本文印刷
全画面プリント
過去の記録
過去の記録 ～04/20｜本日 04/21 | 今後の予定 04/22～
数理人口学・数理生物学セミナー
14:50-16:20 数理科学研究科棟(駒場) 128号室
増田 直紀 氏 (University of Bristol, Department of Engineering Mathematics)
脳のresting-stateネットワークとそのエネルギー地形、睡眠との関係 (JAPANESE)
増田 直紀 氏 (University of Bristol, Department of Engineering Mathematics)
脳のresting-stateネットワークとそのエネルギー地形、睡眠との関係 (JAPANESE)
[ 講演概要 ]
脳の resting-state ネットワークは、様々な認知機能に関わっていると言われている。本発表では、MRI によって安静時にあるヒトから計測された脳信号に、最大エントロピー法(統計物理で知られるイジングモデルと同値)を適用して脳のネットワーク構造を推定する研究について紹介する。最大エントロピー法は、既存手法よりもより高い精度で解剖的な意味での脳ネットワークを推定できることが明らかになった。また、エネルギー地形という概念を用いた解析や、睡眠データへの応用についても述べる。
脳の resting-state ネットワークは、様々な認知機能に関わっていると言われている。本発表では、MRI によって安静時にあるヒトから計測された脳信号に、最大エントロピー法(統計物理で知られるイジングモデルと同値)を適用して脳のネットワーク構造を推定する研究について紹介する。最大エントロピー法は、既存手法よりもより高い精度で解剖的な意味での脳ネットワークを推定できることが明らかになった。また、エネルギー地形という概念を用いた解析や、睡眠データへの応用についても述べる。
2014年07月22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
Jesse Wolfson 氏 (Northwestern University)
The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Jesse Wolfson 氏 (Northwestern University)
The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)
[ 講演概要 ]
In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.
In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.
2014年07月19日(土)
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
大西良博 氏 (名城大学・理工学部) 13:30-14:30
sigma函数の原点でのべき級数展開のHurwitz整性 (JAPANESE)
大西良博 氏 (名城大学・理工学部) 15:00-16:00
種数 3 の trigonal curve から来る Kummer 多様体の定義方程式
と Coble の超平面 (JAPANESE)
大西良博 氏 (名城大学・理工学部) 13:30-14:30
sigma函数の原点でのべき級数展開のHurwitz整性 (JAPANESE)
大西良博 氏 (名城大学・理工学部) 15:00-16:00
種数 3 の trigonal curve から来る Kummer 多様体の定義方程式
と Coble の超平面 (JAPANESE)
2014年07月17日(木)
幾何コロキウム
10:00-11:30 数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
Jingyi Chen 氏 (University of British Columbia)
The space of compact shrinking solutions to Lagrangian mean curvature flow in $C^2$ (ENGLISH)
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
Jingyi Chen 氏 (University of British Columbia)
The space of compact shrinking solutions to Lagrangian mean curvature flow in $C^2$ (ENGLISH)
[ 講演概要 ]
We will discuss compactness and rigidity of compact surfaces which are shrinking solutions to Lagrangian mean curvature flow. This is recent joint work with John Ma.
We will discuss compactness and rigidity of compact surfaces which are shrinking solutions to Lagrangian mean curvature flow. This is recent joint work with John Ma.
2014年07月16日(水)
東京無限可積分系セミナー
10:30-12:00 数理科学研究科棟(駒場) 002号室
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From the Hilbert scheme to m/n Pieri rules (ENGLISH)
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From the Hilbert scheme to m/n Pieri rules (ENGLISH)
[ 講演概要 ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
2014年07月15日(火)
東京無限可積分系セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From the shuffle algebra to the Hilbert scheme (ENGLISH)
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From the shuffle algebra to the Hilbert scheme (ENGLISH)
[ 講演概要 ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
2014年07月14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) 126号室
Gopal Prasad 氏 (University of Michigan)
Higher dimensional analogues of fake projective planes (ENGLISH)
Gopal Prasad 氏 (University of Michigan)
Higher dimensional analogues of fake projective planes (ENGLISH)
[ 講演概要 ]
A fake projective plane is a smooth projective complex algebraic surface which is not isomorphic to the complex projective plane but whose Betti numbers are that of the complex projective plane. The fake projective planes are algebraic surfaces of general type and have smallest possible Euler-Poincare characteristic among them. The first fake projective plane was constructed by D. Mumford using p-adic uniformization, and it was known that there can only be finitely many of them. A complete classification of the fake projective planes was obtained by Sai-Kee Yeung and myself. We showed that there are 28 classes of them, and constructed at least one explicit example in each class. Later, using long computer assisted computations, D. Cartwright and Tim Steger found that the 28 families altogether contain precisely 100 fake projective planes. Using our work, they also found a very interesting smooth projective complex algebraic surface whose Euler-Poincare characteristic is 3 but whose first Betti
number is 2. We have a natural notion of higher dimensional analogues of fake projective planes and to a large extent determined them. My talk will be devoted to an exposition of this work.
