## 過去の記録

### 2018年08月08日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室
Srinivasan Raman 氏 (Chennai Mathematical Institute)
$E_0$-semigroups on factors

### 2018年07月31日(火)

#### 解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

#### 数値解析セミナー

14:00-15:00   数理科学研究科棟(駒場) 056号室
Jichun Li 氏 (University of Nevada Las Vegas)
Recent advances on numerical analysis and simulation of invisibility cloaks with metamaterials (English)
[ 講演概要 ]
In the June 23, 2006's issue of Science magazine, Pendry et al. and Leonhardt independently published their seminar papers on electromagnetic cloaking. Since then, there is a growing interest in using metamaterials to design invisibility cloaks. In this talk, I will first give a brief introduction to invisibility cloaks with metamaterials, then I will focus on some time-domain cloaking models we studied in the last few years. Well-posedness study and time-domain finite element method for these models will be presented. I will conclude the talk with some open issues.

### 2018年07月30日(月)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]
ランダム行列モデルにおいて, サンプル行列がひとつしかなければ, 経験尤度関数に基づいたパラメータ推定は様々な（現実的でない）仮定が必要です. 今回, 経験尤度ではなく経験固有値分布に基づいた,そのような仮定を必要としない手法を紹介します. ひとつのポイントは, 経験固有値分布をCauchy noiseで摂動させた分布を使うことです. この摂動された分布を使うのは, (自由確率論のFree Deterministic Equivalentという良い道具に基づき）, それがなめらかでアクセス可能な密度を持つ分布でfittingされるからです.

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~hayase/

### 2018年07月27日(金)

#### 数理人口学・数理生物学セミナー

15:00-16:00   数理科学研究科棟(駒場) 118号室
Somdatta Sinha 氏 (Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)
Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches
[ 講演概要 ]
Malaria has existed in India since antiquity. Different periods of
elimination and control policies have been adopted by the government for
tackling the disease. Malaria parasite was dissevered in India by Sir
Ronald Ross who also developed the simplest mathematical model in early
1900. Malaria modelling has since come through many variations that
incorporated various intrinsic and extrinsic/environmental factors to
describe the disease progression in population. Collection of disease
incidence and prevalence data, however, has been quite variable with both
governmental and non-governmental agencies independently collecting data at
different space and time scales. In this talk I will describe our work on
modelling malaria prevalence using three different approaches. For monthly
prevalence data, I will discuss (i) a regression-based statistical model
based on a specific data-set, and (ii) a general mathematical model that
fits the same data. For more coarse-grained temporal (yearly) data, I will
show graphical analysis that uncovers some useful information from the mass
of data tables. This presentation aims to highlight the suitability of
multiple modelling methods for disease prevalence from variable quality data.

### 2018年07月26日(木)

#### 数値解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 128号室

Categories of operators for multicategories with various symmetries
(多彩な対称性を持つマルチ圏のオペレーターの圏)
(JAPANESE)

