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過去の記録
過去の記録 ～01/25｜本日 01/26 | 今後の予定 01/27～
2018年12月07日(金)
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 002号室
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (5)
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (5)
2018年12月06日(木)
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
Francesco Ravanini 氏 (University of Bologna)
Integrability and TBA in non-equilibrium emergent hydrodynamics (ENGLISH)
Francesco Ravanini 氏 (University of Bologna)
Integrability and TBA in non-equilibrium emergent hydrodynamics (ENGLISH)
[ 講演概要 ]
The paradigm of investigating non-equilibrium phenomena by considering stationary states of emergent hydrodynamics has attracted a lot of attention in the last years. Recent proposals of an exact approach in integrable cases, making use of TBA techniques, are presented and discussed.
The paradigm of investigating non-equilibrium phenomena by considering stationary states of emergent hydrodynamics has attracted a lot of attention in the last years. Recent proposals of an exact approach in integrable cases, making use of TBA techniques, are presented and discussed.
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 128号室
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (4)
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (4)
2018年12月05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
Frederic Latremoliere 氏 (Univ. Denver)
The Gromov-Hausdorff Propinquity
Frederic Latremoliere 氏 (Univ. Denver)
The Gromov-Hausdorff Propinquity
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 002号室
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (3)
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (3)
統計数学セミナー
13:00-15:00 数理科学研究科棟(駒場) 156号室
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 2:Representation results for the Gaussian processes. Financial applications of fractional Brownian motion
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 2:Representation results for the Gaussian processes. Financial applications of fractional Brownian motion
[ 講演概要 ]
Arbitrage with fBm: why it appears. How to present any contingent claim via self-financing strategy on the financial market involving fBm. Absence of arbitrage for the mixed models. Fractional -Uhlenbeck and fractional Cox-Ingersoll-Ross processes as the models for stochastic volatility.
Arbitrage with fBm: why it appears. How to present any contingent claim via self-financing strategy on the financial market involving fBm. Absence of arbitrage for the mixed models. Fractional -Uhlenbeck and fractional Cox-Ingersoll-Ross processes as the models for stochastic volatility.
統計数学セミナー
15:00-17:00 数理科学研究科棟(駒場) 156号室
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 3:Statistical parameter estimation for the diffusion processes and in the models involving fBm
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 3:Statistical parameter estimation for the diffusion processes and in the models involving fBm
[ 講演概要 ]
Drift parameter estimation in the standard diffusion model and its strong consistency. Hurst and drift parameter estimation in the models involving fBm and in the mixed models. Asymptotic properties. Estimation of the diffusion parameter.
Drift parameter estimation in the standard diffusion model and its strong consistency. Hurst and drift parameter estimation in the models involving fBm and in the mixed models. Asymptotic properties. Estimation of the diffusion parameter.
2018年12月04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
Vincent Florens 氏 (Université de Pau et des Pays de l'Adour)
Slopes and concordance of links (ENGLISH)
Tea: Common Room 16:30-17:00
Vincent Florens 氏 (Université de Pau et des Pays de l'Adour)
Slopes and concordance of links (ENGLISH)
[ 講演概要 ]
We define the slope of a link associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a multivariate generalization of the Kojima-Yamasaki η-function. It is the ratio of two Conway potentials, provided that the latter makes sense; otherwise, it is a new invariant. We present several examples and discuss the invariance by concordance. Joint with A. Degtyarev and A. Lecuona.
We define the slope of a link associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a multivariate generalization of the Kojima-Yamasaki η-function. It is the ratio of two Conway potentials, provided that the latter makes sense; otherwise, it is a new invariant. We present several examples and discuss the invariance by concordance. Joint with A. Degtyarev and A. Lecuona.
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 002号室
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (2)
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (2)
統計数学セミナー
15:00-17:00 数理科学研究科棟(駒場) 126号室
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 1: Elements of fractional calculus
How to connect the fractional Brownian motion to the Wiener process. Stochastic integration w.r.t. fBm and stochastic differential equations involving fB
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 1: Elements of fractional calculus
How to connect the fractional Brownian motion to the Wiener process. Stochastic integration w.r.t. fBm and stochastic differential equations involving fB
[ 講演概要 ]
Fractional integrals and fractional derivatives. Wiener and stochastic integration w.r.t. the fractional Brownian motion. Representations of fBm via a Wiener process and vice versa. Elements of the fractional stochastic calculus. Stochastic differential equations involving fBm: existence, uniqueness, properties of the solutions. Simplest models: fractional Ornstein-Uhlenbeck and fractional Cox-Ingersoll-Ross processes.