A fake projective plane is a smooth projective complex algebraic surface which is not isomorphic to the complex projective plane but whose Betti numbers are that of the complex projective plane. The fake projective planes are algebraic surfaces of general type and have smallest possible Euler-Poincare characteristic among them. The first fake projective plane was constructed by D. Mumford using p-adic uniformization, and it was known that there can only be finitely many of them. A complete classification of the fake projective planes was obtained by Sai-Kee Yeung and myself. We showed that there are 28 classes of them, and constructed at least one explicit example in each class. Later, using long computer assisted computations, D. Cartwright and Tim Steger found that the 28 families altogether contain precisely 100 fake projective planes. Using our work, they also found a very interesting smooth projective complex algebraic surface whose Euler-Poincare characteristic is 3 but whose first Betti
number is 2. We have a natural notion of higher dimensional analogues of fake projective planes and to a large extent determined them. My talk will be devoted to an exposition of this work.
2014年07月13日(日)
東京無限可積分系セミナー
14:00-15:00 数理科学研究科棟(駒場) 002号室
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From vertex operators to the shuffle algebra (ENGLISH)
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From vertex operators to the shuffle algebra (ENGLISH)
[ 講演概要 ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
2014年07月12日(土)
Lie群論・表現論セミナー
13:20-17:00 数理科学研究科棟(駒場) 126号室
Mikhail Kapranov 氏 (Kavli IPMU) 13:20-14:20
Perverse sheaves on hyperplane arrangements (ENGLISH)
Upper global nasis, cluster algebra and simplicity of tensor products of simple modules (ENGLISH)
Branching Problems of Representations of Real Reductive Groups (ENGLISH)
Mikhail Kapranov 氏 (Kavli IPMU) 13:20-14:20
Perverse sheaves on hyperplane arrangements (ENGLISH)
[ 講演概要 ]
Given an arrangement of hyperplanes in $R^n$, one has the complexified arrangement in $C^n$ and the corresponding category of perverse sheaves (smooth along the strata of the natural stratification).
The talk, based in a joint work with V. Schechtman, will present an explicit description of this category in terms of data associated to the face complex of the real arrangement. Such a description suggests a possibility of categorifying the concept of a oerverse sheaf in this and possibly in more general cases.
柏原正樹 氏 (京都大学数理解析研究所) 14:40-15:40Given an arrangement of hyperplanes in $R^n$, one has the complexified arrangement in $C^n$ and the corresponding category of perverse sheaves (smooth along the strata of the natural stratification).
The talk, based in a joint work with V. Schechtman, will present an explicit description of this category in terms of data associated to the face complex of the real arrangement. Such a description suggests a possibility of categorifying the concept of a oerverse sheaf in this and possibly in more general cases.
Upper global nasis, cluster algebra and simplicity of tensor products of simple modules (ENGLISH)
[ 講演概要 ]
One of the motivation of cluster algebras introduced by
Fomin and Zelevinsky is
multiplicative properties of upper global basis.
In this talk, I explain their relations, related conjectures by Besrnard Leclerc and the recent progress by the speaker with Seok-Jin Kang, Myungho Kima and Sejin Oh.
小林俊行 氏 (東京大学大学院数理科学研究科) 16:00-17:00One of the motivation of cluster algebras introduced by
Fomin and Zelevinsky is
multiplicative properties of upper global basis.
