## 過去の記録

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室

A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory

### 2017年06月28日(水)

#### 数理人口学・数理生物学セミナー

14:55-15:45   数理科学研究科棟(駒場) 122号室
Malay Banerjee 氏 (Department of Mathematics & Statistics，IIT Kanpur)
Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)
[ 講演概要 ]
Discrete and continuous time delays are often introduced into mathematical models of interacting populations to take into account stage-structuring of one or more species. There are other aspects for the incorporation of time delays. In prey-predator models, maturation time delay is introduced to the growth equation of predators to implicitly model the stage-structure of predators. Most of the prey-predator models with maturation delay are known to exhibit regular and rregular, even chaotic, oscillations due to destabilization of coexistence steady-state when maturation time period is significantly large. However, such kind of instability can results in due to the introduction of maturation delay into predator’s growth equation with lack of ecological justification and inappropriate choice of the length of time delay. Recently we have worked on a class of delayed prey-predator models, where discrete time delay represents the maturation time for specialist predator implicitly, with ratio-dependent functional response [1] and Michaelis-Menten type
functional response [2]. We have established (i) the stabilizing role of maturation delay, (ii)extinction of predator for significantly long maturation period and (iii) suppression of Hopf bifurcation for large time delay, when the delayed model is constructed with appropriate biological rationale. Main objective of this talk is to discuss analytical results for the stable coexistence of both the species for a class of delayed prey-predator models with maturation delay for specialist predator. Analytical results will be illustrated with the help of numerical simulation results and appropriate bifurcation diagrams with time delay as bifurcation parameter. Main content of this talk is based upon the recent work with Prof. Y. Takeuchi [2].
References:
[1] M. Sen, M. Banerjee, A. Morozov. (2014). Stage-structured ratio-dependent predatorprey models revisited: When should the maturation lag result in systems destabilization?, Ecological Complexity, 19(2), 23–34.
[2] M. Banerjee, Y. Takeuchi. (2017). Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models, Journal of Theoretical Biology, 412, 154–171.

#### 数理人口学・数理生物学セミナー

15:50-16:40   数理科学研究科棟(駒場) 122号室
Moitri Sen 氏 (Department. of Mathematics, National Institute of Technology Patna)
Allee effect induced rich dynamics of a two prey one predator model where the predator is
generalist (ENGLISH)
[ 講演概要 ]
One of the important ecological challenges is to capture the chaotic dynamics and understand the underlying regulating factors. Allee effect is one of the important factors in ecology and taking it into account can cause signi cant changes to the system dynamics. In this work we propose a two prey-one predator model where the growth of both the prey population is governed by Allee effect, and the predator is generalist and hence survived on both the prey populations. We analyze the role of Allee e ect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee e ect enriches the dynamics of the system. Specially after a certain threshold of the Allee e ect, it has a very signi cant e ect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurca-tions such as namely the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.

### 2017年06月27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) 122号室

Cylinders in del Pezzo fibrations (English )
[ 講演概要 ]
The cylinder is, by definition, an algebraic variety of the form Z × A1 . Certainly it is geometrically a very simple object, but it plays often an important role to connect unipotent group actions on special kinds of affine algebraic varieties to projective geometry. From the point of view of birational geometry, it is essential to look into cylinders found on Mori fiber spaces. In this talk, we shall focus mainly on Mori fiber spaces of relative dimension two or three. One of main results asserts that a del Pezzo fibration π : V → W contains a cylinder respecting the structure of π (so-called a vertical cylinder) if and only if the degree deg π of π is greater than or equal to 5 and π admits a rational section. Especially, in case of dim V = 3, the existence of a vertical cylinder is equivalent to saying deg π ≧ 5 in consideration of Tsen’s theorem, nevertheless, it is worthwhile to note that the affine 3-space A3C is embedded into certains del Pezzo fibrations π : V → P1C of deg π ≦ 4 in a twisted way. This is a joint work with Adrien Dubouloz (Universit ́e de Bourgogne).