Fractional integrals and fractional derivatives. Wiener and stochastic integration w.r.t. the fractional Brownian motion. Representations of fBm via a Wiener process and vice versa. Elements of the fractional stochastic calculus. Stochastic differential equations involving fBm: existence, uniqueness, properties of the solutions. Simplest models: fractional Ornstein-Uhlenbeck and fractional Cox-Ingersoll-Ross processes.
2018年12月03日(月)
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 002号室
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (1)
戸松玲治 氏 (北海道大学)
従順C*テンソル圏のvon Neumann環への中心的自由作用について (1)
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
細野元気 氏 (東京大学)
多変数関数論における変動理論 (JAPANESE)
細野元気 氏 (東京大学)
多変数関数論における変動理論 (JAPANESE)
[ 講演概要 ]
関数論において、領域の擬凸変動に関する様々な量の劣調和性が知られている。例えば、山口によるRobin定数の変動、米谷-山口によるBergman核の変動が知られている。また、Bergman核の変動理論のある種の一般化として、Berndtssonにより、$L^2$正則関数のなす空間の変動に関する正曲率性が知られている。これらの理論は$L^2$拡張定理とも深い関係が知られており、その意味でも興味深い。本講演では、これらの理論に関して知られている結果を紹介し、Robin定数の変動問題の多変数化として東川擬距離の変動問題についての考察を行う。
関数論において、領域の擬凸変動に関する様々な量の劣調和性が知られている。例えば、山口によるRobin定数の変動、米谷-山口によるBergman核の変動が知られている。また、Bergman核の変動理論のある種の一般化として、Berndtssonにより、$L^2$正則関数のなす空間の変動に関する正曲率性が知られている。これらの理論は$L^2$拡張定理とも深い関係が知られており、その意味でも興味深い。本講演では、これらの理論に関して知られている結果を紹介し、Robin定数の変動問題の多変数化として東川擬距離の変動問題についての考察を行う。
Lie群論・表現論セミナー
17:00-18:00 数理科学研究科棟(駒場) 126号室
Ali Baklouti 氏 (Sfax 大学)
Monomial representations of discrete type and differential operators. (English)
Ali Baklouti 氏 (Sfax 大学)
Monomial representations of discrete type and differential operators. (English)
[ 講演概要 ]
Let $G$ be an exponential solvable Lie group and $\tau$ a monomial representation of $G$, an induced representation from a connected closed subgroup of $G$ of a unitary character. It is well known that $\tau$ disintegrates into irreducible factors and the multiplicities of each isotypic component are explicitly determined. In the case where $G$ is nilpotent, these multiplicities are either finite or infinite almost everywhere, with respect to the disintegration's measure. We associate to $\tau$ an algebra of differential operators and it is shown that in the nilpotent case, the commutativity of this algebra is equivalent to the finiteness of the multiplicities of $\tau$. In the exponential case, we define the notion of monomial representation of discrete type. In this case, we show that such an equivalence does not hold and this answers a question posed by M. Duflo. This is a joint work with H. Fujiwara and J. Ludwig.
Let $G$ be an exponential solvable Lie group and $\tau$ a monomial representation of $G$, an induced representation from a connected closed subgroup of $G$ of a unitary character. It is well known that $\tau$ disintegrates into irreducible factors and the multiplicities of each isotypic component are explicitly determined. In the case where $G$ is nilpotent, these multiplicities are either finite or infinite almost everywhere, with respect to the disintegration's measure. We associate to $\tau$ an algebra of differential operators and it is shown that in the nilpotent case, the commutativity of this algebra is equivalent to the finiteness of the multiplicities of $\tau$. In the exponential case, we define the notion of monomial representation of discrete type. In this case, we show that such an equivalence does not hold and this answers a question posed by M. Duflo. This is a joint work with H. Fujiwara and J. Ludwig.
