## Seminar information archive

Seminar information archive ～02/06｜Today's seminar 02/07 | Future seminars 02/08～

#### GCOE Seminars

14:30-15:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Wave Transport in Random Media and Inverse Problems (ENGLISH)

**Manabu Machida**(University of Michigan)Wave Transport in Random Media and Inverse Problems (ENGLISH)

[ Abstract ]

Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.

Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.

### 2011/12/26

#### Algebraic Geometry Seminar

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

Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces (JAPANESE)

**Takuzo Okada**(Kyoto University)Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces (JAPANESE)

[ Abstract ]

It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.

It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.

### 2011/12/21

#### Number Theory Seminar

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

On Sharifi's conjecture (JAPANESE)

**Kazuya Kato**(University of Chicago)On Sharifi's conjecture (JAPANESE)

### 2011/12/20

#### Tuesday Seminar of Analysis

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

A trace formula for the perturbed Landau Hamiltonian (ENGLISH)

**Gueorgui Raykov**(Catholic University of Chile)A trace formula for the perturbed Landau Hamiltonian (ENGLISH)

[ Abstract ]

The talk will be based on a joint work with A. Pushnitski

and C. Villegas-Blas, the preprint is available here:

http://arxiv.org/abs/1110.3098 .

The talk will be based on a joint work with A. Pushnitski

and C. Villegas-Blas, the preprint is available here:

http://arxiv.org/abs/1110.3098 .

#### Tuesday Seminar on Topology

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

Leafwise symplectic structures on Lawson's Foliation on the 5-sphere (JAPANESE)

**Yoshihiko Mitsumatsu**(Chuo University)Leafwise symplectic structures on Lawson's Foliation on the 5-sphere (JAPANESE)

[ Abstract ]

We are going to show that Lawson's foliation on the 5-sphere

admits a smooth leafwise symplectic sturcture. Historically, Lawson's

foliation is the first one among foliations of codimension one which are

constructed on the 5-sphere. It is obtained by modifying the Milnor

fibration associated with the Fermat type cubic polynominal in three

variables.

Alberto Verjovsky proposed a question whether if the Lawson's

foliation or slighty modified ones admit a leafwise smooth symplectic

structure and/or a leafwise complex structure. As Lawson's one has a

Kodaira-Thurston nil 4-manifold as a compact leaf, the question can not

be solved simultaneously both for the symplectic and the complex cases.

The main part of the construction is to show that the Fermat type

cubic surface admits an `end-periodic' symplectic structure, while the

natural one as an affine surface is conic at the end. Even though for

the other two families of the simple elliptic hypersurface singularities

almost the same construction works, at present, it seems very limited

where a Stein manifold admits an end-periodic symplectic structure. If

the time allows, we also discuss the existence of such structures on

globally convex symplectic manifolds.

We are going to show that Lawson's foliation on the 5-sphere

admits a smooth leafwise symplectic sturcture. Historically, Lawson's

foliation is the first one among foliations of codimension one which are

constructed on the 5-sphere. It is obtained by modifying the Milnor

fibration associated with the Fermat type cubic polynominal in three

variables.

Alberto Verjovsky proposed a question whether if the Lawson's

foliation or slighty modified ones admit a leafwise smooth symplectic

structure and/or a leafwise complex structure. As Lawson's one has a

Kodaira-Thurston nil 4-manifold as a compact leaf, the question can not

be solved simultaneously both for the symplectic and the complex cases.

The main part of the construction is to show that the Fermat type

cubic surface admits an `end-periodic' symplectic structure, while the

natural one as an affine surface is conic at the end. Even though for

the other two families of the simple elliptic hypersurface singularities

almost the same construction works, at present, it seems very limited

where a Stein manifold admits an end-periodic symplectic structure. If

the time allows, we also discuss the existence of such structures on

globally convex symplectic manifolds.