### 2018年07月25日(水)

#### FMSPレクチャーズ

10:15-12:15   数理科学研究科棟(駒場) 118号室

Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf

### 2018年07月24日(火)

#### FMSPレクチャーズ

10:15-12:15   数理科学研究科棟(駒場) 118号室

Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf

### 2018年07月23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
Filippo Bracci 氏 (University of Rome Tor Vergata)
Strange Fatou components of automorphisms of $\mathbb{C}^2$ and Runge embedding of $\mathbb{C} \times \mathbb{C}^*$ into $\mathbb{C}^2$. (ENGLISH)
[ 講演概要 ]
The classification of Fatou components for automorphisms of the complex space of dimension greater than $1$ is an interesting and difficult task. Recent deep results prove that the one-dimensional setting is deeply different from the higher dimensional one. Given an automorphism F of $\mathbb{C}^k$, the first bricks in the theory that one would like to understand are invariant Fatou components, namely, those connected open sets $U$, completely invariant under $F$, where the dynamics of $F$ is not chaotic. Among those, we consider “attracting” Fatou components, that is, those components on which the iterates of $F$ converge to a single point. Attracting Fatou components can be recurrent, if the limit point is inside the component or non-recurrent. Recurrent attracting Fatou components are always biholomorphic to $\mathbb{C}^k$, since it was proved by H. Peters, L. Vivas and E. F. Wold that in such a case the point is an attracting (hyperbolic) fixed point, and the Fatou component coincides with the global basin of attraction. Also, as a consequence of works of Ueda and Peters-Lyubich, it is know that all attracting non-recurrent Fatou components of polynomial automorphisms of $\mathbb{C}^2$ are biholomorphic to $\mathbb{C}^2$. One can quite easily find non-simply connected non-recurrent attracting Fatou components in $\mathbb{C}^3$ (mixing a two- dimensional dynamics with a dynamics with non-isolated fixed points in one- variable). In this talk I will explain how to construct a non-recurrent attracting Fatou component in $\mathbb{C}^2$ which is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. This“fantastic beast” is obtained by globalizing, using a result of F. Forstneric, a local construction due to the speaker and Zaitsev, which allows to create a global basin of attraction for an automorphism, and a Fatou coordinate on it. The Fatou coordinate turns out to be a fiber bundle map on $\mathbb{C}$, whose fiber is $\mathbb{C}^*$, then the global basin is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. The most subtle point is to show that such a basin is indeed a Fatou component. This is done exploiting Poschel's results about existence of local Siegel discs and suitable estimates for the Kobayashi distance.

Since attracting Fatou components are Runge, it turns out that this construction gives also an example of a Runge embedding of $\mathbb{C}\times\mathbb{C}^*$ into $\mathbb{C}^2$. Moreover, this example shows an automorphism of $\mathbb{C}^2$ leaving invariant two analytic discs intersecting transversally at the origin.

The talk is based on a joint work with J. Raissy and B. Stensones.

#### FMSPレクチャーズ

10:15-12:15   数理科学研究科棟(駒場) 118号室

Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf

### 2018年07月20日(金)

#### FMSPレクチャーズ

10:15-12:15   数理科学研究科棟(駒場) 118号室

Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf

### 2018年07月19日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 118号室

Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent
(Japanese)
[ 講演概要 ]
This talk is devoted to studying the uniqueness and nondegeneracy of ground states to a nonlinear scalar field equation on the whole space. The nonlinearity consists of two power functions, and their growths are subcritical and critical in the Sobolev sense respectively. Under some assumptions, it is known that the equation admits a positive radial ground state and other ground states are made from the positive radial one. We show that if the dimensions are greater than or equal to 5 and the frequency is sufficiently large, then the positive radial ground state is unique and nondegenerate. This is based on joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria), Hiroaki Kikuchi (Tsuda Univ.) and Hayato Nawa (Meiji Univ.).

### 2018年07月18日(水)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

Jun-Muk Hwang 氏 (KIAS)
Normal Legendrian singularities (English)
[ 講演概要 ]
A germ of a Legendrian subvariety in a holomorphic contact manifold
is called a Legendrian singularity. Legendrian singularities are usually not normal.
We look at some examples of normal Legendrian singularities and discuss their rigidity under deformation.

#### 数理人口学・数理生物学セミナー

15:00-16:00   数理科学研究科棟(駒場) 118号室
Malay Banerjee 氏 (Department of Mathematics & Statistics, IIT Kanpur)
Effect of demographic stochasticity on large amplitude oscillation
[ 講演概要 ]

Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.

