sinestrari and S. Brendle.

[ Reference URL ]We study the motion of hypersurfaces in a Riemannian manifold

with normal velocity equal to the mean curvature of the

evolving hypersurface. In general this quasilinear, parabolic

evolution system may have complicated singularities in finite time.

However, under natural assumptions such as embeddedness of the surface

and positivity of the mean curvature (case of 2-dimensional surfaces)

all singularities can be classified and developing "necks" can be

removed by a surgery procedure similar to techniques employed

by Hamilton and Perelman in the Ricci-flow of Riemannian metrics.

The lecture describes results and techniques for mean curvature flow

with surgery developed in joint work with C. Sinestrari and S. Brendle.

http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken

#### Classical Analysis

16:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Confluence of general Schlesinger systems from the viewpoint of Twistor theory (JAPANESE)

**Damiran Tseveennamjil**(Mongolian University of Life Sciences)Confluence of general Schlesinger systems from the viewpoint of Twistor theory (JAPANESE)

### 2015/09/17

#### Seminar on Probability and Statistics

15:00-16:10 Room #052 (Graduate School of Math. Sci. Bldg.)

The use of S4 classes and methods in the Yuima R package

**Stefano Iacus**(University of Milan)The use of S4 classes and methods in the Yuima R package

[ Abstract ]

In this talk we present the basic concept of S4 classes and methods approach for object oriented programming in R. As a working example, we introduce the structure of the Yuima package for simulation and inference of stochastic differential equations. We will describe the basic classes and objects as well as some recent extensions which allows for Carma and Co-Garch processes handling in Yuima.

In this talk we present the basic concept of S4 classes and methods approach for object oriented programming in R. As a working example, we introduce the structure of the Yuima package for simulation and inference of stochastic differential equations. We will describe the basic classes and objects as well as some recent extensions which allows for Carma and Co-Garch processes handling in Yuima.

#### Infinite Analysis Seminar Tokyo

14:00-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Classifying simple modules at admissible levels through

symmetric polynomials (ENGLISH)

**Simon Wood**(The Australian National University)Classifying simple modules at admissible levels through

symmetric polynomials (ENGLISH)

[ Abstract ]

From infinite dimensional Lie algebras such as the Virasoro

algebra or affine Lie (super)algebras one can construct universal

vertex operator algebras. These vertex operator algebras are simple at

generic central charges or levels and only contain proper ideals at so

called admissible levels. The simple quotient vertex operator algebras

at these admissible levels are called minimal model algebras. In this

talk I will present free field realisations of the universal vertex

operator algebras and show how they allow one to elegantly classify

the simple modules over the simple quotient vertex operator algebras

by using a deep connection to symmetric polynomials.

From infinite dimensional Lie algebras such as the Virasoro

algebra or affine Lie (super)algebras one can construct universal

vertex operator algebras. These vertex operator algebras are simple at

generic central charges or levels and only contain proper ideals at so

called admissible levels. The simple quotient vertex operator algebras

at these admissible levels are called minimal model algebras. In this

talk I will present free field realisations of the universal vertex

operator algebras and show how they allow one to elegantly classify

the simple modules over the simple quotient vertex operator algebras

by using a deep connection to symmetric polynomials.

### 2015/09/11

#### FMSP Lectures

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Operads and their applications to Mathematical Physics (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

**Alexander Voronov**(Univ. of Minnesota)Operads and their applications to Mathematical Physics (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

### 2015/09/10

#### FMSP Lectures

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Operads and their applications to Mathematical Physics (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

**Alexander Voronov**(Univ. of Minnesota)Operads and their applications to Mathematical Physics (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

#### FMSP Lectures

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Lifting of maps between surfaces (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ZhiChen.pdf

**Zhi Chen**(Hefei University of Technology)Lifting of maps between surfaces (ENGLISH)

[ Abstract ]

The Thom conjecture says the algebraic curves have minimal genus among those surfaces Imbedded in CP^2 having fixed degree. This conjecture was solved by Kronheimer and Mrowka by using Seiberg-Witten invariants. In this talk we try to understand the content of this conjecture. We will construct these imbedded surface with minimal genus explicitly, and present some kind of generalization of this conjecture.

