## 過去の記録

### 2018年10月09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
Boris Hasselblatt 氏 (Tufts University)
Foulon surgery, new contact flows, and dynamical complexity (ENGLISH)
[ 講演概要 ]
A refinement of Dehn surgery produces new contact flows that are unusual and interesting in several ways. The geodesic flow of a hyperbolic surface becomes a nonalgebraic contact Anosov flow with larger orbit growth, and the purely periodic fiber flow becomes parabolic or hyperbolic. Moreover, Reeb flows for other contact forms for the same contact structure have the same complexity. Finally, an idea by Vinhage promises a quantification of the complexity increase.

#### 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

Stability conditions on threefolds with nef tangent bundles (English)
[ 講演概要 ]
The construction of Bridgeland stability conditions on threefolds
is an open problem in general.
The problem is reduced to proving
the so-called Bogomolov-Gieseker (BG) type inequality conjecture,
proposed by Bayer, Macrí, and Toda.
In this talk, I will explain how to prove the BG type inequality
conjecture
for threefolds in the title.

### 2018年10月04日(木)

#### 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) 056号室
Robin Thompson 氏 (University of Oxford, UK)
Modelling the beginnings, middles and ends of infectious disease outbreaks
(ENGLISH)
[ 講演概要 ]
There have been a number of high profile infectious disease epidemics recently. For example, the 2013-16 Ebola epidemic in West Africa led to more than 11,000 deaths, putting it at the centre of the news agenda. However, when a pathogen enters a host population, it is not necessarily the case that a major epidemic follows. The Ebola virus survives in animal populations, and enters human populations every few years. Typically, a small number of individuals are infected in an Ebola outbreak, with the 2013-16 epidemic being anomalous. During this talk, using Ebola as a case study, I will discuss how stochastic epidemiological models can be used at different stages of infectious disease outbreaks. At the beginning of an outbreak, key questions include: how can surveillance be performed effectively, and will the outbreak develop into a major epidemic? When a major epidemic is ongoing, modelling can be used to predict the final size and to plan control interventions. And at the apparent end of an epidemic, an important question is whether the epidemic is really over once there are no new symptomatic cases. If time permits, I will also discuss several current projects that I am working on. One of these - in collaboration with Professor Hiroshi Nishiura at Hokkaido University - involves appropriately modelling disease detection during epidemics, and investigating the impact of the sensitivity of surveillance on the outcome of control interventions.

Relevant references:
Thompson RN, Hart WS, Effect of confusing symptoms and infectiousness on forecasting and control of Ebola outbreaks, Clin. Inf. Dis., In Press, 2018.

Thompson RN, Gilligan CA and Cunniffe NJ, Control fast or control Smart: when should invading pathogens be controlled?, PLoS Comp. Biol., 14(2):e1006014, 2018.

Thompson RN, Gilligan CA and Cunniffe NJ, Detecting presymptomatic infection is necessary to forecast major epidemics in the earliest stages of infectious disease outbreaks, PLoS Comp. Biol., 12(4):e1004836, 2016.

Thompson RN, Cobb RC, Gilligan CA and Cunniffe NJ, Management of invading pathogens should be informed by epidemiology rather than administrative boundaries, Ecol. Model., 324:28-32, 2016.
[ 講演参考URL ]
http://www.robin-thompson.co.uk/

#### 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
Andrew Kels 氏 (東大総合文化)
Integrable quad equations derived from the quantum Yang-Baxter
equation. (ENGLISH)
[ 講演概要 ]
I will give an overview of an explicit correspondence that exists between
two different types of integrable equations; 1) the quantum Yang-Baxter
equation in its star-triangle relation (STR) form, and 2) the classical
classification. The fundamental aspect of this correspondence is that the
equation of the critical point of a STR is equivalent to an ABS quad
equation. The STR's considered here are in fact equivalent to
hypergeometric integral transformation formulas. For example, a STR for
$H1_{(\varepsilon=0)}$ corresponds to the Euler Beta function, a STR for
$Q1_{(\delta=0)}$ corresponds to the $n=1$ Selberg integral, and STR's for
$H2_{\varepsilon=0,1}$, $H1_{(\varepsilon=1)}$, correspond to different
hypergeometric integral formulas of Barnes. I will discuss some of these
examples and some directions for future research.

#### 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

いくつかの微分方程式に対する反応拡散近似 (Japanese)
[ 講演概要 ]

### 2018年10月03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

Structure of bicentralizer algebras and inclusions of type III factors

### 2018年10月02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

An Alexander polynomial for MOY graphs (JAPANESE)
[ 講演概要 ]
An MOY graph is a trivalent graph equipped with a balanced coloring. In this talk, we define a version of Alexander polynomial for an MOY graph. This polynomial is the Euler characteristic of the Heegaard Floer homology of an MOY graph. We give a characterization of the polynomial, which we call MOY-type relations, and show that it is equivalent to Viro’s gl(1 | 1)-Alexander polynomial of a graph. (A part of the talk is a joint work of Zhongtao Wu)

### 2018年09月25日(火)

#### 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

Classification of quad-equations on a cuboctahedron (JAPANESE)
[ 講演概要 ]

### 2018年09月21日(金)

#### 講演会

17:00-18:00   数理科学研究科棟(駒場) 056号室
Laurent Fargues 氏 (CNRS, Institut Mathématique de Jussieu)
On the geometry of some p-adic period domains (ENGLISH)
[ 講演概要 ]
p-adic period spaces have been introduced by Rapoport and Zink as a generalization of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic p-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties. I will explain a recent theorem characterizing when the period space coincides with the weakly admissible locus. As an application we can compute the p-adic period space of K3 surfaces with supersingular reduction. The talk will be mainly introductory, presenting the objects showing up in this theorem. This is joint work with Miaofen Chen and Xu Shen.

### 2018年09月18日(火)

#### 講演会

17:00-18:00   数理科学研究科棟(駒場) 056号室
Alexander Beilinson 氏 (University of Chicago)
Topological epsilon-factors (ENGLISH)
[ 講演概要 ]
I will explain (following mostly my old article arXiv:0610055) how the Kashiwara-Shapira Morse theory construction of the characteristic cycle of a constructible R-sheaf can be refined to yield the cycle with coefficients in the K-theory spectrum K(R). The construction can be viewed as a topological analog of the arithmetic theory of epsilon-factors.

### 2018年08月24日(金)

#### 博士論文発表会

13:30-14:45   数理科学研究科棟(駒場) 128号室

Studies on the ascending chain condition for F-pure thresholds
(F純閾値の昇鎖条件に関する研究）
(JAPANESE)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 002号室
Lucas Teyssier 氏 (Ecole Normale Superieure)
Limit profile for the card shuffle by random transpositions

### 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 ]
https://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.).