### 2011/12/19

#### Number Theory Seminar

16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Galois Theory: Past and Present (ENGLISH)

**Tamas Szamuely**(Budapest)Galois Theory: Past and Present (ENGLISH)

### 2011/12/17

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On the finite order Q-rational points on J_1 (N) (JAPANESE)

) 15:00-16:00

On the affineness of distinguished Deligne-Lusztig varieties (JAPANESE)

**Masami Ohta**(Professor Emeritus of Tokai Univeristy) 13:30-14:30On the finite order Q-rational points on J_1 (N) (JAPANESE)

**Shushi Harashita**(Yokohama National University) 15:00-16:00

On the affineness of distinguished Deligne-Lusztig varieties (JAPANESE)

### 2011/12/16

#### Colloquium

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Application of positive characteristic methods to singularity theory (JAPANESE)

**TAKAGI, Shunsuke**(Graduate School of Mathematical Sciences, University of Tokyo)Application of positive characteristic methods to singularity theory (JAPANESE)

[ Abstract ]

As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.

As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.

### 2011/12/14

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Good and bad reduction for algebraic dynamical systems (ENGLISH)

**Lucien Szpiro**(City University of New York)Good and bad reduction for algebraic dynamical systems (ENGLISH)

[ Abstract ]

We will report on a recent work with collaborators in New York on the

different ways to look at degenerations of a dynamical system in a one

parameter family. Resultants, conductors and isotriviality will be analyzed.

We will report on a recent work with collaborators in New York on the

different ways to look at degenerations of a dynamical system in a one

parameter family. Resultants, conductors and isotriviality will be analyzed.

### 2011/12/13

#### Tuesday Seminar of Analysis

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

Trivializable subriemannian structures and spectral analysis of associated operators (ENGLISH)

**Wolfram Bauer**(Mathematisches Institut, Georg-August-Universität)Trivializable subriemannian structures and spectral analysis of associated operators (ENGLISH)

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)

**Hung Yean Loke**(National University of Singapore)Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)

[ Abstract ]

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.

We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.

We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)

**Hung Yean Loke**(National University of Singapore)Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)

[ Abstract ]

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.

We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.

We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

#### Tuesday Seminar on Topology

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

Remarks on filtrations of the singular homology of real varieties. (ENGLISH)

**Mircea Voineagu**(IPMU, The University of Tokyo)Remarks on filtrations of the singular homology of real varieties. (ENGLISH)

[ Abstract ]

We discuss various conjectures about filtrations on the singular homology of real and complex varieties. We prove that a conjecture relating niveau filtration on Borel-Moore homology of real varieties and the image of generalized cycle maps from reduced Lawson homology is false. In the end, we discuss a certain decomposition of Borel-Haeflinger cycle map. This is a joint work with J.Heller.

We discuss various conjectures about filtrations on the singular homology of real and complex varieties. We prove that a conjecture relating niveau filtration on Borel-Moore homology of real varieties and the image of generalized cycle maps from reduced Lawson homology is false. In the end, we discuss a certain decomposition of Borel-Haeflinger cycle map. This is a joint work with J.Heller.

### 2011/12/12

#### Seminar on Geometric Complex Analysis

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

Brody curves and mean dimension (JAPANESE)

**Shinichiroh MATSUO**(Kyoto University)Brody curves and mean dimension (JAPANESE)

[ Abstract ]

We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.

We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.

#### Algebraic Geometry Seminar

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

A version of Barth's theorem for singular varieties (cancelled) (JAPANESE)

**Robert Laterveer**(CNRS, IRMA, Université de Strasbourg)A version of Barth's theorem for singular varieties (cancelled) (JAPANESE)

### 2011/12/09

#### Lectures

10:40-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

An iterative construction of solutions of the TAP equation (ENGLISH)

**Erwin Bolthausen**(University of Zurich)An iterative construction of solutions of the TAP equation (ENGLISH)

[ Abstract ]

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

#### Lectures

10:40-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

An iterative construction of solutions of the TAP equation (ENGLISH)

**Erwin Bolthausen**(University of Zurich)An iterative construction of solutions of the TAP equation (ENGLISH)

[ Abstract ]

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

#### GCOE Seminars

11:40-12:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Eigenvalue order statistics and mass concentration in the parabolic Anderson model (ENGLISH)

**Wolfgang Koenig**(Weierstrass Institute Berlin)Eigenvalue order statistics and mass concentration in the parabolic Anderson model (ENGLISH)

[ Abstract ]

We consider the random Schr\\"odinger operator on the lattice with i.i.d. potential, which is double-exponentially distributed. In a large box, we look at the lowest eigenvalues, together with the location of the centering of the corresponding eigenfunction, and derive a Poisson process limit law, after suitable rescaling and shifting, towards an explicit Poisson point process. This is a strong form of Anderson localization at the bottom of the spectrum. Since the potential is unbounded, also the eigenvalues are, and it turns out that the gaps between them are much larger than of inverse volume order. We explain an application to concentration properties of the corresponding Cauchy problem, the parabolic Anderson model. In fact, it will turn out that the total mass of the solution comes from just one island, asymptotically for large times. This is joint work in progress with Marek Biskup (Los Angeles and Budweis).

