## Seminar information archive

Seminar information archive ～10/03｜Today's seminar 10/04 | Future seminars 10/05～

### 2013/12/17

#### Tuesday Seminar on Topology

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

Satellites of an oriented surface link and their local moves (JAPANESE)

**Inasa Nakamura**(The University of Tokyo)Satellites of an oriented surface link and their local moves (JAPANESE)

[ Abstract ]

For an oriented surface link $F$ in $\\mathbb{R}^4$,

we consider a satellite construction of a surface link, called a

2-dimensional braid over $F$, which is in the form of a covering over

$F$. We introduce the notion of an $m$-chart on a surface diagram

$p(F)\\subset \\mathbb{R}^3$ of $F$, which is a finite graph on $p(F)$

satisfying certain conditions and is an extended notion of an

$m$-chart on a 2-disk presenting a surface braid.

A 2-dimensional braid over $F$ is presented by an $m$-chart on $p(F)$.

It is known that two surface links are equivalent if and only if their

surface diagrams are related by a finite sequence of ambient isotopies

of $\\mathbb{R}^3$ and local moves called Roseman moves.

We show that Roseman moves for surface diagrams with $m$-charts can be

well-defined. Further, we give some applications.

For an oriented surface link $F$ in $\\mathbb{R}^4$,

we consider a satellite construction of a surface link, called a

2-dimensional braid over $F$, which is in the form of a covering over

$F$. We introduce the notion of an $m$-chart on a surface diagram

$p(F)\\subset \\mathbb{R}^3$ of $F$, which is a finite graph on $p(F)$

satisfying certain conditions and is an extended notion of an

$m$-chart on a 2-disk presenting a surface braid.

A 2-dimensional braid over $F$ is presented by an $m$-chart on $p(F)$.

It is known that two surface links are equivalent if and only if their

surface diagrams are related by a finite sequence of ambient isotopies

of $\\mathbb{R}^3$ and local moves called Roseman moves.

We show that Roseman moves for surface diagrams with $m$-charts can be

well-defined. Further, we give some applications.

#### Tuesday Seminar of Analysis

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

Dispersion and observability for completely integrable Schrödinger flows (ENGLISH)

**Fabricio Macia**(Universidad Politécnica de Madrid)Dispersion and observability for completely integrable Schrödinger flows (ENGLISH)

[ Abstract ]

I will present some results on weak dispersion and unique continuation (observability) for linear Schrödinger

equations that are obtained as the quantization of a completely integrable Hamiltonian system.

The model case corresponds to the linear Schrödinger equation (with a potential) on the flat torus.

Our results are obtained through a detailed analysis of semiclassical measures corresponding to

sequences of solutions, which is performed using a two-microlocal approach.

This is a joint work with Nalini Anantharaman and Clotilde Fermanian-Kammerer.

I will present some results on weak dispersion and unique continuation (observability) for linear Schrödinger

equations that are obtained as the quantization of a completely integrable Hamiltonian system.

The model case corresponds to the linear Schrödinger equation (with a potential) on the flat torus.

Our results are obtained through a detailed analysis of semiclassical measures corresponding to

sequences of solutions, which is performed using a two-microlocal approach.

This is a joint work with Nalini Anantharaman and Clotilde Fermanian-Kammerer.

#### Lie Groups and Representation Theory

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

A characterization of the $L^{2}$-range of the

Poisson transform on symmetric spaces of noncompact type (JAPANESE)

**Koichi Kaizuka**(University of Tsukuba)A characterization of the $L^{2}$-range of the

Poisson transform on symmetric spaces of noncompact type (JAPANESE)

[ Abstract ]

Characterizations of the joint eigenspaces of invariant

differential operators in terms of the Poisson transform have been one of the central problems in harmonic analysis on symmetric spaces.

From the point of view of spectral theory, Strichartz (J. Funct.

Anal.(1989)) formulated a conjecture concerning a certain image

characterization of the Poisson transform of the $L^{2}$-space on the boundary on symmetric spaces of noncompact type. In this talk, we employ techniques in scattering theory to present a positive answer to the Strichartz conjecture.

Characterizations of the joint eigenspaces of invariant

differential operators in terms of the Poisson transform have been one of the central problems in harmonic analysis on symmetric spaces.

From the point of view of spectral theory, Strichartz (J. Funct.

Anal.(1989)) formulated a conjecture concerning a certain image

characterization of the Poisson transform of the $L^{2}$-space on the boundary on symmetric spaces of noncompact type. In this talk, we employ techniques in scattering theory to present a positive answer to the Strichartz conjecture.

