## Seminar information archive

Seminar information archive ～05/23｜Today's seminar 05/24 | Future seminars 05/25～

### 2016/12/14

#### Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On vanishing cycles and duality, after A. Beilinson (English)

**Luc Illusie**(Université Paris-Sud)On vanishing cycles and duality, after A. Beilinson (English)

[ Abstract ]

It was proved by Gabber in the early 1980's that $R\Psi$ commutes with duality, and that R\Phi preserves perversity up to shift. It had been in the folklore since then that this last result was in fact a consequence of a finer one, namely the compatibility of $R\Phi$ with duality. In this talk I'll give a proof of this, using a method explained to me by A. Beilinson.

It was proved by Gabber in the early 1980's that $R\Psi$ commutes with duality, and that R\Phi preserves perversity up to shift. It had been in the folklore since then that this last result was in fact a consequence of a finer one, namely the compatibility of $R\Phi$ with duality. In this talk I'll give a proof of this, using a method explained to me by A. Beilinson.

### 2016/12/13

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Plane fields on 3-manifolds and asymptotic linking of the tangential incompressible flows (JAPANESE)

**Yoshihiko Mitsumatsu**(Chuo University)Plane fields on 3-manifolds and asymptotic linking of the tangential incompressible flows (JAPANESE)

[ Abstract ]

This is a report on a project in (a very slow) progress which aims to prove the tightness of contact structures associated with algebraic Anosov flows without using Bennequin's nor Gromov's results.

After introducing an interpretation of asymptotic linking pairing in terms of differential forms, we attach a subspaces of exact 2-forms to each plane field. We analyze this space in the case where the plane field is an algebraic Anosov foliation and explain what can be done using results from foliated cohomology and frameworks for secondary characteristic classes. We also show some explicit computations.

To close the talk, a quantization phenomenon which happens when a foliation is deformed into a contact structure is explained and we state some perspectives on applying the results on foliations to the tightness.

This is a report on a project in (a very slow) progress which aims to prove the tightness of contact structures associated with algebraic Anosov flows without using Bennequin's nor Gromov's results.

After introducing an interpretation of asymptotic linking pairing in terms of differential forms, we attach a subspaces of exact 2-forms to each plane field. We analyze this space in the case where the plane field is an algebraic Anosov foliation and explain what can be done using results from foliated cohomology and frameworks for secondary characteristic classes. We also show some explicit computations.

To close the talk, a quantization phenomenon which happens when a foliation is deformed into a contact structure is explained and we state some perspectives on applying the results on foliations to the tightness.

#### Tuesday Seminar of Analysis

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

Distribution of eigenfunction mass on some really simple domains (English)

**Hans Christianson**(North Carolina State University)Distribution of eigenfunction mass on some really simple domains (English)

[ Abstract ]

Eigenfunctions are fundamental objects of study in spectral geometry and quantum chaos. On a domain or manifold, they determine the behaviour of solutions to many evolution type equations using, for example, separation of variables. Eigenfunctions are very sensitive to background geometry, so it is important to understand what the eigenfunctions look like: where are they large and where are they small? There are many different ways to measure what "large" and "small" mean. One can consider local $L^2$ distribution, local and global $L^p$ distribution, as well as restrictions and boundary values. I will give an overview of what is known, and then discuss some very recent works in progress demonstrating that complicated things can happen even in very simple geometric settings.

Eigenfunctions are fundamental objects of study in spectral geometry and quantum chaos. On a domain or manifold, they determine the behaviour of solutions to many evolution type equations using, for example, separation of variables. Eigenfunctions are very sensitive to background geometry, so it is important to understand what the eigenfunctions look like: where are they large and where are they small? There are many different ways to measure what "large" and "small" mean. One can consider local $L^2$ distribution, local and global $L^p$ distribution, as well as restrictions and boundary values. I will give an overview of what is known, and then discuss some very recent works in progress demonstrating that complicated things can happen even in very simple geometric settings.

### 2016/12/12

#### Tokyo Probability Seminar

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

**Takuma Akimoto**(Keio University)#### Seminar on Geometric Complex Analysis

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

(JAPANESE)

**Yu Kawakami**(Kanazawa University)(JAPANESE)

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

The Roe cocycle and an index theorem on partitioned manifolds, and toward generalizations

(Japanese)

**Tatsuki Seto**(Nagoya Univ.)The Roe cocycle and an index theorem on partitioned manifolds, and toward generalizations

(Japanese)

### 2016/12/07

#### Colloquium

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

On a conjecture of Bloch and Kato, and a local analogue.