[ Reference URL ]The Thom conjecture says the algebraic curves have minimal genus among those surfaces Imbedded in CP^2 having fixed degree. This conjecture was solved by Kronheimer and Mrowka by using Seiberg-Witten invariants. In this talk we try to understand the content of this conjecture. We will construct these imbedded surface with minimal genus explicitly, and present some kind of generalization of this conjecture.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ZhiChen.pdf

### 2015/09/09

#### Number Theory Seminar

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

The hyperbolic Ax-Lindemann conjecture (English)

**Emmanuel Ullmo**(IHES)The hyperbolic Ax-Lindemann conjecture (English)

[ Abstract ]

The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.

The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.

### 2015/09/08

#### Seminar on Mathematics for various disciplines

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

Duality based approaches to total variation-like flows with applications to image processing (English)

**Monika Muszkieta**(Wroclaw University of Technology)Duality based approaches to total variation-like flows with applications to image processing (English)

[ Abstract ]

During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of differentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.

This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.

During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of differentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.

This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.

#### Tuesday Seminar of Analysis

16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)

Global-in-time Strichartz estimates for Schr\"odinger equations with long-range repulsive potentials (Japanese)

**Haruya Mizutani**(School of Science, Osaka University)Global-in-time Strichartz estimates for Schr\"odinger equations with long-range repulsive potentials (Japanese)

[ Abstract ]

We will discuss a resent result on global-in-time Strichartz estimates for Schr\"odinger equations with slowly decreasing repulsive potentials. If the potential is of very short-range type, there is a simple method due to Rodnianski-Schlag or Burq et al, which seems to be difficult to apply for the present case. The proof instead follows a similar line as in speaker’s resent joint work with J.-M. Bouclet. In particular, we employ both Morawetz type estimates and the methods of micro local analysis such as the Isozaki-Kitada parametrix, even in the low frequency regime.

We will discuss a resent result on global-in-time Strichartz estimates for Schr\"odinger equations with slowly decreasing repulsive potentials. If the potential is of very short-range type, there is a simple method due to Rodnianski-Schlag or Burq et al, which seems to be difficult to apply for the present case. The proof instead follows a similar line as in speaker’s resent joint work with J.-M. Bouclet. In particular, we employ both Morawetz type estimates and the methods of micro local analysis such as the Isozaki-Kitada parametrix, even in the low frequency regime.

### 2015/09/02

#### FMSP Lectures

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Operads and their applications to Mathematical Physics (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

**Alexander Voronov**(Univ. of Minnesota)Operads and their applications to Mathematical Physics (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

### 2015/08/31

#### thesis presentations

16:30-17:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Approximate Controllability, Non-homogeneous Boundary Value Problems and Inverse Source Problems for Fractional Diffusion Equations（非整数階拡散方程式に対する近似可制御性、非斉次境界値問題およびソース項決定逆問題） (JAPANESE)

**藤城 謙一**(東京大学大学院数理科学研究科)Approximate Controllability, Non-homogeneous Boundary Value Problems and Inverse Source Problems for Fractional Diffusion Equations（非整数階拡散方程式に対する近似可制御性、非斉次境界値問題およびソース項決定逆問題） (JAPANESE)

### 2015/08/28

#### Colloquium

16:50-17:50 Room #002 (Graduate School of Math. Sci. Bldg.)

On the development of Riemann surfaces and moduli (ENGLISH)

**Athanase Papadopoulos**(Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS)On the development of Riemann surfaces and moduli (ENGLISH)

[ Abstract ]

I will describe a selection of major fundamental ideas in the theory

of Riemann surfaces and moduli, starting from the work of Riemann, and

ending with recent works.

I will describe a selection of major fundamental ideas in the theory

of Riemann surfaces and moduli, starting from the work of Riemann, and

ending with recent works.

### 2015/08/07

#### Seminar on Probability and Statistics

14:40-15:50 Room #052 (Graduate School of Math. Sci. Bldg.)