#### 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, RIKEN iTHEMS と共催

Braids and hyperbolic 3-manifolds from simple mixing devices (JAPANESE)
[ 講演概要 ]
Taffy pullers are devices for pulling candy. One can build braids from the motion of rods for taffy pullers. According to a beautiful article A mathematical history of taffy pullers" by Jean-Luc Thiffeault, all taffy pullers (except the first one) give rise to pseudo-Anosov braids. This means that the devices mix candies effectively. Following a study of Thiffeault, I will discuss which pseudo-Anosov braid is realized by taffy pullers. I will explain an interesting connection between braids coming from taffy pullers. I also discuss the hyperbolic mapping tori obtained from taffy pullers. Intriguingly, the two most common taffy pullers give rise to the complements of the the minimally twisted 4-chain link and 5-chain link which are important examples for the study of cusped hyperbolic 3-manifolds with small volumes.

Reference: A mathematical history of taffy pullers, Jean-Luc Thiffeault, https://arxiv.org/pdf/1608.00152.pdf

### 2017年06月26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

Volume minimization and obstructions to geometric problems
[ 講演概要 ]
We discuss on the volume minimization principle for conformally Kaehler Einstein-Maxwell metrics in the similar spirit as the Kaehler-Ricci solitons and Sasaki-Einstein metrics. This talk is base on a joint work with Hajime Ono.

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
David Kerr 氏 (Texas A & M Univ.)
Dimension, comparison, and almost finiteness (English)

### 2017年06月20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
Anh Tran 氏 (The University of Texas at Dallas)
Introduction to the AJ conjecture (ENGLISH)
[ 講演概要 ]
The AJ conjecture was proposed by Garoufalidis about 15 years ago. It predicts a strong connection between two important knot invariants derived from very different background, namely the colored Jones function (a quantum invariant) and the A-polynomial (a geometric invariant). The colored Jones function is a sequence of Laurent polynomials which is known to satisfy a linear q-difference equation. The AJ conjecture states that by writing the linear q-difference equation into an operator form and setting q=1, one gets the A-polynomial. In this talk, I will give an introduction to this conjecture.

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 002号室
Nicolas Bacaër 氏 (研究開発研究所/東大数理)
Some stochastic population models in a random environment (English)
[ 講演概要 ]
Two population models will be considered: an epidemic model [1] and a linear birth-and-death process [2]. The goal is to study the first non-zero eigenvalue, which is related to the speed of convergence towards extinction, using either WKB approximations or probabilistic arguments.
[1] "Le modèle stochastique SIS pour une épidémie dans un environnement aléatoire". Journal of Mathematical Biology (2016)
[2] "Sur les processus linéaires de naissance et de mort sous-critiques dans un environnement aléatoire". Journal of Mathematical Biology (2017)
[ 参考URL ]
http://www.ummisco.ird.fr/perso/bacaer/

### 2017年06月19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

$Q$-prime curvature and Sasakian $\eta$-Einstein manifolds
[ 講演概要 ]
The $Q$-prime curvature is defined for a pseudo-Einstein contact form on a strictly pseudoconvex CR manifold, and its integral, the total $Q$-prime curvature, defines a global CR invariant under some assumptions. In this talk, we will compute the $Q$-prime curvature for Sasakian $\eta$-Einstein manifolds. We will also study the first and the second variation of the total $Q$-prime curvature under deformations of real hypersurfaces at Sasakian $\eta$-Einstein manifolds.

#### 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

Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals (JAPANESE)
[ 講演概要 ]
In this presentation, we present a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples.