### 2013/12/16

#### FMSP Lectures

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

The discrete Schrodinger equation for compact support potentials (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_%20NIMMO.pdf

**Jon Nimmo**(Univ. of Glasgow)The discrete Schrodinger equation for compact support potentials (ENGLISH)

[ Abstract ]

We consider the exact form of the Jost solutions of the discrete Schrodinger equation for arbitrary potentials with compact support. Remarkably, these solutions may be written in terms of certain explicitly defined polynomials in the non-trivial values of the potential. These polynomials also arise in the work of Yamada (2000) in connection with a birational representation of the symmetric group.

Applications of this approach to the udKdV are also discussed.

[ Reference URL ]We consider the exact form of the Jost solutions of the discrete Schrodinger equation for arbitrary potentials with compact support. Remarkably, these solutions may be written in terms of certain explicitly defined polynomials in the non-trivial values of the potential. These polynomials also arise in the work of Yamada (2000) in connection with a birational representation of the symmetric group.

Applications of this approach to the udKdV are also discussed.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_%20NIMMO.pdf

#### Seminar on Geometric Complex Analysis

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

Shilov boundaries of the pluricomplex Green function's level sets (JAPANESE)

**Yusaku Tiba**(Tokyo Institute of Technology)Shilov boundaries of the pluricomplex Green function's level sets (JAPANESE)

[ Abstract ]

In this talk, we study a relation between the Shilov boundaries of the pluricomplex Green function's level sets and supports of Monge-Ampére type currents.

In this talk, we study a relation between the Shilov boundaries of the pluricomplex Green function's level sets and supports of Monge-Ampére type currents.

### 2013/12/12

#### Applied Analysis

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

A theoretical study on the spontaneous radiation of atmospheric gravity waves using the renormalization group method (JAPANESE)

**Yuki Yasuda**(University of Tokyo (Department of Earth and Planetary Science))A theoretical study on the spontaneous radiation of atmospheric gravity waves using the renormalization group method (JAPANESE)

### 2013/12/10

#### FMSP Lectures

13:00-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

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

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

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

Corks, plugs, and local moves of 4-manifolds. (JAPANESE)

**Motoo Tange**(University of Tsukuba)Corks, plugs, and local moves of 4-manifolds. (JAPANESE)

[ Abstract ]

Akbulut and Yasui defined cork, and plug

to produce many exotic pairs.

In this talk, we introduce a plug

with respect to Fintushel-Stern's knot surgery

or more 4-dimensional local moves and

and argue by using Heegaard Fleor theory.

Akbulut and Yasui defined cork, and plug

to produce many exotic pairs.

In this talk, we introduce a plug

with respect to Fintushel-Stern's knot surgery

or more 4-dimensional local moves and

and argue by using Heegaard Fleor theory.

#### Tuesday Seminar of Analysis

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

Quantitative unique continuation principle, local behavior of solutions, and bounds on the density of states for Schr\\"odinger operators (ENGLISH)

**Abel Klein**(UC Irvine)Quantitative unique continuation principle, local behavior of solutions, and bounds on the density of states for Schr\\"odinger operators (ENGLISH)

[ Abstract ]

We establish bounds on the density of states measure for Schr\\"odinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a ``density of states outer-measure'' that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-H\\"older continuity for this density of states outer-measure in one, two, and three dimensions for Schr\\"odinger operators, and in any dimension for discrete Schr\\"odinger operators. Our proofs use a quantitative unique continuation principle and the local behavior of approximate solutions of the stationary Schr\\"odinger equation.

(Joint work with Jean Bourgain.)

References: Jean Bourgain and Abel Klein: Bounds on the density of states for Schr\\"odinger operators. Invent. Math. 194, 41-72 (2013).

We establish bounds on the density of states measure for Schr\\"odinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a ``density of states outer-measure'' that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-H\\"older continuity for this density of states outer-measure in one, two, and three dimensions for Schr\\"odinger operators, and in any dimension for discrete Schr\\"odinger operators. Our proofs use a quantitative unique continuation principle and the local behavior of approximate solutions of the stationary Schr\\"odinger equation.

(Joint work with Jean Bourgain.)

References: Jean Bourgain and Abel Klein: Bounds on the density of states for Schr\\"odinger operators. Invent. Math. 194, 41-72 (2013).

