## Seminar information archive

Seminar information archive ～02/23｜Today's seminar 02/24 | Future seminars 02/25～

### 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)

#### Numerical Analysis Seminar

16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)

Gauss-Kronrod quadrature formulae (English)

**Sotirios E. Notaris**(National and Kapodistrian University of Athens)Gauss-Kronrod quadrature formulae (English)

[ Abstract ]

In 1964, the Russian mathematician A.S. Kronrod, in an attempt to estimate practically the error term of the well-known Gauss quadrature formula, presented a new quadrature rule, which since then bears his name. It turns out that the new rule was related to some polynomials that Stieltjes developed some 70 years earlier, through his work on continued fractions and the moment problem. We give an overview of the Gauss-Kronrod quadrature formulae, which are interesting from both the mathematical and the applicable point of view.

The talk will be expository without requiring any previous knowledge of numerical integration.

In 1964, the Russian mathematician A.S. Kronrod, in an attempt to estimate practically the error term of the well-known Gauss quadrature formula, presented a new quadrature rule, which since then bears his name. It turns out that the new rule was related to some polynomials that Stieltjes developed some 70 years earlier, through his work on continued fractions and the moment problem. We give an overview of the Gauss-Kronrod quadrature formulae, which are interesting from both the mathematical and the applicable point of view.

The talk will be expository without requiring any previous knowledge of numerical integration.

#### Operator Algebra Seminars

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

Finite-dimensional representations constructed from random walks (joint work with A. Erschler)

**Narutaka Ozawa**(RIMS, Kyoto Univ.)Finite-dimensional representations constructed from random walks (joint work with A. Erschler)

#### Tokyo Probability Seminar

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

On scaling limit of a cost in adhoc network model

**Yukio Nagahata**(Faculty of Engineering, Niigata University)On scaling limit of a cost in adhoc network model

### 2016/11/19

#### Discrete mathematical modelling seminar

14:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

(JAPANESE)

**Takayuki Hasegawa**(Toyama National College of Technology) 14:00-15:15(JAPANESE)

**Hironobu Fujishima**(Canon) 15:45-17:00(JAPANESE)

### 2016/11/18

#### FMSP Lectures

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

Introduction to Logarithmic Geometry III (ENGLISH)

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

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

### 2016/11/17

#### Seminar on Mathematics for various disciplines

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

Convexity preserving properties for nonlinear evolution equations (English)

**Qing Liu**(Fukuoka University)Convexity preserving properties for nonlinear evolution equations (English)

[ Abstract ]

It is well known that convexity of solutions to a general class of nonlinear parabolic equations in the Euclidean space is preserved as time develops. In this talk, we first revisit this property for the normalized infinity Laplace equation and the curvature flow equation by introducing an alternative approach based on discrete game theory. We then extend our discussion to Hamilton-Jacobi equations in the Heisenberg group and in more general geodesic metric spaces.

It is well known that convexity of solutions to a general class of nonlinear parabolic equations in the Euclidean space is preserved as time develops. In this talk, we first revisit this property for the normalized infinity Laplace equation and the curvature flow equation by introducing an alternative approach based on discrete game theory. We then extend our discussion to Hamilton-Jacobi equations in the Heisenberg group and in more general geodesic metric spaces.

### 2016/11/16

#### FMSP Lectures

10:25-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)

Introduction to Logarithmic Geometry II (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 ]

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

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

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

### 2016/11/15

#### Tuesday Seminar on Topology

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

Cohomology of the moduli space of graphs and groups of homology cobordisms of surfaces (JAPANESE)

**Takuya Sakasai**(The University of Tokyo)Cohomology of the moduli space of graphs and groups of homology cobordisms of surfaces (JAPANESE)

[ Abstract ]

We construct an abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra generated by the fundamental representation of the symplectic group. It gives an alternative proof of the fact first shown by Bartholdi that the top rational homology group of the moduli space of metric graphs of rank 7 is one dimensional. As an application, we construct a non-trivial abelian quotient of the homology cobordism group of a surface of positive genus. This talk is based on joint works with Shigeyuki Morita, Masaaki Suzuki and Gwénaël Massuyeau.

We construct an abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra generated by the fundamental representation of the symplectic group. It gives an alternative proof of the fact first shown by Bartholdi that the top rational homology group of the moduli space of metric graphs of rank 7 is one dimensional. As an application, we construct a non-trivial abelian quotient of the homology cobordism group of a surface of positive genus. This talk is based on joint works with Shigeyuki Morita, Masaaki Suzuki and Gwénaël Massuyeau.

### 2016/11/14

#### FMSP Lectures

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

Introduction to Logarithmic Geometry I (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 ]

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

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

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)

**Sachiko Hamano**(Osaka City University)(JAPANESE)

### 2016/11/10

#### FMSP Lectures

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

The BV space in variational and evolution problems (9) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (9) (ENGLISH)

[ Abstract ]

http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

[ Reference URL ]http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

#### FMSP Lectures

13:15-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (10) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (10) (ENGLISH)

[ Abstract ]

http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

[ Reference URL ]http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

#### Infinite Analysis Seminar Tokyo

15:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Superconducting phase in the BCS model with imaginary

magnetic field (JAPANESE)

**Yohei Kashima**(Graduate School of Mathematical Scineces, The University of Tokyo)Superconducting phase in the BCS model with imaginary

magnetic field (JAPANESE)

[ Abstract ]

We prove that in the BCS model with an imaginary magnetic field

at positive temperature a spontaneous symmetry breaking (SSB) and

an off-diagonal long range order (ODLRO) occur. Here the BCS model

is meant to be a self-adjoint operator on the Fermionic Fock space,

consisting of a free part describing the electrons' nearest neighbor

hopping and a quartic interacting part describing a long range

interaction between Cooper pairs. The interaction with the imaginary

magnetic field is given by the z-component of the spin operator

multiplied by a pure imaginary parameter. The SSB and the ODLRO are

shown in the infinite-volume limit of the thermal average over the

full Fermionic Fock space. The insertion of the imaginary magnetic

field changes the gap equation. Consequently the SSB and the ODLRO

are shown in high temperature, weak coupling regimes where these

phenomena do not take place in the conventional BCS model. The proof

is based on the method of Grassmann integration.

We prove that in the BCS model with an imaginary magnetic field

at positive temperature a spontaneous symmetry breaking (SSB) and

an off-diagonal long range order (ODLRO) occur. Here the BCS model

is meant to be a self-adjoint operator on the Fermionic Fock space,

consisting of a free part describing the electrons' nearest neighbor

hopping and a quartic interacting part describing a long range

interaction between Cooper pairs. The interaction with the imaginary

magnetic field is given by the z-component of the spin operator

multiplied by a pure imaginary parameter. The SSB and the ODLRO are

shown in the infinite-volume limit of the thermal average over the

full Fermionic Fock space. The insertion of the imaginary magnetic

field changes the gap equation. Consequently the SSB and the ODLRO

are shown in high temperature, weak coupling regimes where these

phenomena do not take place in the conventional BCS model. The proof

is based on the method of Grassmann integration.

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