### 2017年06月14日(水)

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Yongquan Hu 氏 (Chinese Academy of Sciences, Morningside Center of Mathematics)
Multiplicity one for the mod p cohomology of Shimura curves (ENGLISH)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~t-saito/title_Hu.pdf

### 2017年06月13日(火)

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 002号室

Numerical analysis of viscoelastic fluid models (Japanese)
[ 講演概要 ]
Numerical methods for viscoelastic fluid models are studied. In viscoelastic fluid models the stress tensor is often written as a sum of the viscous stress tensor depending linearly on the strain rate tensor and the extra stress tensor for the viscoelastic contribution. In order to describe the viscoelastic contribution another equation for the extra stress tensor is required. In the talk we mainly deal with the Oldroyd-B and the Peterlin models among several proposed viscoelastic fluid models, and present error estimates of finite element schemes based on the method of characteristics. The key issue in the estimates is the treatment of the divergence of the extra stress tensor appearing in the equation for the velocity and the pressure.

#### 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

Local criteria for non-embeddability of Levi-flat manifolds (JAPANESE)
[ 講演概要 ]
In this talk, we consider the Levi-flat embedding problem. Barrett showed that a smooth Reeb foliation on S^3 cannot be realized as a Levi-flat hypersurface in any complex surfaces. To do this, he focused the relationship between the holonomy along the compact leaf and a system of its defining functions. We will show a new criterion for non-embeddability of Levi-flat manifolds. Our result is a higher dimensional analogue of Barrett's theorem. In particular, this enables us to weaken the compactness assumption. For this purpose, we pose a partial generalization of Ueda theory on the analytic neighborhood structure of complex hypersurfaces. This talk is based on a joint work with Takayuki Koike (Kyoto University).

### 2017年06月12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

On Sp(2)-invariant asymptotically complex hyperbolic Einstein metrics on the 8-ball
[ 講演概要 ]
Following a pioneering work of Pedersen, Hitchin studied SU(2)-invariant asymptotically real/complex hyperbolic (often abbreviated as AH/ACH) solution to the Einstein equation on the 4-dimensional unit open ball. We discuss a similar problem on the 8-ball, on which the quaternionic unitary group Sp(2) acts naturally, focusing on ACH solutions rather than AH ones. The Einstein equation is treated as an asymptotic Dirichlet problem, and the Dirichlet data are Sp(2)-invariant “partially integrable” CR structures on the 7-sphere. A remarkable point is that most of such structures are actually non-integrable. I will present how we can practically compute the formal series expansion of the Einstein ACH metric corresponding to a given Dirichlet data, that is, an invariant partially integrable CR structure on the sphere.

#### 代数幾何学セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室

Ivan Cheltsov 氏 (The University of Edinburgh)
Rational and irrational singular quartic threefolds (English)
[ 講演概要 ]
Burkhardt and Igusa quartics admit a faithful action of the symmetric group of degree 6.
There are other quartic threefolds with this property. All of them are singular.
Beauville proved that all but four of them are irrational. Burkhardt and Igusa quartics are known to be rational.
Two constructions of Todd imply the rationality of the remaining two quartic threefolds.
In this talk, I will give an alternative proof of both these (irrationality and rationality) results.
This proof is based on explicit small resolutions of the so-called Coble fourfold.
This fourfold is the double cover of the four-dimensional projective space branched over Igusa quartic.
This is a joint work with Sasha Kuznetsov and Costya Shramov.

### 2017年06月06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) 122号室
Chen Jiang 氏 (IPMU)
Fano varieties: K-stability and boundedness (English)
[ 講演概要 ]
There are two interesting problems for Fano varieties, K-stability and boundedness.
Significant progress has been made for both problems recently.
In this talk, I will show the boundedness of K-semistable Fano varieties with anti-canonical degree bounded from below, by using methods from birational geometry.
[ 参考URL ]

#### 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

A formula for the action of Dehn twists on the HOMFLY-PT type skein algebra and its application (JAPANESE)
[ 講演概要 ]
We give an explicit formula for the action of the Dehn twist along a simple closed curve of a surface on the completed HOMFLY-PT type skein modules of the surface in terms of the action of the completed HOMFLY-PT type skein algebra of the surface. As an application, using this formula, we construct an invariant for an integral homology 3-sphere which is an element of Q[ρ] [[h]].

