## Seminar information archive

Seminar information archive ～08/09｜Today's seminar 08/10 | Future seminars 08/11～

#### Operator Algebra Seminars

15:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Introduction to $C^*$-tensor categories

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to $C^*$-tensor categories

#### Tuesday Seminar on Topology

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Ricci-mean curvature flows in gradient shrinking Ricci solitons (JAPANESE)

**Hikaru Yamamoto**(The University of Tokyo)Ricci-mean curvature flows in gradient shrinking Ricci solitons (JAPANESE)

[ Abstract ]

A Ricci-mean curvature flow is a coupled parabolic PDE system of a mean

curvature flow and a Ricci flow.

In this talk, we consider a Ricci-mean curvature flow in a gradient

shrinking Ricci soliton, and give a generalization of a well-known result

of Huisken which states that if a mean curvature flow in a Euclidean space

develops a singularity of type I, then its parabolic rescaling near the singular

point converges to a self-shrinker.

A Ricci-mean curvature flow is a coupled parabolic PDE system of a mean

curvature flow and a Ricci flow.

In this talk, we consider a Ricci-mean curvature flow in a gradient

shrinking Ricci soliton, and give a generalization of a well-known result

of Huisken which states that if a mean curvature flow in a Euclidean space

develops a singularity of type I, then its parabolic rescaling near the singular

point converges to a self-shrinker.

#### PDE Real Analysis Seminar

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

Well-posedness and stability of the full Ericksen-Leslie system for incompressible nematic liquid crystal flows

**Hao Wu**(Fudan University)Well-posedness and stability of the full Ericksen-Leslie system for incompressible nematic liquid crystal flows

[ Abstract ]

In this talk, the general Ericksen-Leslie (E-L) system modelling the incompressible nematic liquid crystal flow will be discussed.

We shall prove the well-posedness and long-time behavior of the E-L system under proper assumptions on the viscous Leslie coefficients.

In particular, we shall discuss the connection between Parodi's relation and stability of the E-L system.

In this talk, the general Ericksen-Leslie (E-L) system modelling the incompressible nematic liquid crystal flow will be discussed.

We shall prove the well-posedness and long-time behavior of the E-L system under proper assumptions on the viscous Leslie coefficients.

In particular, we shall discuss the connection between Parodi's relation and stability of the E-L system.

### 2016/01/18

#### Seminar on Geometric Complex Analysis

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

Holomorphic motions and the monodromy (Japanese)

**Hiroshige Shiga**(Tokyo Institute of Technology)Holomorphic motions and the monodromy (Japanese)

[ Abstract ]

Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.

Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.

#### FMSP Lectures

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Functor categories and stable homology of groups (1) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (1) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSP Lectures

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

Functor categories and stable homology of groups (2) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (2) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### Operator Algebra Seminars

15:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Introduction to $C^*$-tensor categories (日本語)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to $C^*$-tensor categories (日本語)

#### Seminar on Probability and Statistics

13:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Fractional calculus and some applications to stochastic processes

**Enzo Orsingher**(Sapienza University of Rome)Fractional calculus and some applications to stochastic processes

[ Abstract ]

1) Riemann-Liouville fractional integrals and derivatives

2) integrals of derivatives and derivatives of integrals

3) Dzerbayshan-Caputo fractional derivatives

4) Marchaud derivative

5) Riesz potential and fractional derivatives

6) Hadamard derivatives and also Erdelyi-Kober derivatives

7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives

8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)

9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)

10) Time-fractional telegraph Poisson process

11) Space fractional Poisson process

13) Other fractional point processes (birth and death processes)

14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.

1) Riemann-Liouville fractional integrals and derivatives

2) integrals of derivatives and derivatives of integrals

3) Dzerbayshan-Caputo fractional derivatives

4) Marchaud derivative

5) Riesz potential and fractional derivatives

6) Hadamard derivatives and also Erdelyi-Kober derivatives

7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives

8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)

9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)

10) Time-fractional telegraph Poisson process

11) Space fractional Poisson process

13) Other fractional point processes (birth and death processes)

14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.

