## Seminar information archive

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

#### 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)

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

**Arthur Ogus**(University of California, Berkeley)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 ]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)

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

**Arthur Ogus**(University of California, Berkeley)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 ]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.

### 2016/11/09

#### FMSP Lectures

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

The BV space in variational and evolution problems (7) (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 (7) (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 (8) (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 (8) (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

#### Number Theory Seminar

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

Flows on Abelian Varieties and Shimura Varieties (English)

**Emmanuel Ullmo**(Institut des Hautes Études Scientifiques)Flows on Abelian Varieties and Shimura Varieties (English)

[ Abstract ]

I will discuss several questions and some results about algebraic flows, o-minimal flows and holomorphic flows on abelian varieties and Shimura varieties.

I will discuss several questions and some results about algebraic flows, o-minimal flows and holomorphic flows on abelian varieties and Shimura varieties.

#### FMSP Lectures

17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Conditional stability in Gelfand-Levitan problem (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov161109.pdf

**Oleg Emanouilov**(Colorado State University)Conditional stability in Gelfand-Levitan problem (ENGLISH)

[ Abstract ]

We consider the Laplace-Beltrami operator in the bounded domain on the plane.

The eigenvalues and the traces of the eigenfunctions on part of the boundary are given.

We obtain the double logarithmic stability for the determination of metric up to the gauge equivalence.

[ Reference URL ]We consider the Laplace-Beltrami operator in the bounded domain on the plane.

The eigenvalues and the traces of the eigenfunctions on part of the boundary are given.

We obtain the double logarithmic stability for the determination of metric up to the gauge equivalence.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov161109.pdf

### 2016/11/08

#### Tuesday Seminar on Topology

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

Second mod 2 homology of Artin groups (JAPANESE)

**Toshiyuki Akita**(Hokkaido University)Second mod 2 homology of Artin groups (JAPANESE)

[ Abstract ]

After a brief survey on the K($\pi$,1) conjecture and homology of Artin groups, I will introduce our recent result: we determined second mod 2 homology of arbitrary Artin groups without assuming the K($\pi$,1)-conjecture. The key ingredients are Hopf's formula and a result of Howlett on Schur multipliers of Coxeter groups. This is a joint work with Ye Liu.

After a brief survey on the K($\pi$,1) conjecture and homology of Artin groups, I will introduce our recent result: we determined second mod 2 homology of arbitrary Artin groups without assuming the K($\pi$,1)-conjecture. The key ingredients are Hopf's formula and a result of Howlett on Schur multipliers of Coxeter groups. This is a joint work with Ye Liu.

#### FMSP Lectures

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

The BV space in variational and evolution problems (5) (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 (5) (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 (6) (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 (6) (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

#### Algebraic Geometry Seminar

15:30-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Minimal model theory for relatively trivial log canonical pairs

**Kenta Hashizume**(Department of Mathematics, Kyoto University)Minimal model theory for relatively trivial log canonical pairs

[ Abstract ]

The good minimal model conjecture is an important open problem in the birational geometry, and inductive arguments on the dimension of varieties are useful when we work on this conjecture. In fibration with a log canoinical pair having some good properties, it is expected that the above conjecture for the log canonical pair on total space can be proved by investigating the general fiber and base variety of the fibration. In this talk, I will explain an inductive argument in fibrations with relatively trivial log canonical pairs and introduce some applications of the inductive argument.

The good minimal model conjecture is an important open problem in the birational geometry, and inductive arguments on the dimension of varieties are useful when we work on this conjecture. In fibration with a log canoinical pair having some good properties, it is expected that the above conjecture for the log canonical pair on total space can be proved by investigating the general fiber and base variety of the fibration. In this talk, I will explain an inductive argument in fibrations with relatively trivial log canonical pairs and introduce some applications of the inductive argument.

### 2016/11/07

#### Seminar on Geometric Complex Analysis

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

(JAPANESE)

**Hideyuki Ishi**(Nagoya University)(JAPANESE)

### 2016/11/04

#### FMSP Lectures

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

The BV space in variational and evolution problems (3) (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 (3) (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

13:00-14:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (4) (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 (4) (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

### 2016/11/02

#### Number Theory Seminar

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

Direct summand conjecture and perfectoid Abhyankar lemma: an overview (English)

**Yves André**(CNRS, Institut de Mathématiques de Jussieu)Direct summand conjecture and perfectoid Abhyankar lemma: an overview (English)

[ Abstract ]

According to Hochster's direct summand conjecture (1973), a regular ring R is a direct summand, as an R-module, of every finite extension ring. We shall outline our recent proof which relies on perfectoid techniques. Similar arguments also establish the existence of big Cohen-Macaulay algebras for complete local domains of mixed characteristics.

According to Hochster's direct summand conjecture (1973), a regular ring R is a direct summand, as an R-module, of every finite extension ring. We shall outline our recent proof which relies on perfectoid techniques. Similar arguments also establish the existence of big Cohen-Macaulay algebras for complete local domains of mixed characteristics.

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