2018年11月30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
三竹大寿 氏 (東京大学大学院数理科学研究科)
粘性解理論とAubry-Mather理論 (日本語)
三竹大寿 氏 (東京大学大学院数理科学研究科)
粘性解理論とAubry-Mather理論 (日本語)
[ 講演概要 ]
力学系におけるAubry-Mather理論は，偏微分方程式論の粘性解理論を導入することで相互の理論がより明瞭なものとなった．この理論は，Kolmogorov-Arnold-Moser (KAM) 理論を背景に偏微分方程式論における弱解を利用した理論ということで，弱KAM 理論と提唱された．講演者は，最適確率制御問題に現れる退化粘性HJ方程式と呼ばれるクラスの方程式に適用できるよう，弱KAM理論の一般化に取り組んできた．従来の弱KAM理論は決定論的な力学系しか扱えないため，新しい道具立てを必要とした．この点を偏微分方程式論から見直すことで決定論及び確率論を統一する一つの新しい枠組みを作ることに成功してきた．その応用として，漸近解析（長時間挙動，ディスカウント近似）ついて解決した．本講演では，関連した内容について，次の２点に焦点をおいて話す．
(i) 非線形随伴法を利用した漸近解析：非線形随伴法を利用した漸近解析として，退化粘性HJ方程式の長時間挙動，ディスカウント近似の極限に関する結果について紹介する．
(ii) 均質化問題の解の収束率 ：HJ方程式の均質化問題は，1987年にLions,Papanicolaou, Varadhanによる有名な未発表論文により提唱された後，劇的に研究が進展し，大多数の論文が発表された．しかし，PDE的手法だけでは収束率について得ることは難しかった．本講演では，Aubry-Mather理論の観点から問題を見直すことで得られた収束率の結果について紹介する．
力学系におけるAubry-Mather理論は，偏微分方程式論の粘性解理論を導入することで相互の理論がより明瞭なものとなった．この理論は，Kolmogorov-Arnold-Moser (KAM) 理論を背景に偏微分方程式論における弱解を利用した理論ということで，弱KAM 理論と提唱された．講演者は，最適確率制御問題に現れる退化粘性HJ方程式と呼ばれるクラスの方程式に適用できるよう，弱KAM理論の一般化に取り組んできた．従来の弱KAM理論は決定論的な力学系しか扱えないため，新しい道具立てを必要とした．この点を偏微分方程式論から見直すことで決定論及び確率論を統一する一つの新しい枠組みを作ることに成功してきた．その応用として，漸近解析（長時間挙動，ディスカウント近似）ついて解決した．本講演では，関連した内容について，次の２点に焦点をおいて話す．
(i) 非線形随伴法を利用した漸近解析：非線形随伴法を利用した漸近解析として，退化粘性HJ方程式の長時間挙動，ディスカウント近似の極限に関する結果について紹介する．
(ii) 均質化問題の解の収束率 ：HJ方程式の均質化問題は，1987年にLions,Papanicolaou, Varadhanによる有名な未発表論文により提唱された後，劇的に研究が進展し，大多数の論文が発表された．しかし，PDE的手法だけでは収束率について得ることは難しかった．本講演では，Aubry-Mather理論の観点から問題を見直すことで得られた収束率の結果について紹介する．
2018年11月28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
山下真由子 氏 (東大数理)
Localization of signature for singular fiber bundles
山下真由子 氏 (東大数理)
Localization of signature for singular fiber bundles
2018年11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
原伸生 氏 (東京農工大)
Frobenius summands and the finite F-representation type (TBA)
原伸生 氏 (東京農工大)
Frobenius summands and the finite F-representation type (TBA)
[ 講演概要 ]
We are motivated by a question arising from commutative algebra, asking what kind of
graded rings in positive characteristic p have finite F-representation type. In geometric
setting, this is related to the problem to looking out for Frobenius summands. Namely,
given aline bundle L on a projective variety X, we want to know how many and what
kind of indecomposable direct summands appear in the direct sum decomposition of
the iterated Frobenius push-forwards of L. We will consider the problem in the following
two cases, although the present situation in (2) is far from satisfactory.
(1) two-dimensional normal graded rings (a joint work with Ryo Ohkawa)
(2) the anti-canonical ring of a quintic del Pezzo surface
We are motivated by a question arising from commutative algebra, asking what kind of
graded rings in positive characteristic p have finite F-representation type. In geometric
setting, this is related to the problem to looking out for Frobenius summands. Namely,
given aline bundle L on a projective variety X, we want to know how many and what
kind of indecomposable direct summands appear in the direct sum decomposition of
the iterated Frobenius push-forwards of L. We will consider the problem in the following
two cases, although the present situation in (2) is far from satisfactory.