**Uwe Jannsen**On a conjecture of Bloch and Kato, and a local analogue.

[ Abstract ]

In their seminal paper on Tamagawa Numbers of motives,

Bloch and Kato introduced a notion of motivic pairs, without

loss of generality over the rational numbers, which should

satisfy certain properties (P1) to (P4). The last property

postulates the existence of a Galois stable lattice T in the

associated adelic Galois representation V such that for each

prime p the fixed module of the inertia group of Q_p of

V/T is l-divisible for almost all primes l different from p.

I postulate an analogous local conjecture and show that it

implies the global conjecture.

In their seminal paper on Tamagawa Numbers of motives,

Bloch and Kato introduced a notion of motivic pairs, without

loss of generality over the rational numbers, which should

satisfy certain properties (P1) to (P4). The last property

postulates the existence of a Galois stable lattice T in the

associated adelic Galois representation V such that for each

prime p the fixed module of the inertia group of Q_p of

V/T is l-divisible for almost all primes l different from p.

I postulate an analogous local conjecture and show that it

implies the global conjecture.

### 2016/12/06

#### Tuesday Seminar of Analysis

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

On the trivialization of Bloch bundles and the construction of localized Wannier functions (English)

**Horia Cornean**(Aalborg University, Denmark)On the trivialization of Bloch bundles and the construction of localized Wannier functions (English)

[ Abstract ]

We shall present an introductory lecture on the trivialization of Bloch bundles and its physical implications. Simply stated, the main question we want to answer is the following: given a rank $N＼geq 1$ family of orthogonal projections $P(k)$ where $k＼in ＼mathbb{R}^d$, $P(＼cdot)$ is smooth and $＼mathbb{Z}^d$-periodic, is it possible to construct an orthonormal basis of its range which consists of vectors which are both smooth and periodic in $k$? We shall explain in detail the connection with solid state physics. This is joint work with I. Herbst and G. Nenciu.

We shall present an introductory lecture on the trivialization of Bloch bundles and its physical implications. Simply stated, the main question we want to answer is the following: given a rank $N＼geq 1$ family of orthogonal projections $P(k)$ where $k＼in ＼mathbb{R}^d$, $P(＼cdot)$ is smooth and $＼mathbb{Z}^d$-periodic, is it possible to construct an orthonormal basis of its range which consists of vectors which are both smooth and periodic in $k$? We shall explain in detail the connection with solid state physics. This is joint work with I. Herbst and G. Nenciu.

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Union of 3-punctured spheres in a hyperbolic 3-manifold (JAPANESE)

**Ken'ichi Yoshida**(The University of Tokyo)Union of 3-punctured spheres in a hyperbolic 3-manifold (JAPANESE)

[ Abstract ]

An essential 3-punctured sphere in a hyperbolic 3-manifold is isotopic to a totally geodesic one. We will classify the topological types for components of union of the totally geodesic 3-punctured spheres in an orientable hyperbolic 3-manifold. There are special types each of which appears in precisely one manifold.

An essential 3-punctured sphere in a hyperbolic 3-manifold is isotopic to a totally geodesic one. We will classify the topological types for components of union of the totally geodesic 3-punctured spheres in an orientable hyperbolic 3-manifold. There are special types each of which appears in precisely one manifold.

#### Classical Analysis

16:45-18:15 Room #154 (Graduate School of Math. Sci. Bldg.)

Introduction to resurgence on the example of saddle-node singularities (ENGLISH)

**David Sauzin**(CNRS)Introduction to resurgence on the example of saddle-node singularities (ENGLISH)

[ Abstract ]

Divergent power series naturally appear when solving such an elementary differential equation as x^2 dy = (x+y) dx, which is the simplest example of saddle-node singularity. I will discuss the formal classification of saddle-node singularities and illustrate on that case Ecalle's resurgence theory, which allows one to analyse the divergence of the formal solutions. One can also deal with resonant saddle-node singularities with one more dimension, a situation which covers the local study at infinity of some Painlevé equations.

