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過去の記録
過去の記録 ～04/26｜本日 04/27 | 今後の予定 04/28～
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
岸本 崇 氏 (埼玉大学)
Cylinders in del Pezzo fibrations (English )
岸本 崇 氏 (埼玉大学)
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).
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
金 英子 氏 (大阪大学)
Braids and hyperbolic 3-manifolds from simple mixing devices (JAPANESE)
Tea: Common Room 16:30-17:00, RIKEN iTHEMS と共催
金 英子 氏 (大阪大学)
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
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
二木 昭人 氏 (東京大学)
Volume minimization and obstructions to geometric problems
二木 昭人 氏 (東京大学)
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.
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)
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)
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.
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)
http://www.ummisco.ird.fr/perso/bacaer/
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 ]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)
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
竹内 有哉 氏 (東京大学)
$Q$-prime curvature and Sasakian $\eta$-Einstein manifolds
竹内 有哉 氏 (東京大学)
$Q$-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.
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
石谷 謙介 氏 (首都大学東京 大学院理工学研究科)
Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals (JAPANESE)
石谷 謙介 氏 (首都大学東京 大学院理工学研究科)
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.
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
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
野津裕史 氏 (金沢大学理工研究域)
Numerical analysis of viscoelastic fluid models (Japanese)
野津裕史 氏 (金沢大学理工研究域)
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.
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
小川 竜 氏 (東海大学)
Local criteria for non-embeddability of Levi-flat manifolds (JAPANESE)
Tea: Common Room 16:30-17:00
小川 竜 氏 (東海大学)
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).
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
松本 佳彦 氏 (大阪大学)
On Sp(2)-invariant asymptotically complex hyperbolic Einstein metrics on the 8-ball
松本 佳彦 氏 (大阪大学)
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.
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
普段と曜日・部屋が異なります
Ivan Cheltsov 氏 (The University of Edinburgh)
Rational and irrational singular quartic threefolds (English)
普段と曜日・部屋が異なります
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.
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)
https://sites.google.com/site/chenjiangmath/
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 ]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.
https://sites.google.com/site/chenjiangmath/
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
辻 俊輔 氏 (東京大学大学院数理科学研究科)
A formula for the action of Dehn twists on the HOMFLY-PT type skein algebra and its application (JAPANESE)
Tea: Common Room 16:30-17:00
辻 俊輔 氏 (東京大学大学院数理科学研究科)
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]].
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
池田 曉志 氏 (東京大学 IPMU)
Homological and monodromy representations of framed braid groups
(JAPANESE)
池田 曉志 氏 (東京大学 IPMU)
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.
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
坂本龍太郎 氏 (東京大学数理科学研究科)
Stark Systems over Gorenstein Rings (JAPANESE)
坂本龍太郎 氏 (東京大学数理科学研究科)
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．
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
森藤 孝之 氏 (慶應義塾大学)
On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)
Tea: Common Room 16:30-17:00
森藤 孝之 氏 (慶應義塾大学)
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.
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
岡田 聡一 氏 (名大多元数理)
$C$ 型ルート系に付随した $Q$ 関数 (JAPANESE)
岡田 聡一 氏 (名大多元数理)
$C$ 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，$C$
型のルート系に付随した Hall-Littlewood 関数において $t=-1$
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．
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，$C$
型のルート系に付随した Hall-Littlewood 関数において $t=-1$
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
長岡 大 氏 (東大数理)
Contractible affine threefolds in smooth Fano threefolds (English or Japanese)
長岡 大 氏 (東大数理)
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.
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
澤井 洋 氏 (沼津工業高等専門学校)
LCK structures on compact solvmanifolds
澤井 洋 氏 (沼津工業高等専門学校)
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.
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
磯野優介 氏 (京大数理研)
On fundamental groups of tensor product II$_1$ factors (English)
磯野優介 氏 (京大数理研)
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
中島 秀太 氏 (京都大学 数理解析研究所)
最速浸透問題での原点出発の無限測地線の数について (JAPANESE)
中島 秀太 氏 (京都大学 数理解析研究所)
最速浸透問題での原点出発の無限測地線の数について (JAPANESE)
[ 講演概要 ]
本講演ではFirst Passage Percolationのgeodesicsについて、最近得られたcoalescenceと呼ばれる性質について述べる。その性質を用いて、infinite geodesics全体の数と原点出発に制限したときの数が一致すること、その系として原点出発のinfinite geodesicの数が定数であることを示す。
本講演ではFirst Passage Percolationのgeodesicsについて、最近得られたcoalescenceと呼ばれる性質について述べる。その性質を用いて、infinite geodesics全体の数と原点出発に制限したときの数が一致すること、その系として原点出発のinfinite geodesicの数が定数であることを示す。
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
会田茂樹 氏 (東京大学大学院数理科学研究科)
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)
会田茂樹 氏 (東京大学大学院数理科学研究科)
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
自然な確率過程が定義でき、ブラウン運動を通して解析および幾何の問題を
研究することができる。
一方、このブラウン運動が定める道の空間やループ空間上の
確率測度は道のエネルギーを指数の肩にのせた汎関数を重みに持つ形式的
経路積分表示を持つ。この事から、極めて良い状況ならば
ループ空間上のディリクレ形式で定まる作用素の
分散0の極限(準古典極限に相当する)の下でのスペクトルギャップの漸近挙動
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、
何が知られているかをお話したい。
リーマン多様体上にはブラウン運動などの
自然な確率過程が定義でき、ブラウン運動を通して解析および幾何の問題を
研究することができる。
一方、このブラウン運動が定める道の空間やループ空間上の
確率測度は道のエネルギーを指数の肩にのせた汎関数を重みに持つ形式的
経路積分表示を持つ。この事から、極めて良い状況ならば
ループ空間上のディリクレ形式で定まる作用素の
分散0の極限(準古典極限に相当する)の下でのスペクトルギャップの漸近挙動
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、
何が知られているかをお話したい。
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)
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.
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.
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