## 過去の記録

### 2016年11月17日(木)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
※ 通常の曜日と異なります。

Convexity preserving properties for nonlinear evolution equations (English)
[ 講演概要 ]
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年11月16日(水)

#### FMSPレクチャーズ

10:25-12:10   数理科学研究科棟(駒場) 128号室
Arthur Ogus 氏 (University of California, Berkeley)
Introduction to Logarithmic Geometry II (ENGLISH)
[ 講演概要 ]
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.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ogus.pdf

### 2016年11月15日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

Cohomology of the moduli space of graphs and groups of homology cobordisms of surfaces (JAPANESE)
[ 講演概要 ]
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年11月14日(月)

#### FMSPレクチャーズ

10:25-12:10   数理科学研究科棟(駒場) 126号室
Arthur Ogus 氏 (University of California, Berkeley)
Introduction to Logarithmic Geometry I (ENGLISH)
[ 講演概要 ]
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.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ogus.pdf

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

### 2016年11月10日(木)

#### FMSPレクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (9) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### FMSPレクチャーズ

13:15-14:15   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (10) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### 東京無限可積分系セミナー

15:00-17:00   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

（ＳＳＢ）と非対角長距離秩序（ＯＤＬＲＯ）が存在することを証明する。
ここでＢＣＳモデルとは、最近接格子点間のホッピングを仮定した自由な項
とクーパー対長距離相互作用を仮定した4点の相互作用項からなるフェルミオ
ンフォック空間上の自己共役演算子である。ここで複素磁場との相互作用は
Ｚ方向のスピン演算子に純虚数をかけた演算子で表す。ＳＳＢとＯＤＬＲＯは

### 2016年11月09日(水)

#### FMSPレクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (7) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### FMSPレクチャーズ

13:15-14:15   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (8) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
Emmanuel Ullmo 氏 (Institut des Hautes Études Scientifiques)
Flows on Abelian Varieties and Shimura Varieties (English)
[ 講演概要 ]
I will discuss several questions and some results about algebraic flows, o-minimal flows and holomorphic flows on abelian varieties and Shimura varieties.

（本講演は東京北京パリ数論幾何セミナー」として, The Second Sino-French Conference in Arithmetic Geometry, Sanyaより中継します．インターネットによる東大数理，Morningside Center of Mathematics，IHES及びSanyaの双方向同時中継を行います.）

#### FMSPレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 118号室
Oleg Emanouilov 氏 (Colorado State University)
Conditional stability in Gelfand-Levitan problem (ENGLISH)
[ 講演概要 ]
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.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov161109.pdf

### 2016年11月08日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

Second mod 2 homology of Artin groups (JAPANESE)
[ 講演概要 ]
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レクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (5) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### FMSPレクチャーズ

13:15-14:15   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (6) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 118号室
いつもと部屋が異なります。

Minimal model theory for relatively trivial log canonical pairs
[ 講演概要 ]
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年11月07日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

### 2016年11月04日(金)

#### FMSPレクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (3) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### FMSPレクチャーズ

13:00-14:00   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (4) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

### 2016年11月02日(水)

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
Yves André 氏 (CNRS, Institut de Mathématiques de Jussieu)
Direct summand conjecture and perfectoid Abhyankar lemma: an overview (English)
[ 講演概要 ]
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.

(本講演は「東京北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,
Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

### 2016年11月01日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

Higher-dimensional contact manifolds with infinitely many Stein fillings (JAPANESE)
[ 講演概要 ]
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レクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (1) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### FMSPレクチャーズ

13:15-14:15   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (2) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### 統計数学セミナー

10:40-11:30   数理科学研究科棟(駒場) 123号室
Yuta Koike 氏 (Tokyo Metropolitan University, JST CREST)
Wavelet-based methods for high-frequency lead-lag analysis
[ 講演概要 ]
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).

#### 統計数学セミナー

11:30-12:30   数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (University du Luxembourg)
Second order fluctuations for zeros of arithmetic random waves
[ 講演概要 ]
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).