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過去の記録 ～09/23｜本日 09/24 | 今後の予定 09/25～
2010年09月28日(火)
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Pavel Exner 氏 (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
Pavel Exner 氏 (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
[ 講演概要 ]
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.
2010年09月14日(火)
東京無限可積分系セミナー
10:30-14:00 数理科学研究科棟(駒場) 117号室
柳田 伸太郎 氏 (神戸大) 10:30-11:30
AGT予想とrecursion formula (JAPANESE)
山田 裕二 氏 (立教大) 13:00-14:00
BelavinのR行列の3角極限に対する反射方程式の解の分類 (JAPANESE)
柳田 伸太郎 氏 (神戸大) 10:30-11:30
AGT予想とrecursion formula (JAPANESE)
山田 裕二 氏 (立教大) 13:00-14:00
BelavinのR行列の3角極限に対する反射方程式の解の分類 (JAPANESE)
2010年09月13日(月)
東京無限可積分系セミナー
10:30-15:30 数理科学研究科棟(駒場) 117号室
笠谷 昌弘 氏 (東大数理) 10:30-11:30
$C^¥vee C$型DAHAの多項式表現と境界付きqKZ方程式について (JAPANESE)
CFT , モノドロミー保存変形, Nekrasov関数 (JAPANESE)
Twisted de Rham theory---resonances and the non-resonance (JAPANESE)
笠谷 昌弘 氏 (東大数理) 10:30-11:30
$C^¥vee C$型DAHAの多項式表現と境界付きqKZ方程式について (JAPANESE)
[ 講演概要 ]
まずC-check-C型ダブルアフィンヘッケ代数と
その多項式表現について基本的な事柄を復習する.
次に, 多項式表現の観点から
境界付きqKZ方程式を導入しその解を構成する.
山田 泰彦 氏 (神戸大) 13:00-14:00まずC-check-C型ダブルアフィンヘッケ代数と
その多項式表現について基本的な事柄を復習する.
次に, 多項式表現の観点から
境界付きqKZ方程式を導入しその解を構成する.
CFT , モノドロミー保存変形, Nekrasov関数 (JAPANESE)
[ 講演概要 ]
共形場理論の相関関数と超対称ゲージ理論の分配関数の関係
(Alday-Gaiotto-Tachikawa予想)に関して, 微分方程式
(特に
モノドロミー保存変形)の観点から紹介する.
三町 勝久 氏 (東工大) 14:30-15:30共形場理論の相関関数と超対称ゲージ理論の分配関数の関係
(Alday-Gaiotto-Tachikawa予想)に関して, 微分方程式
(特に
モノドロミー保存変形)の観点から紹介する.
Twisted de Rham theory---resonances and the non-resonance (JAPANESE)
2010年09月12日(日)
東京無限可積分系セミナー
10:30-17:00 数理科学研究科棟(駒場) 117号室
森田 英章 氏 (室蘭工大) 10:30-11:30
マクドナルド多項式のベキ根における分解公式 (JAPANESE)
W代数と対称多項式 (JAPANESE)
Quantizing the difference Painlev¥'e VI equation (JAPANESE)
1の巾根でのMacdonald多項式の分解公式の組合せ論的証明について (JAPANESE)
森田 英章 氏 (室蘭工大) 10:30-11:30
マクドナルド多項式のベキ根における分解公式 (JAPANESE)
[ 講演概要 ]
We consider a combinatorial property of Macdonald polynomials at roots
of unity.
If we made some plethystic substitution to the variables,
Macdonald polynomials are subjected to a certain decomposition rule
when a parameter is specialized at roots of unity.
We review the result and give an outline of the proof.
This talk is based on a joint work with F. Descouens.
白石 潤一 氏 (東大数理) 13:00-14:00We consider a combinatorial property of Macdonald polynomials at roots
of unity.
If we made some plethystic substitution to the variables,
Macdonald polynomials are subjected to a certain decomposition rule
when a parameter is specialized at roots of unity.
We review the result and give an outline of the proof.
This talk is based on a joint work with F. Descouens.