(1) two-dimensional normal graded rings (a joint work with Ryo Ohkawa)
(2) the anti-canonical ring of a quintic del Pezzo surface
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
加藤 本子 氏 (東京大学大学院数理科学研究科)
Fixed points for group actions on non-positively curved spaces (JAPANESE)
Tea: Common Room 16:30-17:00
加藤 本子 氏 (東京大学大学院数理科学研究科)
Fixed points for group actions on non-positively curved spaces (JAPANESE)
[ 講演概要 ]
In this talk, we introduce a fixed point property of groups which is a broad generalization of Serre's property FA, and give a criterion for groups to have such a property. We also apply the criterion to show that various generalizations of Thompson's group T have fixed points whenever they act on finite dimensional non-positively curved metric spaces, including CAT(0) spaces. Since Thompson's group T is known to have fixed point free actions on infinite dimensional CAT(0) spaces, it follows that there is a group which acts on infinite dimensional CAT(0) spaces without global fixed points, but not on finite dimensional ones.
In this talk, we introduce a fixed point property of groups which is a broad generalization of Serre's property FA, and give a criterion for groups to have such a property. We also apply the criterion to show that various generalizations of Thompson's group T have fixed points whenever they act on finite dimensional non-positively curved metric spaces, including CAT(0) spaces. Since Thompson's group T is known to have fixed point free actions on infinite dimensional CAT(0) spaces, it follows that there is a group which acts on infinite dimensional CAT(0) spaces without global fixed points, but not on finite dimensional ones.
2018年11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
糟谷久矢 氏 (大阪大学)
DGA-Models of variations of mixed Hodge structures (JAPANESE)
糟谷久矢 氏 (大阪大学)
DGA-Models of variations of mixed Hodge structures (JAPANESE)
[ 講演概要 ]
Mixed Hodge structureは（Projectiveとは限らない)代数多様体のコホモロジー等に現れる非常に重要な構造です。Variations of mixed Hodge structures(VMHS)とは複素多様体をパラメーターとして複素幾何学的に良い振る舞いをしながら変化するMixed Hodge structureたちのことです。今回のお話ではこのVMHSの代数的なモデルについて考えてみたいと思いいます。具体的にはMorganの Mixed Hodge diagramと呼ばれるケーラー多様体のde Rham複体（あるいは対数的 de Rham複体）を積構造込みで模した代数的な対象に対して、”(Unipotent)VMHSのようなもの"を定義します。このVMHSのようなものは純粋に代数的に定義されたものであるため、本来のVMHSのようにベースとなる空間のパラメーターごとにMixed Hodge structureをとる（ファイバーをとる）ことを自然にはできません。本講演ではこの"VMHSのようなもの”からいかにファイバーを取るかということをメインテーマにしてお話ししたいと思います。さらに時間があれば、本結果の幾何学的応用についてもお話ししたいと思います。特に今回の結果によりMorganのMixed Hodge structureとHainのMixed Hodge structureの深い関係が見えることをお話ししたいと思います。
Mixed Hodge structureは（Projectiveとは限らない)代数多様体のコホモロジー等に現れる非常に重要な構造です。Variations of mixed Hodge structures(VMHS)とは複素多様体をパラメーターとして複素幾何学的に良い振る舞いをしながら変化するMixed Hodge structureたちのことです。今回のお話ではこのVMHSの代数的なモデルについて考えてみたいと思いいます。具体的にはMorganの Mixed Hodge diagramと呼ばれるケーラー多様体のde Rham複体（あるいは対数的 de Rham複体）を積構造込みで模した代数的な対象に対して、”(Unipotent)VMHSのようなもの"を定義します。このVMHSのようなものは純粋に代数的に定義されたものであるため、本来のVMHSのようにベースとなる空間のパラメーターごとにMixed Hodge structureをとる（ファイバーをとる）ことを自然にはできません。本講演ではこの"VMHSのようなもの”からいかにファイバーを取るかということをメインテーマにしてお話ししたいと思います。さらに時間があれば、本結果の幾何学的応用についてもお話ししたいと思います。特に今回の結果によりMorganのMixed Hodge structureとHainのMixed Hodge structureの深い関係が見えることをお話ししたいと思います。
2018年11月21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
Yves André 氏 (Université Pierre et Marie Curie)
Poncelet games, confinement of algebraic integers, and hyperbolic Ax-Schanuel (ENGLISH)
Yves André 氏 (Université Pierre et Marie Curie)
Poncelet games, confinement of algebraic integers, and hyperbolic Ax-Schanuel (ENGLISH)
[ 講演概要 ]
We shall theorize and exemplify the problem of torsion values of sections of abelian schemes. This « unlikely intersection problem », which arises in various diophantine and algebro-geometric contexts, can be reformulated in a non-trivial way in terms of Kodaira-Spencer maps. A key tool toward its general solution is then provided by recent theorems of Ax-Schanuel type (joint work with P. Corvaja, U. Zannier, and partly Z. Gao).