Effectiveness of time-varying minimum value at risk and expected shortfall hedging

**UBUKATA, Masato**(Kushiro Public University of Economics)Effectiveness of time-varying minimum value at risk and expected shortfall hedging

[ Abstract ]

This paper assesses the incremental value of time-varying minimum value at risk (VaR) and expected shortfall (ES) hedging strategies over unconditional hedging strategy. The conditional futures hedge ratios are calculated through estimation of multivariate volatility models under a skewed and leptokurtic distribution and Monte Carlo simulation for conditional skewness and kurtosis of hedged portfolio returns. We examine DCC-GJR models with or without encompassing realized covariance measure (RCM) from high-frequency data under a multivariate skewed Student's t-distribution. In the out-of-sample analysis with a daily rebalancing approach, the empirical results show that the conditional minimum VaR and ES hedging strategies outperform the unconditional hedging strategy. We find that the use of RCM improves the futures hedging performance for a short hedge, although the degree of improvement is small relative to that when switching from unconditional to conditional.

This paper assesses the incremental value of time-varying minimum value at risk (VaR) and expected shortfall (ES) hedging strategies over unconditional hedging strategy. The conditional futures hedge ratios are calculated through estimation of multivariate volatility models under a skewed and leptokurtic distribution and Monte Carlo simulation for conditional skewness and kurtosis of hedged portfolio returns. We examine DCC-GJR models with or without encompassing realized covariance measure (RCM) from high-frequency data under a multivariate skewed Student's t-distribution. In the out-of-sample analysis with a daily rebalancing approach, the empirical results show that the conditional minimum VaR and ES hedging strategies outperform the unconditional hedging strategy. We find that the use of RCM improves the futures hedging performance for a short hedge, although the degree of improvement is small relative to that when switching from unconditional to conditional.

#### Seminar on Probability and Statistics

13:20-14:30 Room #052 (Graduate School of Math. Sci. Bldg.)

ESTIMATION OF INTEGRATED QUADRATIC COVARIATION BETWEEN TWO ASSETS WITH ENDOGENOUS SAMPLING TIMES

**Yoann Potiron**(University of Chicago)ESTIMATION OF INTEGRATED QUADRATIC COVARIATION BETWEEN TWO ASSETS WITH ENDOGENOUS SAMPLING TIMES

[ Abstract ]

When estimating integrated covariation between two assets based on high-frequency data,simple assumptions are usually imposed on the relationship between the price processes and the observation times. In this paper, we introduce an endogenous 2-dimensional model and show that it is more general than the existing endogenous models of the literature. In addition, we establish a central limit theorem for the Hayashi-Yoshida estimator in this general endogenous model in the case where prices follow pure-diffusion processes.

When estimating integrated covariation between two assets based on high-frequency data,simple assumptions are usually imposed on the relationship between the price processes and the observation times. In this paper, we introduce an endogenous 2-dimensional model and show that it is more general than the existing endogenous models of the literature. In addition, we establish a central limit theorem for the Hayashi-Yoshida estimator in this general endogenous model in the case where prices follow pure-diffusion processes.

### 2015/07/30

#### thesis presentations

10:30-11:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Theory and application of a meta lambda calculus with cross-level computation （レベル横断的計算機構を持つメタラムダ計算の理論と応用） (JAPANESE)

**飛澤 和則**(東京大学大学院数理科学研究科)Theory and application of a meta lambda calculus with cross-level computation （レベル横断的計算機構を持つメタラムダ計算の理論と応用） (JAPANESE)

### 2015/07/29

#### thesis presentations

16:00-17:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Accelerating convergence and tractability of multivariate numerical integration when the L1-norms of the higher order derivatives of the integrand grow at most exponentially（被積分関数の高階偏微分のL1ノルムの増大度が高々指数的である場合の多次元数値積分の加速的な収束と計算容易性） (JAPANESE)

**鈴木 航介**(東京大学大学院数里科学研究科)Accelerating convergence and tractability of multivariate numerical integration when the L1-norms of the higher order derivatives of the integrand grow at most exponentially（被積分関数の高階偏微分のL1ノルムの増大度が高々指数的である場合の多次元数値積分の加速的な収束と計算容易性） (JAPANESE)

#### thesis presentations

17:30-18:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Research on Walsh figure of merit for higher order convergent Quasi-Monte Carlo integration（高次収束準モンテカルロ積分のためのWalsh figure of meritの研究） (JAPANESE)