W代数と対称多項式 (JAPANESE)
[ 講演概要 ]
It is well known that we have the factorization property of the Macdonald polynomials under the principal specialization $x=(1,t,t^2,t^3,¥cdots)$. We try to better understand this situation in terms of the Ding-Iohara algebra or the deformend $W$-algebra. Some conjectures are presented in the case of $N$-fold tensor representation of the Fock modules.
長谷川 浩司 氏 (東北大) 14:30-15:30It is well known that we have the factorization property of the Macdonald polynomials under the principal specialization $x=(1,t,t^2,t^3,¥cdots)$. We try to better understand this situation in terms of the Ding-Iohara algebra or the deformend $W$-algebra. Some conjectures are presented in the case of $N$-fold tensor representation of the Fock modules.
Quantizing the difference Painlev¥'e VI equation (JAPANESE)
[ 講演概要 ]
I will review two constructions for quantum (=non-commutative) version of
q-difference Painleve VI equation.
沼田 泰英 氏 (東大情報理工) 16:00-17:00I will review two constructions for quantum (=non-commutative) version of
q-difference Painleve VI equation.
1の巾根でのMacdonald多項式の分解公式の組合せ論的証明について (JAPANESE)
[ 講演概要 ]
The subject of this talk is a factorization formula for the special
values of modied Macdonald polynomials at roots of unity.
We give a combinatorial proof of the formula, via a result by
Haglund--Haiman--Leohr, for some special classes of partitions,
including two column partitions.
(This talk is based on a joint work with F. Descouens and H. Morita.)
The subject of this talk is a factorization formula for the special
values of modied Macdonald polynomials at roots of unity.
We give a combinatorial proof of the formula, via a result by
Haglund--Haiman--Leohr, for some special classes of partitions,
including two column partitions.
(This talk is based on a joint work with F. Descouens and H. Morita.)
2010年09月11日(土)
東京無限可積分系セミナー
13:00-17:00 数理科学研究科棟(駒場) 117号室
伊藤 雅彦 氏 (東京電機大 未来科学部 数学系列) 13:00-14:00
$BC_n$型$q$-超幾何関数の三項間隣接関係式とその応用 (JAPANESE)
TBA (JAPANESE)
瀧 雅人 氏 (京大基礎物理学研究所) 16:00-17:00
AGT予想と幾何工学 (JAPANESE)
伊藤 雅彦 氏 (東京電機大 未来科学部 数学系列) 13:00-14:00
$BC_n$型$q$-超幾何関数の三項間隣接関係式とその応用 (JAPANESE)
[ 講演概要 ]
この講演における$BC_n$型$q$-超幾何関数とは、
ガウスの超幾何関数の積分表示のある種の$q$-類似であり、
古典的には(very-)well-poised と呼ばれるクラスの$q$-超幾何級数で、
一般には$C_n$型ワイル群対称性をもつ多重$q$-積分($q$-級数)で定義される。
この$q$-超幾何級数に含まれるパラメータの個数が6+1個の場合に、
ある対称多項式の族を定義すると(ここではBC型補間多項式と呼ぶ)、
ガウスの超幾何関数の隣接関係式に類似の三項間関係式が
成立することがわかったので紹介する。三項間関係式を繰り返し使うことにより、
この$q$-超幾何級数が満たすランクn+1の一階連立$q$-差分方程式系を
具体的に表示することができる。応用として、この具体的表示から、
Gustafson の$q$-積分の無限積表示の別証明が得られるので、
それも紹介したい。
野海 正俊 氏 (神戸大) 14:30-15:30この講演における$BC_n$型$q$-超幾何関数とは、
ガウスの超幾何関数の積分表示のある種の$q$-類似であり、
古典的には(very-)well-poised と呼ばれるクラスの$q$-超幾何級数で、
一般には$C_n$型ワイル群対称性をもつ多重$q$-積分($q$-級数)で定義される。
この$q$-超幾何級数に含まれるパラメータの個数が6+1個の場合に、
ある対称多項式の族を定義すると(ここではBC型補間多項式と呼ぶ)、
ガウスの超幾何関数の隣接関係式に類似の三項間関係式が
成立することがわかったので紹介する。三項間関係式を繰り返し使うことにより、
この$q$-超幾何級数が満たすランクn+1の一階連立$q$-差分方程式系を
具体的に表示することができる。応用として、この具体的表示から、
Gustafson の$q$-積分の無限積表示の別証明が得られるので、
それも紹介したい。
TBA (JAPANESE)
瀧 雅人 氏 (京大基礎物理学研究所) 16:00-17:00
AGT予想と幾何工学 (JAPANESE)
[ 講演概要 ]
共形場理論における共形blockと超対称gauge理論の分配関数の間に成立していると考
えられている
AGT予想について議論する。
特に超対称gauge理論における表面演算子とそのAGT対応を、
位相的string理論を用いることで理解する。
その結果、局所Calabi-Yau多様体上のcurve countingから、
表面演算子に対応したramified instanton分配関数の明示公式が予想として与えられ
る。
共形場理論における共形blockと超対称gauge理論の分配関数の間に成立していると考
えられている
AGT予想について議論する。
特に超対称gauge理論における表面演算子とそのAGT対応を、
位相的string理論を用いることで理解する。
その結果、局所Calabi-Yau多様体上のcurve countingから、
表面演算子に対応したramified instanton分配関数の明示公式が予想として与えられ
る。
2010年09月09日(木)
講演会
16:30-18:00 数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (3/3) (ENGLISH)