Divergent power series naturally appear when solving such an elementary differential equation as x^2 dy = (x+y) dx, which is the simplest example of saddle-node singularity. I will discuss the formal classification of saddle-node singularities and illustrate on that case Ecalle's resurgence theory, which allows one to analyse the divergence of the formal solutions. One can also deal with resonant saddle-node singularities with one more dimension, a situation which covers the local study at infinity of some Painlevé equations.

### 2016/12/05

#### Seminar on Geometric Complex Analysis

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

(JAPANESE)

**Takahiro Oba**(Tokyo Institute of Technology )(JAPANESE)

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

On a generalized Fraïssé limit construction (English)

**Shuhei Masumoto**(Univ.Tokyo)On a generalized Fraïssé limit construction (English)

### 2016/12/01

#### Seminar on Probability and Statistics

16:00-18:00 Room #052 (Graduate School of Math. Sci. Bldg.)

On the determinant of the Malliavin matrix and density of random vector on Wiener chaos

**Ciprian Tudor**(Université Lille 1)On the determinant of the Malliavin matrix and density of random vector on Wiener chaos

[ Abstract ]

A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order, we prove that two random variables in the same Wiener chaos either admit a joint density, either are proportional and that the result is not true for random variables in Wiener chaoses of different orders.

A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order, we prove that two random variables in the same Wiener chaos either admit a joint density, either are proportional and that the result is not true for random variables in Wiener chaoses of different orders.

### 2016/11/29

#### Algebraic Geometry Seminar

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

Etale fundamental groups of F-regular schemes (English)

**Karl Schwede**(University of Utah)Etale fundamental groups of F-regular schemes (English)

[ Abstract ]

I will discuss recent work studying etale fundamental groups of the regular locus of F-regular schemes. I will describe how to use F-signature to bound the size of the fundamental group of an F-regular scheme, similar to a result of Xu. I will then discuss a recent extension showing that every F-regular scheme X has a finite cover Y, etale over the regular lcous of X, so that the etale fundamental groups of Y and the regular locus of Y agree. This is analogous to results of Greb-Kebekus-Peternell.

All the work discussed is joint with Carvajal-Rojas and Tucker or with with Bhatt, Carvajal-Rojas, Graf and Tucker.

I will discuss recent work studying etale fundamental groups of the regular locus of F-regular schemes. I will describe how to use F-signature to bound the size of the fundamental group of an F-regular scheme, similar to a result of Xu. I will then discuss a recent extension showing that every F-regular scheme X has a finite cover Y, etale over the regular lcous of X, so that the etale fundamental groups of Y and the regular locus of Y agree. This is analogous to results of Greb-Kebekus-Peternell.

All the work discussed is joint with Carvajal-Rojas and Tucker or with with Bhatt, Carvajal-Rojas, Graf and Tucker.

#### Tuesday Seminar on Topology

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

Generalized spectral theory and its application to coupled oscillators on networks (JAPANESE)

**Hayato Chiba**(Kyushu University)Generalized spectral theory and its application to coupled oscillators on networks (JAPANESE)

[ Abstract ]

For a system of large coupled oscillators on networks, we show that the transition from the de-synchronous state to the synchronization occurs as the coupling strength increases. For the proof, the generalized spectral theory of linear operators is employed.

For a system of large coupled oscillators on networks, we show that the transition from the de-synchronous state to the synchronization occurs as the coupling strength increases. For the proof, the generalized spectral theory of linear operators is employed.

#### Tuesday Seminar of Analysis

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

Interior transmission eigenvalue problems on manifolds (Japanese)

**Naotaka Shouji**(Graduate School of Pure and Applied Sciences, University of Tsukuba)Interior transmission eigenvalue problems on manifolds (Japanese)

### 2016/11/28

#### Seminar on Geometric Complex Analysis

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

(JAPANESE)

**Satoshi Nakamura**(Tohoku University)(JAPANESE)

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Fock space deformed by Coxeter groups (English)

**Takahiro Hasebe**(Hokkaido University)Fock space deformed by Coxeter groups (English)

#### Discrete mathematical modelling seminar

17:15-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Who cares about integrability ? (ENGLISH)

**Alfred Ramani**(IMNC, Universite de Paris 7 et 11)Who cares about integrability ? (ENGLISH)

[ Abstract ]