### 2013/12/09

#### Seminar on Geometric Complex Analysis

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

Donaldson-Tian-Yau 予想と K-安定性について (JAPANESE)

**Toshiki Mabuchi**(Osaka University)Donaldson-Tian-Yau 予想と K-安定性について (JAPANESE)

#### Algebraic Geometry Seminar

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

On birationally tririgid Q-Fano threefolds (JAPANESE)

**Takuzo Okada**(Saga University)On birationally tririgid Q-Fano threefolds (JAPANESE)

[ Abstract ]

I will talk about birational geometry of Q-Fano threefolds. A Mori

fiber space birational to a given Q-Fano threefold is called a birational Mori fiber structure of the threefold. The existence of Q-Fano threefolds with a unique birational Mori fiber structure (resp. with two birational Mori fiber structures) is known. In this talk I will give an example of Q-Fano threefolds with three birational Mori fiber structures and also discuss about the behavior of birational Mori fiber structures in a family.

I will talk about birational geometry of Q-Fano threefolds. A Mori

fiber space birational to a given Q-Fano threefold is called a birational Mori fiber structure of the threefold. The existence of Q-Fano threefolds with a unique birational Mori fiber structure (resp. with two birational Mori fiber structures) is known. In this talk I will give an example of Q-Fano threefolds with three birational Mori fiber structures and also discuss about the behavior of birational Mori fiber structures in a family.

### 2013/12/06

#### Geometry Colloquium

17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Normalized entropy versus volume for pseudo-Anosovs (JAPANESE)

**Sadayoshi KOJIMA**(Tokyo Institute of Technology)Normalized entropy versus volume for pseudo-Anosovs (JAPANESE)

[ Abstract ]

We establish an explicit linear inequality between the normalized entropy of pseudo-Anosov automorphisms and the hyperbolic volume of their mapping tori, based on a recent result by Jean-Marc Schlenker on renormalized volume of quasi-Fuchsian

manifolds. This is a joint work with Greg McShane.

We establish an explicit linear inequality between the normalized entropy of pseudo-Anosov automorphisms and the hyperbolic volume of their mapping tori, based on a recent result by Jean-Marc Schlenker on renormalized volume of quasi-Fuchsian

manifolds. This is a joint work with Greg McShane.

#### FMSP Lectures

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Horospheres: geometry and analysis (II) (ENGLISH)

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

**Simon Gindikin**(Rutgers University)Horospheres: geometry and analysis (II) (ENGLISH)

[ Abstract ]

About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

[ Reference URL ]About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

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

#### Colloquium

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

Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

**Naoki Imai**(Graduate School of Mathematical Scinences, The University of Tokyo)Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

#### Colloquium

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

Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

**Naoki Imai**(Graduate School of Mathematical Sciences, The University of Tokyo)Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

### 2013/12/05

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Variational characterizations of exact solutions of the Einstein equation (JAPANESE)

**Sumio Yamada**(Gakushuin University)Variational characterizations of exact solutions of the Einstein equation (JAPANESE)

[ Abstract ]

There are a set of well-known exact solutions to the Einstein equation. The most important one is the Schwarzschild metric, and it models a Ricci-flat space-time, which is asymptotically flat. In addition, there are the Reissner-Nordstrom metric and the Majumdar-Papapetrou metric, which satisfy the Einstein-Maxwell equation, instead of the vacuum Einstein equation. In a jointwork with Marcus Khuri and Gilbert Weinstein, it is shown that those metrics are characterized as the equality

cases of a set of so-called Penrose-type inequalities. The method of proof is a

conformal deformation of Riemannian metrics defined on the space-like slice of the space-time.

There are a set of well-known exact solutions to the Einstein equation. The most important one is the Schwarzschild metric, and it models a Ricci-flat space-time, which is asymptotically flat. In addition, there are the Reissner-Nordstrom metric and the Majumdar-Papapetrou metric, which satisfy the Einstein-Maxwell equation, instead of the vacuum Einstein equation. In a jointwork with Marcus Khuri and Gilbert Weinstein, it is shown that those metrics are characterized as the equality

cases of a set of so-called Penrose-type inequalities. The method of proof is a

conformal deformation of Riemannian metrics defined on the space-like slice of the space-time.

### 2013/12/04

#### Seminar on Probability and Statistics

13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)

A quantile-based likelihood estimator for information theoretic clustering (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/09.html

**HINO, Hideitsu**(University of Tsukuba)A quantile-based likelihood estimator for information theoretic clustering (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/09.html

#### FMSP Lectures

15:00-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Horospheres: geometry and analysis (I) (ENGLISH)

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

**Simon Gindikin**(Rutgers University)Horospheres: geometry and analysis (I) (ENGLISH)

[ Abstract ]

About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

[ Reference URL ]About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

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

### 2013/12/03

#### Tuesday Seminar on Topology

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

Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)

**Bruno Martelli**(Univ. di Pisa)Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)

[ Abstract ]

(joint work with A. Kolpakov)

We introduce a simple algorithm which transforms every

four-dimensional cubulation into a cusped finite-volume hyperbolic

four-manifold. Combinatorially distinct cubulations give rise to

topologically distinct manifolds. Using this algorithm we construct

the first examples of finite-volume hyperbolic four-manifolds with one

cusp. More generally, we show that the number of k-cusped hyperbolic

four-manifolds with volume smaller than V grows like C^{V log V} for

any fixed k. As a corollary, we deduce that the 3-torus bounds

geometrically a hyperbolic manifold.