#### 博士論文発表会

15:30-16:45   数理科学研究科棟(駒場) 128号室

Mean curvature flow with driving force
(駆動力付きの平均曲率流方程式)
(JAPANESE)

#### FMSPレクチャーズ

10:15-12:15   数理科学研究科棟(駒場) 118号室

Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf

### 2018年07月17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

Positive flow-spines and contact 3-manifolds (JAPANESE)
[ 講演概要 ]
A contact structure is a smooth distribution of hyperplanes on an odd-dimensional manifold that is non-integrable everywhere. In the case of dimension 3, there is a nice relationship between open book decompositions of 3-manifolds and contact structures up to contactomorphisms, called Giroux correspondence. A flow-spine is a spine of a 3-manifold admitting a flow such that it is transverse to the spine and the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. In this talk, we introduce some results in progress that give a correspondence between contact structures and positive flow-spines by regarding Reeb vector fields as flows of spines. This is a joint work with Y. Koda (Hiroshima) and H. Naoe (Tohoku).

#### 博士論文発表会

15:30-16:45   数理科学研究科棟(駒場) 128号室

Mathematical analysis of evolution equations in curved thin domains or on moving surfaces
(曲がった薄膜領域や動く曲面上の発展方程式の数学解析)
(ENGLISH)

#### 東京無限可積分系セミナー

16:00-17:00   数理科学研究科棟(駒場) 002号室
Valerii Sopin 氏 (Higher School of Economics (Moscow))
Operator algebra for statistical model of square ladder (ENGLISH)
[ 講演概要 ]
In this talk we will define operator algebra for square ladder on the basis
of semi-infinite forms.

Keywords: hard-square model, square ladder, operator algebra, semi-infinite
forms, fermions, quadratic algebra, cohomology, Demazure modules,
Heisenberg algebra.

### 2018年07月13日(金)

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 056号室
DINH Tien Cuong 氏 (National University of Singapore )
Pluripotential theory and complex dynamics in higher dimension

[ 講演概要 ]
Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.

### 2018年07月11日(水)

#### 作用素環セミナー

17:15-18:45   数理科学研究科棟(駒場) 126号室
George Elliott 氏 (Univ. Toronto)
Recent progress in the classification of amenable C*-algebras (cont'd)

### 2018年07月10日(火)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 002号室
いつもと部屋が違います。The room is different from usual.

The effective bound of anticanonical volume of Fano threefolds (English)
[ 講演概要 ]
According to Mori's program, varieties covered by rational curves are
built up from anti-canonically polarized varieties, aka Fano varieties. After fixed the
dimension and singularity type, Fano varieties form a bounded family by Birkar's proof (2016)
of Borisov-Alexeev-Borisov conjecture, which In particular implies that the anticanonical
volume -K^\dim is bounded. In this talk, we focus on canonical Fano threefolds,
where boundedness was established by Koll\'ar-Miyaoka-Mori-Takagi (2000).
Our aim is to find an effective bound of the anticanonical volume -K^3, which is
not explicit either from the work of Koll\'ar-Miyaoka-Mori-Takagi or Birkar. We will discuss
some effectiveness results related to this problem and prove that -K_X^3\leq 72 if \rho(X)\leq 2.
This partially extends early work of Mori, Mukai, Y. Prokhorov, et al.

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 128号室
Canceled!! (諸事情により,講演は取りやめとなりました.)
Sam Nariman 氏 (Northwestern University)
On the moduli space of flat symplectic surface bundles
[ 講演概要 ]
There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.

In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of
Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.

#### 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
Emmy Murphy 氏 (Northwestern University)
Loose Legendrians and arboreal singularities (ENGLISH)
[ 講演概要 ]
Given a Stein manifold X, under what conditions can we ensure that X is symplectomorphic to C^n? For n>2 the condition of X being diffeomorphic to C^n does not suffice, and many counterexamples have been constructed which are detected by symplectic cohomology and the Fukaya category. One might conjecture that the diffeomorphism type together with a vanishing Fukaya category characterizes C^n. While this question is currently well of of reach, we present some new partial results. The main tools we'll discuss are arboreal singularities, constructable sheaf theory, and loose Legendrians -- and how they fit together to approach this question.