We consider the random Schr\\"odinger operator on the lattice with i.i.d. potential, which is double-exponentially distributed. In a large box, we look at the lowest eigenvalues, together with the location of the centering of the corresponding eigenfunction, and derive a Poisson process limit law, after suitable rescaling and shifting, towards an explicit Poisson point process. This is a strong form of Anderson localization at the bottom of the spectrum. Since the potential is unbounded, also the eigenvalues are, and it turns out that the gaps between them are much larger than of inverse volume order. We explain an application to concentration properties of the corresponding Cauchy problem, the parabolic Anderson model. In fact, it will turn out that the total mass of the solution comes from just one island, asymptotically for large times. This is joint work in progress with Marek Biskup (Los Angeles and Budweis).

#### GCOE Seminars

14:00-14:50 Room #122 (Graduate School of Math. Sci. Bldg.)

Gradient Gibbs models with non-convex potentials (ENGLISH)

**Roman Kotecky**(Charles University Prague/University of Warwick)Gradient Gibbs models with non-convex potentials (ENGLISH)

[ Abstract ]

A motivation for gradient Gibbs measures in the study of macroscopic elasticity and in proving the Cauchy-Born rule will be explained. Results concerning strict convexity of the free energy will be formulated and discussed. Based on joint works with S. Adams and S. Mueller and with S. Luckhaus.

A motivation for gradient Gibbs measures in the study of macroscopic elasticity and in proving the Cauchy-Born rule will be explained. Results concerning strict convexity of the free energy will be formulated and discussed. Based on joint works with S. Adams and S. Mueller and with S. Luckhaus.

#### GCOE Seminars

15:00-15:50 Room #122 (Graduate School of Math. Sci. Bldg.)

Einstein relation and linear response for random walks in random environment (ENGLISH)

**Stefano Olla**(University Paris - Dauphine)Einstein relation and linear response for random walks in random environment (ENGLISH)

### 2011/12/08

#### Number Theory Seminar

18:30-19:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Nonabelian p-adic Hodge theory and Frobenius (ENGLISH)

**Gerd Faltings**(Max Planck Institute for Mathematics, Bonn)Nonabelian p-adic Hodge theory and Frobenius (ENGLISH)

[ Abstract ]

Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

### 2011/12/07

#### Lectures

16:00-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

"Inverse problems associated with linear and non-linear parabolic systems " (ENGLISH)

"Hautus test for the approximate controllability of linear systems" (ENGLISH)

**Michel Cristofol**(マルセイユ大学) 16:00-17:00"Inverse problems associated with linear and non-linear parabolic systems " (ENGLISH)

[ Abstract ]

In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.

In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.

**Guillaume Olive**(マルセイユ大学) 17:00-18:00"Hautus test for the approximate controllability of linear systems" (ENGLISH)

[ Abstract ]

We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.

We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.

### 2011/12/06

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Development of high order CFD solver for aerospace applications (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/saito/

**Kanako Yasue**(JAXA)Development of high order CFD solver for aerospace applications (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/saito/

### 2011/12/05

#### Algebraic Geometry Seminar

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

Obstructions to deforming curves on a uniruled 3-fold (JAPANESE)

**Hirokazu Nasu**(Tokai University)Obstructions to deforming curves on a uniruled 3-fold (JAPANESE)

[ Abstract ]

In this talk, I review some results from a joint work with Mukai:

1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and

2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.

As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.

In this talk, I review some results from a joint work with Mukai:

1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and

2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.

As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.

### 2011/12/01

#### Lectures

16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Stability of topological phases of matter (ENGLISH)

**Spyridon Michalakis**(Caltech)Stability of topological phases of matter (ENGLISH)

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