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (3/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
The third lecture will be then devoted to classification results,
mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.
This is Part 3 of a 3-part lecture.
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
The third lecture will be then devoted to classification results,
mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.
This is Part 3 of a 3-part lecture.
2010年09月06日(月)
代数幾何学セミナー
16:40-18:10 数理科学研究科棟(駒場) 126号室
Prof. Remke Kloosterman 氏 (Humboldt University, Berlin)
Non-reduced components of the Noether-Lefschetz locus (ENGLISH)
Prof. Remke Kloosterman 氏 (Humboldt University, Berlin)
Non-reduced components of the Noether-Lefschetz locus (ENGLISH)
[ 講演概要 ]
Let $M_d$ be the moduli space of complex smooth degree $d$ surfaces in $\\mathbb{P}3$. Let $NL_d \\subset M_d$ be the subset corresponding to surfaces with Picard number at least 2. It is known that $NL_r$ is Zariski-constructable, and each irreducible component of $NL_r$ has a natural scheme structure. In this talk we describe the largest non-reduced components of $NL_r$. This extends work of Maclean and Otwinowska.
This is joint work with my PhD student Ananyo Dan.
Let $M_d$ be the moduli space of complex smooth degree $d$ surfaces in $\\mathbb{P}3$. Let $NL_d \\subset M_d$ be the subset corresponding to surfaces with Picard number at least 2. It is known that $NL_r$ is Zariski-constructable, and each irreducible component of $NL_r$ has a natural scheme structure. In this talk we describe the largest non-reduced components of $NL_r$. This extends work of Maclean and Otwinowska.
This is joint work with my PhD student Ananyo Dan.
2010年09月04日(土)
講演会
09:30-11:00 数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (1/3) (ENGLISH)
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (1/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.
This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.
This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.
講演会
11:10-12:40 数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (2/3) (ENGLISH)
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (2/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my second lecture I will start with chamber systems and coset
geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.
This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my second lecture I will start with chamber systems and coset
geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.
This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.
2010年09月03日(金)
講演会
14:30-15:30 数理科学研究科棟(駒場) 370号室
Luc Robbiano 氏 (University of Versailles)
Carleman estimates and boundary problems. (JAPANESE)
Luc Robbiano 氏 (University of Versailles)
Carleman estimates and boundary problems. (JAPANESE)
[ 講演概要 ]
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.
One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.
If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.
One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.
If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.
2010年09月01日(水)
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
いつもと場所が違います
Bernhard M\"uhlherr 氏 (Justus-Liebig-Universit\"at Giessen)
Groups of Kac-Moody type (ENGLISH)
いつもと場所が違います
Bernhard M\"uhlherr 氏 (Justus-Liebig-Universit\"at Giessen)
Groups of Kac-Moody type (ENGLISH)
[ 講演概要 ]
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.
In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.
In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.