#### FMSP Lectures

14:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Blind deconvolution for human speech signals (ENGLISH)

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

**Samuli Siltanen**(University of Helsinki)Blind deconvolution for human speech signals (ENGLISH)

[ Abstract ]

The structure of vowel sounds in human speech can be divided into two independent components. One of them is the “excitation signal,” which is a kind of buzzing sound created by the vocal folds flapping against each other. The other is the “filtering effect” caused by resonances in the vocal tract, or the confined space formed by the mouth and throat. The Glottal Inverse Filtering (GIF) problem is to (algorithmically) divide a microphone recording of a vowel sound into its two components. This “blind deconvolution” type task is an ill-posed inverse problem. Good-quality GIF filtering is essential for computer-generated speech needed for example by disabled people (think Stephen Hawking). Also, GIF affects the quality of synthetic speech in automatic information announcements and car navigation systems. Accurate estimation of the voice source from recorded speech is known to be difficult with current glottal inverse filtering (GIF) techniques, especially in the case of high-pitch speech of female or child subjects. In order to tackle this problem, the present study uses two different solution methods for GIF: Bayesian inversion and alternating minimization. The first method takes advantage of the Markov chain Monte Carlo (MCMC) modeling in defining the parameters of the vocal tract inverse filter. The filtering results are found to be superior to those achieved by the standard iterative adaptive inverse filtering (IAIF), but the computation is much slower than IAIF. Alternating minimization cuts down the computation time while retaining most of the quality improvement.

[ Reference URL ]The structure of vowel sounds in human speech can be divided into two independent components. One of them is the “excitation signal,” which is a kind of buzzing sound created by the vocal folds flapping against each other. The other is the “filtering effect” caused by resonances in the vocal tract, or the confined space formed by the mouth and throat. The Glottal Inverse Filtering (GIF) problem is to (algorithmically) divide a microphone recording of a vowel sound into its two components. This “blind deconvolution” type task is an ill-posed inverse problem. Good-quality GIF filtering is essential for computer-generated speech needed for example by disabled people (think Stephen Hawking). Also, GIF affects the quality of synthetic speech in automatic information announcements and car navigation systems. Accurate estimation of the voice source from recorded speech is known to be difficult with current glottal inverse filtering (GIF) techniques, especially in the case of high-pitch speech of female or child subjects. In order to tackle this problem, the present study uses two different solution methods for GIF: Bayesian inversion and alternating minimization. The first method takes advantage of the Markov chain Monte Carlo (MCMC) modeling in defining the parameters of the vocal tract inverse filter. The filtering results are found to be superior to those achieved by the standard iterative adaptive inverse filtering (IAIF), but the computation is much slower than IAIF. Alternating minimization cuts down the computation time while retaining most of the quality improvement.

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

#### FMSP Lectures

14:45-15:25 Room #126 (Graduate School of Math. Sci. Bldg.)

Inverse scattering from random potential (ENGLISH)

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

**Tapio Helin**(University of Helsinki)Inverse scattering from random potential (ENGLISH)

[ Abstract ]

We consider an inverse scattering problem with a random potential. We assume that our far-field data at multiple angles and all frequencies are generated by a single realization of the potential. From the frequency-correlated data our aim is to demonstrate that one can recover statistical properties of the potential. More precisely, the potential is assumed to be Gaussian with a covariance operator that can be modelled by a classical pseudodifferential operator. Our main result is to show that the principal symbol of this

covariance operator can be determined uniquely. What is important, our method does not require any approximation and we can analyse also the multiple scattering. This is joint work with Matti Lassas and Pedro Caro.

[ Reference URL ]We consider an inverse scattering problem with a random potential. We assume that our far-field data at multiple angles and all frequencies are generated by a single realization of the potential. From the frequency-correlated data our aim is to demonstrate that one can recover statistical properties of the potential. More precisely, the potential is assumed to be Gaussian with a covariance operator that can be modelled by a classical pseudodifferential operator. Our main result is to show that the principal symbol of this

covariance operator can be determined uniquely. What is important, our method does not require any approximation and we can analyse also the multiple scattering. This is joint work with Matti Lassas and Pedro Caro.

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

#### FMSP Lectures

15:25-16:05 Room #126 (Graduate School of Math. Sci. Bldg.)

Geometric Whitney problem: Reconstruction of a manifold from a point cloud (ENGLISH)

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

**Matti Lassas**(University of Helsinki)Geometric Whitney problem: Reconstruction of a manifold from a point cloud (ENGLISH)

[ Abstract ]

We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold interpolation (or manifold learning) where a smooth $n$-dimensional surface $S¥subset {¥mathbb R}^m$, $m>n$ needs to be constructed to approximate a point cloud in ${¥mathbb R}^m$. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric.

We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary.

Moreover, we characterise the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius.

The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalisation of the Whitney embedding construction where approximative coordinate charts are embedded in ${¥mathbb R}^m$ and interpolated to a smooth surface. We also give algorithms that solve the problems for finite data.

The results are done in collaboration with C. Fefferman, S. Ivanov, Y. Kurylev, and H. Narayanan.