(joint work with A. Kolpakov)

We introduce a simple algorithm which transforms every

four-dimensional cubulation into a cusped finite-volume hyperbolic

four-manifold. Combinatorially distinct cubulations give rise to

topologically distinct manifolds. Using this algorithm we construct

the first examples of finite-volume hyperbolic four-manifolds with one

cusp. More generally, we show that the number of k-cusped hyperbolic

four-manifolds with volume smaller than V grows like C^{V log V} for

any fixed k. As a corollary, we deduce that the 3-torus bounds

geometrically a hyperbolic manifold.

#### FMSP Lectures

13:00-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

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

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

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

### 2013/12/02

#### Seminar on Geometric Complex Analysis

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

A smoothing property of the Bergman projection (ENGLISH)

**Anne-Katrin Herbig**(Nagoya University)A smoothing property of the Bergman projection (ENGLISH)

[ Abstract ]

Let $D$ be a bounded domain with smooth boundary in complex space of dimension $n$. Suppose its Bergman projection $B$ maps the Sobolev space of order $k$ continuously into the one of order $m$. Then the following smoothing result holds: the full Sobolev norm of $Bf$ of order $k$ is controlled by $L^2$-derivatives of $f$ taken along a single, distinguished direction (of order up to $m$). This talk is based on joint work with J. D. McNeal and E. J. Straube.

Let $D$ be a bounded domain with smooth boundary in complex space of dimension $n$. Suppose its Bergman projection $B$ maps the Sobolev space of order $k$ continuously into the one of order $m$. Then the following smoothing result holds: the full Sobolev norm of $Bf$ of order $k$ is controlled by $L^2$-derivatives of $f$ taken along a single, distinguished direction (of order up to $m$). This talk is based on joint work with J. D. McNeal and E. J. Straube.

### 2013/11/29

#### FMSP Lectures

10:40-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

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

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

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

#### FMSP Lectures

14:50-16:20 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

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

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

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

### 2013/11/28

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

The prescribed scalar curvature problem for metrics with unit total volume (JAPANESE)

**Shinichiroh MATSUO**(Osaka University)The prescribed scalar curvature problem for metrics with unit total volume (JAPANESE)

[ Abstract ]

In this talk I will talk about the modified Kazdan-Warner problem.

Kazdan and Warner in 1970's completely solved the prescribed scalar curvature problem. In particular, they proved that every function on a manifold with positive Yamabe invariant is the scalar curvature of some metric. Kobayashi in 1987 proposed the modified problem of finding metrics with prescribed scalar curvature and total volume 1. He proved that every function except positive constants on a manifold with positive Yamabe invariant is the scalar curvature of some metricwith total volume 1.

I have recently settled the remaining case. Applying Taubes tequniques to the scalar curvature equations, we can glue two Yamabe metrics to construct metrics with very large scalar curvature and unit total volume, and prove that every positive constant is the scalar curvature of some metric with total volume 1.

In this talk I will talk about the modified Kazdan-Warner problem.

Kazdan and Warner in 1970's completely solved the prescribed scalar curvature problem. In particular, they proved that every function on a manifold with positive Yamabe invariant is the scalar curvature of some metric. Kobayashi in 1987 proposed the modified problem of finding metrics with prescribed scalar curvature and total volume 1. He proved that every function except positive constants on a manifold with positive Yamabe invariant is the scalar curvature of some metricwith total volume 1.

I have recently settled the remaining case. Applying Taubes tequniques to the scalar curvature equations, we can glue two Yamabe metrics to construct metrics with very large scalar curvature and unit total volume, and prove that every positive constant is the scalar curvature of some metric with total volume 1.

#### GCOE Seminars

17:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Inverse problem for the Maxwell equations (ENGLISH)

**Oleg Emanouilov**(Colorado State Univ.)Inverse problem for the Maxwell equations (ENGLISH)

[ Abstract ]

We consider an analog of Caderon's problem for the system of Maxwell equations in a cylindrical domain.

Under some geometrical assumptions on domain we show that from the partial data one can recover the complete set of parameters.

We consider an analog of Caderon's problem for the system of Maxwell equations in a cylindrical domain.

Under some geometrical assumptions on domain we show that from the partial data one can recover the complete set of parameters.

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