### 2017年06月01日(木)

#### 古典解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Homological and monodromy representations of framed braid groups
(JAPANESE)
[ 講演概要 ]
KZ方程式は配置空間上の可積分な微分方程式であり,そのモノドロミー表現を考えることで組みひも群の様々な表現が得られることはよく知られている. 2008年に神保-名古屋-Sunによって合流型のKZ方程式が導入された. この話では, 合流型のKZ方程式のモノドロミー表現を考えることで,枠付組みひも群(リボンの絡み方を表す群)の表現が得られることを説明する.
また, 枠付組みひも群の表現を, ある空間のホモロジー群を用いて構成し, 合流KZ方程式のモノドロミー表現との関係について説明する.

### 2017年05月31日(水)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室

Stark Systems over Gorenstein Rings (JAPANESE)
[ 講演概要 ]
Gorenstein環上の代数体のGalois表現とSelmer構造に対するStark系の定義について紹介する．
これは佐野昂迪氏とBarry Mazur氏，Karl Rubin氏によって独立に定義された単項イデアル環上のStark系の一般化になっている．
さらに，Stark系の成す加群が階数1の自由加群である事，stark系を用いてSelmer群のFittingイデアル全てを記述できる事を示す．

### 2017年05月30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

On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)
[ 講演概要 ]
The hyperbolic torsion polynomial is defined to be the twisted Alexander polynomial associated to the holonomy representation of a hyperbolic knot. Dunfield, Friedl and Jackson conjecture that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjecture and explain its generalization to hyperbolic links.

#### 東京無限可積分系セミナー

17:30-18:30   数理科学研究科棟(駒場) 002号室

$C$ 型ルート系に付随した $Q$ 関数 (JAPANESE)
[ 講演概要 ]
Schur の $Q$ 関数は，対称群の射影表現の研究の中で Schur によ
って導入された対称関数であり，$A$ 型のルート系に付随した
Hall-Littlewood 対称関数において $t=-1$ としたものでもある．
（$t=0$ としたものが Schur 関数である．）この講演では，$C$

とおいたもの（斜交 $Q$ 関数）を考える．斜交 $Q$ 関数に対する
Pfaffian 公式を紹介し，組合せ論的表示を与えるとともに，いく
つかの正値性予想を提示する．

#### 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

Contractible affine threefolds in smooth Fano threefolds (English or Japanese)
[ 講演概要 ]
By the contribution of M. Furushima, N. Nakayama, Th. Peternell and M.
Schneider, it is completed to classify all projective compactifications
of the affine $3$-space $\mathbb{A}^3$ with Picard number one.
As a similar question, T. Kishimoto raised the problem to classify all
triplets $(V, U, D_1 \cup D_2)$ which consist of smooth Fano threefolds
$V$ of Picard number two, contractible affine threefolds $U$ as open
subsets of $V$, and the complements $D_1 \cup D_2 =V \setminus U$.
He also solved this problem when the log canonical divisors $K_V+D_1+D_2$ are not nef.
In this talk, I will discuss the triplets $(V, U, D_1 \cup D_2)$ whose
log canonical divisors are linearly equivalent to zero.
I will also explain how to determine all Fano threefolds $V$ which
appear in such triplets.

### 2017年05月29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

LCK structures on compact solvmanifolds
[ 講演概要 ]
A locally conformal Kähler (in short LCK) manifold is said to be Vaisman if Lee form is parallel with respect to Levi-Civita connection. In this talk, we prove that a Vaisman structure on a compact solvmanifolds depends only on the form of the fundamental 2-form, and it do not depends on a complex structure. As an application, we give the structure theorem for Vaisman (completely solvable) solvmanifolds and LCK nilmanifolds. Moreover, we show the existence of LCK solvmanifolds without Vaisman structures.

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室

On fundamental groups of tensor product II$_1$ factors (English)