## Seminar information archive

Seminar information archive ～08/17｜Today's seminar 08/18 | Future seminars 08/19～

#### 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.

### 2016/11/01

#### Tuesday Seminar on Topology

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

Higher-dimensional contact manifolds with infinitely many Stein fillings (JAPANESE)

**Takahiro Oba**(Tokyo Institute of Technology)Higher-dimensional contact manifolds with infinitely many Stein fillings (JAPANESE)

[ Abstract ]

A Stein fillings of a given contact manifold is a Stein domain whose boundary is contactomorphic to the given contact manifold.

Open books, Lefschetz fibrations, and mapping class groups of their fibers in particular help us to produce various contact manifolds and their Stein fillings. However, little is known about mapping class groups of higher-dimensional manifolds. This is one of the reasons that it was unknown whether there is a contact manifold of dimension > 3 with infinitely many Stein fillings. In this talk, I will choose a certain symplectic manifold as fibers of open books and Lefschetz fibrations and by using them, construct an infinite family of higher-dimensional contact manifolds with infinitely many Stein fillings.

A Stein fillings of a given contact manifold is a Stein domain whose boundary is contactomorphic to the given contact manifold.

Open books, Lefschetz fibrations, and mapping class groups of their fibers in particular help us to produce various contact manifolds and their Stein fillings. However, little is known about mapping class groups of higher-dimensional manifolds. This is one of the reasons that it was unknown whether there is a contact manifold of dimension > 3 with infinitely many Stein fillings. In this talk, I will choose a certain symplectic manifold as fibers of open books and Lefschetz fibrations and by using them, construct an infinite family of higher-dimensional contact manifolds with infinitely many Stein fillings.

#### FMSP Lectures

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

The BV space in variational and evolution problems (1) (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 (1) (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 (2) (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 (2) (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

#### Seminar on Probability and Statistics

10:40-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Wavelet-based methods for high-frequency lead-lag analysis

**Yuta Koike**(Tokyo Metropolitan University, JST CREST)Wavelet-based methods for high-frequency lead-lag analysis

[ Abstract ]

We propose a novel framework to investigate the lead-lag effect between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice. This talk is based on a joint work of Prof. Takaki Hayashi (Keio University).

We propose a novel framework to investigate the lead-lag effect between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice. This talk is based on a joint work of Prof. Takaki Hayashi (Keio University).

#### Seminar on Probability and Statistics

11:30-12:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Second order fluctuations for zeros of arithmetic random waves

**Giovanni Peccati**(University du Luxembourg)Second order fluctuations for zeros of arithmetic random waves

[ Abstract ]

Originally introduced by Rudnick and Wigman (2007), arithmetic random waves are Gaussian Laplace eigenfunctions on the two-dimensional torus. In this talk, I will describe the high-energy behaviour of the so-called « nodal length » (that, is the volume of the zero set) of such random objects, and show that (quite unexpectedly) it is non-central and non-universal. I will also discuss the connected problem of counting the number of intersections points of independent nodal sets (equivalent to « phase singularities » for complex waves) in the high-energy regime. Both issues are tightly connected to the arithmetic study of lattice points on circles. One key concept in our presentation is that of ‘Berry cancellation phenomenon’ (see M.V. Berry, 2002), for which an explanation in terms of chaos expansions and integration by parts (Green formula) will be provided. Based on joint works (GAFA 2016 & Preprint 2016) with D. Marinucci (Rome Tor Vergata), M. Rossi (Luxembourg) and I. Wigman (King’s College, London), and with F. Dalmao (University of Uruguay), I. Nourdin (Luxembourg) and M. Rossi (Luxembourg).

Originally introduced by Rudnick and Wigman (2007), arithmetic random waves are Gaussian Laplace eigenfunctions on the two-dimensional torus. In this talk, I will describe the high-energy behaviour of the so-called « nodal length » (that, is the volume of the zero set) of such random objects, and show that (quite unexpectedly) it is non-central and non-universal. I will also discuss the connected problem of counting the number of intersections points of independent nodal sets (equivalent to « phase singularities » for complex waves) in the high-energy regime. Both issues are tightly connected to the arithmetic study of lattice points on circles. One key concept in our presentation is that of ‘Berry cancellation phenomenon’ (see M.V. Berry, 2002), for which an explanation in terms of chaos expansions and integration by parts (Green formula) will be provided. Based on joint works (GAFA 2016 & Preprint 2016) with D. Marinucci (Rome Tor Vergata), M. Rossi (Luxembourg) and I. Wigman (King’s College, London), and with F. Dalmao (University of Uruguay), I. Nourdin (Luxembourg) and M. Rossi (Luxembourg).

### 2016/10/31

#### Seminar on Geometric Complex Analysis

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

(JAPANESE)

**Yutaka Ishii**(Kyushu University)(JAPANESE)

#### Numerical Analysis Seminar

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

Numerical methods of a quantum hydrodynamic model for semiconductor devices (日本語)

**Shohiro Sho**(Osaka University)Numerical methods of a quantum hydrodynamic model for semiconductor devices (日本語)

#### Operator Algebra Seminars

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

Dual cocycles and equivariant deformation quantization (English)

**Sergey Neshveyev**(Univ. Oslo)Dual cocycles and equivariant deformation quantization (English)

#### Seminar on Probability and Statistics

10:40-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Martingale expansion revisited

**Nakahiro Yoshida**(University of Tokyo, Institute of Statistical Mathematics, JST CREST)Martingale expansion revisited

[ Abstract ]

The martingale expansion is revisited in this talk. The martingale expansion for a martingale with mixed normal limit evaluates the tangent of the quadratic variation of the martingale and the torsion of an exponential martingale under the measure transform caused by the random limit of the quadratic variation. The martingale expansion has been applied to the realized volatility, quadratic form of an Ito process, p-variation and the QLA estimators of a volatility parametric model. An interpolation in time was used in martingale expansion. We discuss relation between martingale expansion and recently developed asymptotic expansion of Skorohod integrals by interpolation of distributions (a joint work with D. Nualart).

The martingale expansion is revisited in this talk. The martingale expansion for a martingale with mixed normal limit evaluates the tangent of the quadratic variation of the martingale and the torsion of an exponential martingale under the measure transform caused by the random limit of the quadratic variation. The martingale expansion has been applied to the realized volatility, quadratic form of an Ito process, p-variation and the QLA estimators of a volatility parametric model. An interpolation in time was used in martingale expansion. We discuss relation between martingale expansion and recently developed asymptotic expansion of Skorohod integrals by interpolation of distributions (a joint work with D. Nualart).

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