博士論文発表会
16:30-17:45 数理科学研究科棟(駒場) 123号室
今井 直毅 氏 (東京大学大学院数理科学研究科)
On the moduli spaces of finite flat models of Galois representations （Galois表現の有限平坦モデルのモジュライ空間について） (JAPANESE)
今井 直毅 氏 (東京大学大学院数理科学研究科)
On the moduli spaces of finite flat models of Galois representations （Galois表現の有限平坦モデルのモジュライ空間について） (JAPANESE)
2010年08月06日(金)
講演会
15:30-17:45 数理科学研究科棟(駒場) 370号室
Leevan Ling 氏 (Hong Kong Baptist University) 15:30-16:30
A Spectral Method for Space--
Time Fractional Diffusion Equation (ENGLISH)
Mourad Choulli 氏 (University of Metz) 16:45-17:45
A multidimensional Borg-Levinson theorem (ENGLISH)
Leevan Ling 氏 (Hong Kong Baptist University) 15:30-16:30
A Spectral Method for Space--
Time Fractional Diffusion Equation (ENGLISH)
Mourad Choulli 氏 (University of Metz) 16:45-17:45
A multidimensional Borg-Levinson theorem (ENGLISH)
GCOEセミナー
15:00-16:30 数理科学研究科棟(駒場) 122号室
Matthieu Alfaro 氏 (University Montpellier 2)
Motion by mean curvature and Allen-Cahn equations (ENGLISH)
Matthieu Alfaro 氏 (University Montpellier 2)
Motion by mean curvature and Allen-Cahn equations (ENGLISH)
[ 講演概要 ]
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.
2010年08月05日(木)
講演会
16:30-17:30 数理科学研究科棟(駒場) 370号室
Yongzhi Steve Xu 氏 (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse
Problems (ENGLISH)
Yongzhi Steve Xu 氏 (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse
Problems (ENGLISH)
講演会
16:30-17:30 数理科学研究科棟(駒場) 370号室
Yongzhi Steve Xu 氏 (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems (ENGLISH)
Yongzhi Steve Xu 氏 (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems (ENGLISH)
2010年07月30日(金)
GCOEセミナー
16:30-17:30 数理科学研究科棟(駒場) 370号室
Oleg Emanouilov 氏 (Colorado State University)
Global uniqueness in determining a coefficient by boundary data on small subboundaries (ENGLISH)
Oleg Emanouilov 氏 (Colorado State University)
Global uniqueness in determining a coefficient by boundary data on small subboundaries (ENGLISH)
[ 講演概要 ]
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.
2010年07月29日(木)
代数幾何学セミナー
14:30-16:00 数理科学研究科棟(駒場) 126号室
いつもと曜日・時間帯が異なります。ご注意ください。
二木昌宏 氏 (東大数理)
Homological Mirror Symmetry for 2-dimensional toric Fano stacks (JAPANESE)
いつもと曜日・時間帯が異なります。ご注意ください。
二木昌宏 氏 (東大数理)
Homological Mirror Symmetry for 2-dimensional toric Fano stacks (JAPANESE)
[ 講演概要 ]
Homological Mirror Symmetry (HMS for short) is a conjectural
duality between complex and symplectic geometry, originally proposed
for mirror pairs of Calabi-Yau manifolds and later extended to
Fano/Landau-Ginzburg mirrors (both due to Kontsevich, 1994 and 1998).
We explain how HMS is established in the case of 2-dimensional smooth
toric Fano stack X as an equivalence between the derived category of X
and the derived directed Fukaya category of its mirror Lefschetz
fibration W. This is related to Kontsevich-Soibelman's construction of
3d CY category from the quiver with potential.
We also obtain a local mirror extension following Seidel's suspension
theorem, that is, the local HMS for the canonical bundle K_X and the
double suspension W+uv. This talk is joint with Kazushi Ueda (Osaka
U.).
Homological Mirror Symmetry (HMS for short) is a conjectural
duality between complex and symplectic geometry, originally proposed
for mirror pairs of Calabi-Yau manifolds and later extended to
Fano/Landau-Ginzburg mirrors (both due to Kontsevich, 1994 and 1998).
