## 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
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)
[ 講演参考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)
[ 講演参考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.
[ 講演参考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)

#### 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 ]

### 2017年05月26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) 002号室

ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)
[ 講演概要 ]
リーマン多様体上にはブラウン運動などの

ループ空間上のディリクレ形式で定まる作用素の

が予想できることになる。
この講演では、この問題について、どのような点が難しいか、

### 2017年05月23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) 大講義室号室
Tea: 大講義室前ホワイエ 16:40-17:00
Richard Hain 氏 (Duke University)
Johnson homomorphisms, stable and unstable (ENGLISH)
[ 講演概要 ]
In this talk I will recall how motivic structures (Hodge and/or Galois) on the relative completions of mapping class groups yield non-trivial information about Johnson homomorphisms. I will explain how these motivic structures can be pasted, and why I believe that the genus 1 case is of fundamental importance in studying the higher genus (stable) case.

#### 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

Perverse coherent sheaves on blow-ups at codimension two loci (English)
[ 講演概要 ]
I would like to talk about my recent work in progress.
Let us consider the blow-up X of Y along a subvariety C.
Then the following natural question arises:
What is the relation between moduli space of sheaves on Y
and that of X?
H.Nakajima and K.Yoshioka answered the above question
in the case when Y is a surface and C is a point. They
showed that the moduli spaces are connected by a sequence
of flip-like diagrams. The key ingredient of the proof is
to use perverse coherent sheaves in the sense of T.Bridgeland
and M.Van den Bergh.
In this talk, I will explain how to generalize their theorem
to the case when Y is a smooth projective variety of arbitrary
dimension and C is its codimension two subvariety.

#### 講演会

17:00-18:00   数理科学研究科棟(駒場) 126号室

Frédéric Jouhet 氏 (Université Claude Bernard Lyon 1 / Institut Camille Jordan)
Enumeration of fully commutative elements in classical Coxeter groups (English)
[ 講演概要 ]
An element of a Coxeter group W is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. They index naturally a basis of the (generalized) Temperley-Lieb algebra associated with W. In this talk, focusing on the (affine) type A, I will describe how to
enumerate these elements according to their Coxeter length, in all classical finite and affine Coxeter groups. The methods, which generalize previous work of Stembridge,
involve many combinatorial objects, such as heaps, walks, or parallelogram
polyominoes. This talk is based on joint works with R. Biagioli, M. Bousquet-Mélou and
We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective planes at general nine points.