References:

[1] C. Fefferman, S. Ivanov, Y. Kurylev, M. Lassas, H. Narayanan: Reconstruction and interpolation of manifolds I: The geometric Whitney problem. ArXiv:1508.00674

[ Reference URL ]We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold interpolation (or manifold learning) where a smooth $n$-dimensional surface $S¥subset {¥mathbb R}^m$, $m>n$ needs to be constructed to approximate a point cloud in ${¥mathbb R}^m$. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric.

We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary.

Moreover, we characterise the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius.

The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalisation of the Whitney embedding construction where approximative coordinate charts are embedded in ${¥mathbb R}^m$ and interpolated to a smooth surface. We also give algorithms that solve the problems for finite data.

The results are done in collaboration with C. Fefferman, S. Ivanov, Y. Kurylev, and H. Narayanan.

References:

[1] C. Fefferman, S. Ivanov, Y. Kurylev, M. Lassas, H. Narayanan: Reconstruction and interpolation of manifolds I: The geometric Whitney problem. ArXiv:1508.00674

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

### 2016/01/15

#### Seminar on Probability and Statistics

13:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Fractional calculus and some applications to stochastic processes

**Enzo Orsingher**(Sapienza University of Rome)Fractional calculus and some applications to stochastic processes

[ Abstract ]

1) Riemann-Liouville fractional integrals and derivatives

2) integrals of derivatives and derivatives of integrals

3) Dzerbayshan-Caputo fractional derivatives

4) Marchaud derivative

5) Riesz potential and fractional derivatives

6) Hadamard derivatives and also Erdelyi-Kober derivatives

7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives

8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)

9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)

10) Time-fractional telegraph Poisson process

11) Space fractional Poisson process

13) Other fractional point processes (birth and death processes)

14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.

1) Riemann-Liouville fractional integrals and derivatives

2) integrals of derivatives and derivatives of integrals

3) Dzerbayshan-Caputo fractional derivatives

4) Marchaud derivative

5) Riesz potential and fractional derivatives

6) Hadamard derivatives and also Erdelyi-Kober derivatives

7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives

8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)

9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)

10) Time-fractional telegraph Poisson process

11) Space fractional Poisson process

13) Other fractional point processes (birth and death processes)

14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.

### 2016/01/13

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

A Stabilization Theorem for Fell Bundles over Groupoids

**Alexander Kumjian**(Univ. Nevada, Reno)A Stabilization Theorem for Fell Bundles over Groupoids

#### FMSP Lectures

16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

A Carleman estimate for an elliptic operator in a partially anisotropic and discontinuous media (ENGLISH)

[ Reference URL ]

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

**Yves Dermenjian**(Aix-Marseille Universite)A Carleman estimate for an elliptic operator in a partially anisotropic and discontinuous media (ENGLISH)

[ Reference URL ]

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

### 2016/01/12

#### Tuesday Seminar on Topology

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

Heavy subsets and non-contractible trajectories (JAPANESE)

On codimension two contact embeddings in the standard spheres (JAPANESE)

**Morimichi Kawasaki**(The University of Tokyo) 16:30-17:30Heavy subsets and non-contractible trajectories (JAPANESE)

[ Abstract ]

For a compact set Y of an open symplectic manifold $(N,¥omega)$ and a free

homotopy class $¥alpha¥in [S^1,N]$, Biran, Polterovich and Salamon

defined the relative symplectic capacity $C_{BPS}(N,Y;¥alpha)$ which

measures the existence of non-contractible 1-periodic trajectories of

Hamiltonian isotopies.

On the hand, Entov and Polterovich defined heaviness for closed subsets

of a symplectic manifold by using spectral invarinats of the Hamiltonian

Floer theory on contractible trajectories.

Heavy subsets are known to be non-displaceable.

In this talk, we prove the finiteness of $C(M,X,¥alpha)$ (i.e. the

existence of non-contractible 1-periodic trajectories under some setting)

by using heaviness.

For a compact set Y of an open symplectic manifold $(N,¥omega)$ and a free

homotopy class $¥alpha¥in [S^1,N]$, Biran, Polterovich and Salamon

defined the relative symplectic capacity $C_{BPS}(N,Y;¥alpha)$ which

measures the existence of non-contractible 1-periodic trajectories of

Hamiltonian isotopies.

On the hand, Entov and Polterovich defined heaviness for closed subsets

of a symplectic manifold by using spectral invarinats of the Hamiltonian

Floer theory on contractible trajectories.

Heavy subsets are known to be non-displaceable.