We explain how HMS is established in the case of 2-dimensional smooth
toric Fano stack X as an equivalence between the derived category of X
and the derived directed Fukaya category of its mirror Lefschetz
fibration W. This is related to Kontsevich-Soibelman's construction of
3d CY category from the quiver with potential.
We also obtain a local mirror extension following Seidel's suspension
theorem, that is, the local HMS for the canonical bundle K_X and the
double suspension W+uv. This talk is joint with Kazushi Ueda (Osaka
U.).
2010年07月28日(水)
GCOEセミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
数値解析セミナー#008
及川 一誠 氏 (東京大学大学院数理科学研究科)
定常移流拡散方程式に対するハイブリッド型不連続Galerkin法 (JAPANESE)
http://www.infsup.jp/utnas/
数値解析セミナー#008
及川 一誠 氏 (東京大学大学院数理科学研究科)
定常移流拡散方程式に対するハイブリッド型不連続Galerkin法 (JAPANESE)
[ 講演概要 ]
本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
[ 参考URL ]本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
http://www.infsup.jp/utnas/
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
及川一誠 氏 (東京大学大学院数理科学研究科)
定常移流拡散方程式に対するハイブリッド型不連続Galerkin法 (JAPANESE)
http://www.infsup.jp/utnas/
及川一誠 氏 (東京大学大学院数理科学研究科)
定常移流拡散方程式に対するハイブリッド型不連続Galerkin法 (JAPANESE)
[ 講演概要 ]
本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
[ 参考URL ]本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
http://www.infsup.jp/utnas/
2010年07月27日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
井上 歩 氏 (東京工業大学)
Quandle homology and complex volume
(Joint work with Yuichi Kabaya) (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
井上 歩 氏 (東京工業大学)
Quandle homology and complex volume
(Joint work with Yuichi Kabaya) (JAPANESE)
[ 講演概要 ]
For a hyperbolic 3-manifold M, the complex value (Vol(M) + i CS(M)) is called the complex volume of M. Here, Vol(M) denotes the volume of M, and CS(M) the Chern-Simons invariant of M.
In 2004, Neumann defined the extended Bloch group, and showed that there is an element of the extended Bloch group corresponding to a hyperbolic 3-manifold.
He further showed that we can compute the complex volume of the manifold by evaluating the element of the extended Bloch group.
To obtain an element of the extended Bloch group corresponding to a hyperbolic 3-manifold, we have to find an ideal triangulation of the manifold and to solve several equations.
On the other hand, we show that the element of the extended Bloch group corresponding to the exterior of a hyperbolic link is obtained from a quandle shadow coloring.
It means that we can compute the complex volume combinatorially from a link diagram.
For a hyperbolic 3-manifold M, the complex value (Vol(M) + i CS(M)) is called the complex volume of M. Here, Vol(M) denotes the volume of M, and CS(M) the Chern-Simons invariant of M.
In 2004, Neumann defined the extended Bloch group, and showed that there is an element of the extended Bloch group corresponding to a hyperbolic 3-manifold.
He further showed that we can compute the complex volume of the manifold by evaluating the element of the extended Bloch group.
To obtain an element of the extended Bloch group corresponding to a hyperbolic 3-manifold, we have to find an ideal triangulation of the manifold and to solve several equations.
On the other hand, we show that the element of the extended Bloch group corresponding to the exterior of a hyperbolic link is obtained from a quandle shadow coloring.
It means that we can compute the complex volume combinatorially from a link diagram.
博士論文発表会
16:00-17:15 数理科学研究科棟(駒場) 123号室
富安 亮子 氏 (大学院数理科学研究科)
CM体のCM-typesとreflexの体のある代数的性質について (JAPANESE)
富安 亮子 氏 (大学院数理科学研究科)
CM体のCM-typesとreflexの体のある代数的性質について (JAPANESE)
2010年07月22日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Owen Sizemore 氏 (UCLA)
$W^*$ Rigidity for actions of wreath product groups (ENGLISH)
Owen Sizemore 氏 (UCLA)
$W^*$ Rigidity for actions of wreath product groups (ENGLISH)
[ 講演概要 ]
The past 8 years have seen much progress in the classification of
actions of groups on measure spaces. Much of this is due to new powerful
techniques in operator algebras. We will survey some of these results
as well as the new operator algebra techniques. We will then give new
results concerning the classification of actions of wreath product groups.