I will start my talk with an introduction to integrability of continuous systems. Why is it important? Is it possible to give a definition of integrability which will satisfy everybody? (Short answer: No). I will then present the most salient discoveries of integrable systems, from Newton to Toda. Next I will address the question of discrete integrability. This will lead naturally to the question of discretisation (of continuous systems) and its importance in modelling. I will deal with the construction of integrable discretisations of continuous integrable systems and introduce the singularity confinement discrete integrability criterion. The final part of my talk will be devoted to discrete Painlevé equations. Due to obvious time constraints I will concentrate on one special class of these equations, namely those associated to the E8 affine Weyl group. I will present a succinct summary of our recent results as well as indications for future investigations.

I will start my talk with an introduction to integrability of continuous systems. Why is it important? Is it possible to give a definition of integrability which will satisfy everybody? (Short answer: No). I will then present the most salient discoveries of integrable systems, from Newton to Toda. Next I will address the question of discrete integrability. This will lead naturally to the question of discretisation (of continuous systems) and its importance in modelling. I will deal with the construction of integrable discretisations of continuous integrable systems and introduce the singularity confinement discrete integrability criterion. The final part of my talk will be devoted to discrete Painlevé equations. Due to obvious time constraints I will concentrate on one special class of these equations, namely those associated to the E8 affine Weyl group. I will present a succinct summary of our recent results as well as indications for future investigations.

### 2016/11/25

#### FMSP Lectures

10:25-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Logarithmic Geometry V (ENGLISH)

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

**Arthur Ogus**(University of California, Berkeley)Introduction to Logarithmic Geometry V (ENGLISH)

[ Abstract ]

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

[ Reference URL ]Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

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

#### Colloquium

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

An instability mechanism of pulsatile flow along particle trajectories for the axisymmetric Euler equations

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yoneda/index.html

**Tsuyoshi Yoneda**(Graduate School of Mathematical Sciences, The University of Tokyo)An instability mechanism of pulsatile flow along particle trajectories for the axisymmetric Euler equations

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yoneda/index.html

### 2016/11/22

#### PDE Real Analysis Seminar

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

De Giorgi conjecture and minimal surfaces for integro-differential operators (English)

**Yannick Sire (Johns Hopkins University)**De Giorgi conjecture and minimal surfaces for integro-differential operators (English)

[ Abstract ]

I will review the classical De Giorgi conjecture and its link with minimal surfaces. Then I will move on recent results for flatness of level sets of solutions of semi linear equations involving anomalous diffusion. First I will deal with the fractional laplacian; second with quite general integral operators in 2 dimensions.

I will review the classical De Giorgi conjecture and its link with minimal surfaces. Then I will move on recent results for flatness of level sets of solutions of semi linear equations involving anomalous diffusion. First I will deal with the fractional laplacian; second with quite general integral operators in 2 dimensions.

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Sullivan's coproduct on the reduced loop homology (JAPANESE)

**Takahito Naito**(The University of Tokyo)Sullivan's coproduct on the reduced loop homology (JAPANESE)

[ Abstract ]

In string topology, Sullivan introduced a coproduct on the reduced loop homology and showed that the homology has an infinitesimal bialgebra structure with respect to the coproduct and Chas-Sullivan loop product. In this talk, I will give a homotopy theoretic description of Sullivan's coproduct. By using the description, we obtain some computational examples of the structure over the rational number field. Moreover, I will also discuss a based loop space version of the coproduct.

In string topology, Sullivan introduced a coproduct on the reduced loop homology and showed that the homology has an infinitesimal bialgebra structure with respect to the coproduct and Chas-Sullivan loop product. In this talk, I will give a homotopy theoretic description of Sullivan's coproduct. By using the description, we obtain some computational examples of the structure over the rational number field. Moreover, I will also discuss a based loop space version of the coproduct.

### 2016/11/21

#### FMSP Lectures

10:25-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Logarithmic Geometry IV (ENGLISH)

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

**Arthur Ogus**(University of California, Berkeley)Introduction to Logarithmic Geometry IV (ENGLISH)

[ Abstract ]

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

[ Reference URL ]Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

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

#### Seminar on Geometric Complex Analysis

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

(JAPANESE)

**Toshihiro Nose**(Fukuoka Institute of Technology)(JAPANESE)

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