We shall theorize and exemplify the problem of torsion values of sections of abelian schemes. This « unlikely intersection problem », which arises in various diophantine and algebro-geometric contexts, can be reformulated in a non-trivial way in terms of Kodaira-Spencer maps. A key tool toward its general solution is then provided by recent theorems of Ax-Schanuel type (joint work with P. Corvaja, U. Zannier, and partly Z. Gao).
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
守山貴顕 氏 (東大数理)
Orbit equivalence classes for free actions of free products of infinite abelian groups
守山貴顕 氏 (東大数理)
Orbit equivalence classes for free actions of free products of infinite abelian groups
2018年11月20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
中島 幸喜 氏 (東京電機大)
Artin-Mazur height, Yobuko height and
Hodge-Wittt cohomologies
中島 幸喜 氏 (東京電機大)
Artin-Mazur height, Yobuko height and
Hodge-Wittt cohomologies
[ 講演概要 ]
A few years ago Yobuko has introduced the notion of
a delicate invariant for a proper smooth scheme over a perfect field $k$
of finite characteristic. (We call this invariant Yobuko height.)
This generalize the notion of the F-splitness due to Mehta-Srinivas.
In this talk we give relations between Artin-Mazur heights
and Yobuko heights. We also give a finiteness result on
Hodge-Witt cohomologies of a proper smooth scheme $X$ over $k$
with finite Yobuko height. If time permits, we give a cofinite type result on
the $p$-primary torsion part of Chow group of of $X$
of codimension 2 if $\dim X=3$.
A few years ago Yobuko has introduced the notion of
a delicate invariant for a proper smooth scheme over a perfect field $k$
of finite characteristic. (We call this invariant Yobuko height.)
This generalize the notion of the F-splitness due to Mehta-Srinivas.
In this talk we give relations between Artin-Mazur heights
and Yobuko heights. We also give a finiteness result on
Hodge-Witt cohomologies of a proper smooth scheme $X$ over $k$
with finite Yobuko height. If time permits, we give a cofinite type result on
the $p$-primary torsion part of Chow group of of $X$
of codimension 2 if $\dim X=3$.
離散数理モデリングセミナー
15:00-16:30 数理科学研究科棟(駒場) 002号室
甘利俊一 氏 (理化学研究所)
情報幾何とその応用ー深層学習の解明に向けて
甘利俊一 氏 (理化学研究所)
情報幾何とその応用ー深層学習の解明に向けて
[ 講演概要 ]
情報幾何の基本的考えを説明した後で、深層学習にどう関係するのか、統計神経力学の立場から話をする。
情報幾何の基本的考えを説明した後で、深層学習にどう関係するのか、統計神経力学の立場から話をする。
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
逆井 卓也 氏 (東京大学大学院数理科学研究科)
Torelli group, Johnson kernel and invariants of homology 3-spheres (JAPANESE)
Tea: Common Room 16:30-17:00
逆井 卓也 氏 (東京大学大学院数理科学研究科)
Torelli group, Johnson kernel and invariants of homology 3-spheres (JAPANESE)
[ 講演概要 ]
There are two filtrations of the Torelli group: One is the lower central series and the other is the Johnson filtration. They are closely related to Johnson homomorphisms as well as finite type invariants of homology 3-spheres. We compare the associated graded Lie algebras of the filtrations and report our explicit computational results. Then we discuss some applications of our computations. In particular, we give an explicit description of the rational abelianization of the Johnson kernel. This is a joint work with Shigeyuki Morita and Masaaki Suzuki.
There are two filtrations of the Torelli group: One is the lower central series and the other is the Johnson filtration. They are closely related to Johnson homomorphisms as well as finite type invariants of homology 3-spheres. We compare the associated graded Lie algebras of the filtrations and report our explicit computational results. Then we discuss some applications of our computations. In particular, we give an explicit description of the rational abelianization of the Johnson kernel. This is a joint work with Shigeyuki Morita and Masaaki Suzuki.