The past 8 years have seen much progress in the classification of
actions of groups on measure spaces. Much of this is due to new powerful
techniques in operator algebras. We will survey some of these results
as well as the new operator algebra techniques. We will then give new
results concerning the classification of actions of wreath product groups.
2010年07月20日(火)
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: 16:30 - 17:00 コモンルーム
川室 圭子 氏 (University of Iowa)
A polynomial invariant of pseudo-Anosov maps (JAPANESE)
Tea: 16:30 - 17:00 コモンルーム
川室 圭子 氏 (University of Iowa)
A polynomial invariant of pseudo-Anosov maps (JAPANESE)
[ 講演概要 ]
Thurston-Nielsen classified surface homomorphism into three classes. Among them, the pseudo-Anosov class is the most interesting since there is strong connection to the hyperbolic manifolds. As an invariant, the dilatation number has been known. In this talk, I will introduce a new invariant of pseudo-Anosov maps. It is an integer coefficient polynomial, which contains the dilatation as the largest real root and is often reducible. I will show properties of the polynomials, examples, and some application to knot theory. (This is a joint work with Joan Birman and Peter Brinkmann.)
Thurston-Nielsen classified surface homomorphism into three classes. Among them, the pseudo-Anosov class is the most interesting since there is strong connection to the hyperbolic manifolds. As an invariant, the dilatation number has been known. In this talk, I will introduce a new invariant of pseudo-Anosov maps. It is an integer coefficient polynomial, which contains the dilatation as the largest real root and is often reducible. I will show properties of the polynomials, examples, and some application to knot theory. (This is a joint work with Joan Birman and Peter Brinkmann.)
2010年07月15日(木)
Lie群論・表現論セミナー
14:30-16:00 数理科学研究科棟(駒場) 122号室
いつもと曜日、場所、開始時刻が異なります。
Soo Teck Lee 氏 (Singapore National University)
Pieri rule and Pieri algebras for the orthogonal groups (ENGLISH)
いつもと曜日、場所、開始時刻が異なります。
Soo Teck Lee 氏 (Singapore National University)
Pieri rule and Pieri algebras for the orthogonal groups (ENGLISH)
[ 講演概要 ]
The irreducible rational representations of the complex orthogonal
group $\\mathrm{O}_n$ are labeled by a certain set of Young diagrams,
and we denote the representation corresponding to the Young diagram
$D$ by $\\sigma^D_n$. Consider the tensor product
$\\sigma^D_n\\otimes\\sigma^E_n$ of two such representations. It can
be decomposed as
\\[\\sigma^D_n\\otimes\\sigma^E_n=\\bigoplus_Fm_F\\sigma^F_n,\\]
where for each Young diagram $F$ in the sum, $m_F$ is the
multiplicity of $\\sigma^F_n$ in $\\sigma^D_n\\otimes\\sigma^E_n$. In
the case when the Young diagram $E$ consists of only one row, a
description of the multiplicities in $\\sigma^D_n\\otimes\\sigma^E_n$
is called the {\\em Pieri Rule}. In this talk, I shall describe a
family of algebras whose structure encodes a generalization of the
Pieri Rule.
The irreducible rational representations of the complex orthogonal
group $\\mathrm{O}_n$ are labeled by a certain set of Young diagrams,
and we denote the representation corresponding to the Young diagram
$D$ by $\\sigma^D_n$. Consider the tensor product
$\\sigma^D_n\\otimes\\sigma^E_n$ of two such representations. It can
be decomposed as
\\[\\sigma^D_n\\otimes\\sigma^E_n=\\bigoplus_Fm_F\\sigma^F_n,\\]
where for each Young diagram $F$ in the sum, $m_F$ is the
multiplicity of $\\sigma^F_n$ in $\\sigma^D_n\\otimes\\sigma^E_n$. In
the case when the Young diagram $E$ consists of only one row, a
description of the multiplicities in $\\sigma^D_n\\otimes\\sigma^E_n$
is called the {\\em Pieri Rule}. In this talk, I shall describe a
family of algebras whose structure encodes a generalization of the
Pieri Rule.
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