In this talk, we prove the finiteness of $C(M,X,¥alpha)$ (i.e. the

existence of non-contractible 1-periodic trajectories under some setting)

by using heaviness.

**Ryo Furukawa**(The University of Tokyo) 17:30-18:30On codimension two contact embeddings in the standard spheres (JAPANESE)

[ Abstract ]

In this talk we consider codimension two contact

embedding problem by using higher dimensional braids.

First, we focus on embeddings of contact $3$-manifolds to the standard $

S^5$ and give some results, for example, any contact structure on $S^3$

can embed so that it is smoothly isotopic to the standard embedding.

These are joint work with John Etnyre. Second, we consider the relative

Euler number of codimension two contact submanifolds and its Seifert

hypersurfaces which is a generalization of the self-linking number of

transverse knots in contact $3$-manifolds. We give a way to calculate

the relative Euler number of certain contact submanifolds obtained by

braids and as an application we give examples of embeddings of one

contact manifold which are isotopic as smooth embeddings but not

isotopic as contact embeddings in higher dimension.

In this talk we consider codimension two contact

embedding problem by using higher dimensional braids.

First, we focus on embeddings of contact $3$-manifolds to the standard $

S^5$ and give some results, for example, any contact structure on $S^3$

can embed so that it is smoothly isotopic to the standard embedding.

These are joint work with John Etnyre. Second, we consider the relative

Euler number of codimension two contact submanifolds and its Seifert

hypersurfaces which is a generalization of the self-linking number of

transverse knots in contact $3$-manifolds. We give a way to calculate

the relative Euler number of certain contact submanifolds obtained by

braids and as an application we give examples of embeddings of one

contact manifold which are isotopic as smooth embeddings but not

isotopic as contact embeddings in higher dimension.

### 2016/01/09

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The n linear embedding theorem

(日本語)

An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain

(日本語)

**Hitoshi Tanaka**(Tokyo University) 13:30-15:00The n linear embedding theorem

(日本語)

**Kentaro Hirata**(Hiroshima University) 15:30-17:00An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain

(日本語)

### 2016/01/08

#### Colloquium

16:50-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)

Birational geometry through complex dymanics (ENGLISH)

**Keiji Oguiso**(Graduate School of Mathematical Sciences, University of Tokyo)Birational geometry through complex dymanics (ENGLISH)

[ Abstract ]

Birational geometry and complex dymanics are rich subjects having

interactions with many branches of mathematics. On the other hand,

though these two subjects share many common interests hidden especially

when one considers group symmetry of manifolds, it seems rather recent

that their rich interations are really notified, perhaps after breaking

through works for surface automorphisms in the view of topological

entropy by Cantat and McMullen early in this century, by which I was so

mpressed.

The notion of entropy of automorphism is a fundamental invariant which

measures how fast two general points spread out fast under iteration. So,

the exisitence of surface automorphism of positive entropy with Siegel

disk due to McMullen was quite surprizing. The entropy also measures, by

the fundamenal theorem of Gromov-Yomdin, the

logarithmic growth of the degree of polarization under iteration. For

instance, the Mordell-Weil group of an elliptic fibration is a very

intersting rich subject in algebraic geometry and number theory, but the

group preserves the fibration so that it might not be so interesting

from dynamical view point. However, if the surface admits two different

elliptic fibrations, which often happens in K3 surfaces of higher Picard

number, then highly non-commutative dynamically rich phenomena can be

observed.

In this talk, I would like to explain the above mentioned phenomena with

a few unexpected applications that I noticed in these years:

(1) Kodaira problem on small deformation of compact Kaehler manifolds in

higher dimension via K3 surface automorphism with Siegel disk;

(2) Geometric liftability problem of automorphisms in positive

characteristic to chacateristic 0 via Mordell-Weil groups and number

theoretic aspect of entropy;

(3) Existence problem on primitive automorphisms of projective manifolds,

through (relative) dynamical degrees due to Dinh-Sibony, Dinh-Nguyen-

Troung, a powerful refinement of the notion of entropy, with by-product

for Ueno-Campana's problem on (uni)rationality of manifolds of torus

quotient.

Birational geometry and complex dymanics are rich subjects having

interactions with many branches of mathematics. On the other hand,

though these two subjects share many common interests hidden especially

when one considers group symmetry of manifolds, it seems rather recent

that their rich interations are really notified, perhaps after breaking

through works for surface automorphisms in the view of topological

entropy by Cantat and McMullen early in this century, by which I was so

mpressed.