2018年11月19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) 128号室
Fabio Toninelli 氏 (University Lyon 1)
Two-dimensional stochastic interface growth (ENGLISH)
http://math.univ-lyon1.fr/~toninelli/
Fabio Toninelli 氏 (University Lyon 1)
Two-dimensional stochastic interface growth (ENGLISH)
[ 講演概要 ]
I will discuss stochastic growth of two-dimensional, discrete interfaces, especially models in the so-called Anisotropic KPZ (AKPZ) class, that has the same large-scale behavior as the Stochastic Heat equation with additive noise. I will focus in particular on: 1) the relation between AKPZ exponents, convexity properties of the speed of growth and the preservation of the Gibbs property; and 2) the relation between singularities of the speed of growth and the occurrence of "smooth" (i.e. non-rough) stationary states.
[ 講演参考URL ]I will discuss stochastic growth of two-dimensional, discrete interfaces, especially models in the so-called Anisotropic KPZ (AKPZ) class, that has the same large-scale behavior as the Stochastic Heat equation with additive noise. I will focus in particular on: 1) the relation between AKPZ exponents, convexity properties of the speed of growth and the preservation of the Gibbs property; and 2) the relation between singularities of the speed of growth and the occurrence of "smooth" (i.e. non-rough) stationary states.
http://math.univ-lyon1.fr/~toninelli/
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
Gerard Freixas i Montplet 氏 (Centre National de la Recherche Scientifique)
BCOV invariants of Calabi-Yau varieties (ENGLISH)
Gerard Freixas i Montplet 氏 (Centre National de la Recherche Scientifique)
BCOV invariants of Calabi-Yau varieties (ENGLISH)
[ 講演概要 ]
The BCOV invariant of Calabi-Yau threefolds was introduced by Fang-Lu-Yoshikawa, themselves inspired by physicists Bershadsky-Cecotti-Ooguri-Vafa. It is a real number, obtained from a combination of holomorphic analytic torsion, and suitably normalized so that it only depends on the complex structure of the threefold. It is conjecturaly expected to encode genus 1 Gromov-Witten invariants of a mirror Calabi-Yau threefold. In order to confirm this prediction for a remarkable example, Fang-Lu-Yoshikawa studied the asymptotic behavior for degenerating families of Calabi-Yau threefolds acquiring at most ordinary double point (ODP) singularities. Their methods rely on former results by Yoshikawa on the singularities of Quillen metrics, together with more classical arguments in the theory of degenerations of Hodge structures and Hodge metrics. In this talk I will present joint work with Dennis Eriksson (Chalmers) and Christophe Mourougane (Rennes), where we extend the construction of the BCOV invariant to any dimension and we give precise asymptotic formulas for degenerating families of Calabi-Yau manifolds. Under several hypothesis on the geometry of the singularities acquired, our general formulas drastically simplify and prove some conjectures or predictions in the literature (Liu-Xia for semi-stable minimal families in dimension 3, Klemm-Pandharipande for ODP singularities in dimension 4, etc.). For this, we slightly improve Yoshikawa's results on the singularities of Quillen metrics, and we also provide a complement to Schmid's asymptotics of Hodge metrics when the monodromy transformations are non-unipotent.
The BCOV invariant of Calabi-Yau threefolds was introduced by Fang-Lu-Yoshikawa, themselves inspired by physicists Bershadsky-Cecotti-Ooguri-Vafa. It is a real number, obtained from a combination of holomorphic analytic torsion, and suitably normalized so that it only depends on the complex structure of the threefold. It is conjecturaly expected to encode genus 1 Gromov-Witten invariants of a mirror Calabi-Yau threefold. In order to confirm this prediction for a remarkable example, Fang-Lu-Yoshikawa studied the asymptotic behavior for degenerating families of Calabi-Yau threefolds acquiring at most ordinary double point (ODP) singularities. Their methods rely on former results by Yoshikawa on the singularities of Quillen metrics, together with more classical arguments in the theory of degenerations of Hodge structures and Hodge metrics. In this talk I will present joint work with Dennis Eriksson (Chalmers) and Christophe Mourougane (Rennes), where we extend the construction of the BCOV invariant to any dimension and we give precise asymptotic formulas for degenerating families of Calabi-Yau manifolds. Under several hypothesis on the geometry of the singularities acquired, our general formulas drastically simplify and prove some conjectures or predictions in the literature (Liu-Xia for semi-stable minimal families in dimension 3, Klemm-Pandharipande for ODP singularities in dimension 4, etc.). For this, we slightly improve Yoshikawa's results on the singularities of Quillen metrics, and we also provide a complement to Schmid's asymptotics of Hodge metrics when the monodromy transformations are non-unipotent.
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