**芳木 武仁**(東京大学大学院数理科学研究科)Research on Walsh figure of merit for higher order convergent Quasi-Monte Carlo integration（高次収束準モンテカルロ積分のためのWalsh figure of meritの研究） (JAPANESE)

### 2015/07/28

#### Lectures

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

Convergence of some horocyclic deformations to the Gardiner-Masur

boundary of Teichmueller space. (ENGLISH)

**Vincent Alberge**(Université de Strasbourg)Convergence of some horocyclic deformations to the Gardiner-Masur

boundary of Teichmueller space. (ENGLISH)

[ Abstract ]

It is well known that a point of the Teichmueller space and a measured foliation determine an isometric embedding of the hyperbolic disc to the Teichmueller space equipped with the so-called Teichmueller metric. In this talk, we will consider the image by this embedding of a particular horocycle whose points will be called an horocyclic deformation. To be more precise, we will be interested in the closure of this subset in the Gardiner-Masur compactification. As the embedding of the disc does not admit a continuous extension to boundaries, we cannot say that the boundary of the set of horocyclic deformations consists of one point.

However, according to Miyachi's results, we will see that it is the case if the given foliation is either a simple closed curve or a uniquely ergodic foliation.

It is well known that a point of the Teichmueller space and a measured foliation determine an isometric embedding of the hyperbolic disc to the Teichmueller space equipped with the so-called Teichmueller metric. In this talk, we will consider the image by this embedding of a particular horocycle whose points will be called an horocyclic deformation. To be more precise, we will be interested in the closure of this subset in the Gardiner-Masur compactification. As the embedding of the disc does not admit a continuous extension to boundaries, we cannot say that the boundary of the set of horocyclic deformations consists of one point.

However, according to Miyachi's results, we will see that it is the case if the given foliation is either a simple closed curve or a uniquely ergodic foliation.

#### Lie Groups and Representation Theory

17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

On g,K-modules over arbitrary fields and applications to special values of L-functions

**Fabian Januszewski**(Karlsruhe Institute of Technology)On g,K-modules over arbitrary fields and applications to special values of L-functions

[ Abstract ]

I will introduce g,K-modules over arbitrary fields of characteristic 0 and discuss their fundamental properties and constructions, including Zuckerman functors. This may be applied to produce models of certain standard modules over number fields, which has applications to special values of automorphic L-functions, and also furnishes the space of regular algebraic cusp forms of GL(n) with a natural global Q-structure.

I will introduce g,K-modules over arbitrary fields of characteristic 0 and discuss their fundamental properties and constructions, including Zuckerman functors. This may be applied to produce models of certain standard modules over number fields, which has applications to special values of automorphic L-functions, and also furnishes the space of regular algebraic cusp forms of GL(n) with a natural global Q-structure.

### 2015/07/27

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Convergence of Brownian motions on RCD*(K,N) spaces

**Kohei Suzuki**(Graduate School of Science, Kyoto University)Convergence of Brownian motions on RCD*(K,N) spaces

### 2015/07/24

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Applications of Boltzmann's S=k log W in algebra and analysis

**Mikael Pichot**(McGill Univ.)Applications of Boltzmann's S=k log W in algebra and analysis

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

High-dimensional metric-measure limit of Stiefel manifolds (Japanese)

**Asuka Takatsu**(Tokyo Metropolitan University)High-dimensional metric-measure limit of Stiefel manifolds (Japanese)

[ Abstract ]

A metric measure space is the triple of a complete separable metric space with a Borel measure on this space. Gromov defined a concept of convergence of metric measure spaces by the convergence of the sets of 1-Lipschitz functions on the spaces. We study and specify the high-dimensional limit of Stiefel manifolds in the sense of this convergence; the limit is the infinite-dimensional Gaussian space, which is drastically different from the manifolds. This is a joint work with Takashi SHIOYA (Tohoku univ).

A metric measure space is the triple of a complete separable metric space with a Borel measure on this space. Gromov defined a concept of convergence of metric measure spaces by the convergence of the sets of 1-Lipschitz functions on the spaces. We study and specify the high-dimensional limit of Stiefel manifolds in the sense of this convergence; the limit is the infinite-dimensional Gaussian space, which is drastically different from the manifolds. This is a joint work with Takashi SHIOYA (Tohoku univ).

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