The notion of entropy of automorphism is a fundamental invariant which

measures how fast two general points spread out fast under iteration. So,

the exisitence of surface automorphism of positive entropy with Siegel

disk due to McMullen was quite surprizing. The entropy also measures, by

the fundamenal theorem of Gromov-Yomdin, the

logarithmic growth of the degree of polarization under iteration. For

instance, the Mordell-Weil group of an elliptic fibration is a very

intersting rich subject in algebraic geometry and number theory, but the

group preserves the fibration so that it might not be so interesting

from dynamical view point. However, if the surface admits two different

elliptic fibrations, which often happens in K3 surfaces of higher Picard

number, then highly non-commutative dynamically rich phenomena can be

observed.

In this talk, I would like to explain the above mentioned phenomena with

a few unexpected applications that I noticed in these years:

(1) Kodaira problem on small deformation of compact Kaehler manifolds in

higher dimension via K3 surface automorphism with Siegel disk;

(2) Geometric liftability problem of automorphisms in positive

characteristic to chacateristic 0 via Mordell-Weil groups and number

theoretic aspect of entropy;

(3) Existence problem on primitive automorphisms of projective manifolds,

through (relative) dynamical degrees due to Dinh-Sibony, Dinh-Nguyen-

Troung, a powerful refinement of the notion of entropy, with by-product

for Ueno-Campana's problem on (uni)rationality of manifolds of torus

quotient.

### 2016/01/06

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Quantum channels from the free orthogonal quantum group (English)

**Benoit Collins**(Kyoto Univ.)Quantum channels from the free orthogonal quantum group (English)

### 2016/01/05

#### Tuesday Seminar of Analysis

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

Stationary scattering theory on manifolds (English)

**Eric Skibsted**(Aarhus University, Denmark)Stationary scattering theory on manifolds (English)

[ Abstract ]

We present a stationary scattering theory for the Schrödinger operator on Riemannian manifolds with the structure of ends each of which is equipped with an escape function (for example a convex distance function). This includes manifolds with ends modeled as cone-like subsets of the Euclidean space and/or the hyperbolic space. Our results include Rellich’s theorem, the limiting absorption principle, radiation condition bounds, the Sommerfeld uniqueness result, and we give complete characterization/asymptotics of the generalized eigenfunctions in a certain Besov space and show asymptotic completeness (with K. Ito).

We present a stationary scattering theory for the Schrödinger operator on Riemannian manifolds with the structure of ends each of which is equipped with an escape function (for example a convex distance function). This includes manifolds with ends modeled as cone-like subsets of the Euclidean space and/or the hyperbolic space. Our results include Rellich’s theorem, the limiting absorption principle, radiation condition bounds, the Sommerfeld uniqueness result, and we give complete characterization/asymptotics of the generalized eigenfunctions in a certain Besov space and show asymptotic completeness (with K. Ito).

### 2015/12/21

#### Tokyo Probability Seminar

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

Scaling limits of random walks on trees (English)

**David Croydon**(University of Warwick)Scaling limits of random walks on trees (English)

[ Abstract ]

I will survey some recent work regarding the scaling limits of random walks on trees, as well as the scaling of the associated local times and cover time. The trees considered will include self-similar pre-fractal graphs, critical Galton-Watson trees and the uniform spanning tree in two dimensions.

I will survey some recent work regarding the scaling limits of random walks on trees, as well as the scaling of the associated local times and cover time. The trees considered will include self-similar pre-fractal graphs, critical Galton-Watson trees and the uniform spanning tree in two dimensions.

#### Seminar on Geometric Complex Analysis

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

On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties

(Japanese)

**Katsutoshi Yamanoi**(Osaka Univ.)On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties

(Japanese)

[ Abstract ]

A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.

A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.

### 2015/12/17

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Polarization and stability on a derived equivalent abelian variety (English)

http://db.ipmu.jp/member/personal/3989en.html

**Dulip Piyaratne**(IPMU)Polarization and stability on a derived equivalent abelian variety (English)

[ Abstract ]

In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.

[ Reference URL ]In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.

http://db.ipmu.jp/member/personal/3989en.html

### 2015/12/16

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Nuclearity in AQFT and related results

**Yul Otani**(Univ. Tokyo)Nuclearity in AQFT and related results

#### thesis presentations

10:30-11:45 Room #122 (Graduate School of Math. Sci. Bldg.)

Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)

**山本 光**(東京大学大学院数理科学研究科)Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)

#### FMSP Lectures

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

Selected topics in fractional partial differential equations (ENGLISH)

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

**Yuri Luchko**(University of Applied Sciences, Berlin)Selected topics in fractional partial differential equations (ENGLISH)

[ Abstract ]

In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.

[ Reference URL ]In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.

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

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