In this talk, I explain their relations, related conjectures by Besrnard Leclerc and the recent progress by the speaker with Seok-Jin Kang, Myungho Kima and Sejin Oh.
Branching Problems of Representations of Real Reductive Groups (ENGLISH)
[ 講演概要 ]
Branching problems ask how irreducible representations π of groups G "decompose" when restricted to subgroups G'.
For real reductive groups, branching problems include various important special cases, however, it is notorious that "infinite multiplicities" and "continuous spectra" may well happen in general even if (G,G') are natural pairs such as symmetric pairs.
By using analysis on (real) spherical varieties, we give a necessary and sufficient condition on the pair of reductive groups for the multiplicities to be always finite (and also to be of uniformly bounded). Further, we discuss "discretely decomposable restrictions" which allows us to apply algebraic tools in branching problems. Some classification results will be also presented.
If time permits, I will discuss some applications of branching laws of Zuckerman's derived functor modules to analysis on locally symmetric spaces with indefinite metric.
Branching problems ask how irreducible representations π of groups G "decompose" when restricted to subgroups G'.
For real reductive groups, branching problems include various important special cases, however, it is notorious that "infinite multiplicities" and "continuous spectra" may well happen in general even if (G,G') are natural pairs such as symmetric pairs.
By using analysis on (real) spherical varieties, we give a necessary and sufficient condition on the pair of reductive groups for the multiplicities to be always finite (and also to be of uniformly bounded). Further, we discuss "discretely decomposable restrictions" which allows us to apply algebraic tools in branching problems. Some classification results will be also presented.
If time permits, I will discuss some applications of branching laws of Zuckerman's derived functor modules to analysis on locally symmetric spaces with indefinite metric.
Lie群論・表現論セミナー
09:30-11:45 数理科学研究科棟(駒場) 126号室
大島利雄 氏 (城西大学) 09:30-10:30
超幾何系とKac-Moodyルート系 (ENGLISH)
Representations of covering groups with multiplicity free K-types (ENGLISH)
大島利雄 氏 (城西大学) 09:30-10:30
超幾何系とKac-Moodyルート系 (ENGLISH)
[ 講演概要 ]
帯球関数やそれの一般化のHeckmann-Opdamの超幾何の解析のため,1次元
の特異集合への制限から常微分方程式の研究に興味を持った.
Fuchs型常微分方程式全体の空間にEuler変換などを通じてKac-Moodyルー
ト系のWeyl群が作用することが分かり,局所モノドロミーで決まらない
モジュライ空間の次元を不変量として,群軌道の有限性が明らかになった.
モジュライがないrigidな場合は自明な方程式に変換されるので具体的
解析が可能になり,逆にモジュライのある場合はPainleve方程式の構成
と分類への応用がある.これらは分岐のない不確定特異点も許す場合に
拡張されると共に,リジッドな場合は自然に多変数の超幾何への延長が
定義され,その解析に役立つ.古典的なAppellの超幾何などは後者に含
まれ,モノドロミーの可約性などがルート系の言葉で一般的に記述でき
る.これらの概説と共に,最近の結果や今後の問題ついて解説する.
Gordan Savin 氏 (the University of Utah) 10:45-11:45帯球関数やそれの一般化のHeckmann-Opdamの超幾何の解析のため,1次元
の特異集合への制限から常微分方程式の研究に興味を持った.
Fuchs型常微分方程式全体の空間にEuler変換などを通じてKac-Moodyルー
ト系のWeyl群が作用することが分かり,局所モノドロミーで決まらない
モジュライ空間の次元を不変量として,群軌道の有限性が明らかになった.
モジュライがないrigidな場合は自明な方程式に変換されるので具体的
解析が可能になり,逆にモジュライのある場合はPainleve方程式の構成
と分類への応用がある.これらは分岐のない不確定特異点も許す場合に
拡張されると共に,リジッドな場合は自然に多変数の超幾何への延長が
定義され,その解析に役立つ.古典的なAppellの超幾何などは後者に含
まれ,モノドロミーの可約性などがルート系の言葉で一般的に記述でき
る.これらの概説と共に,最近の結果や今後の問題ついて解説する.
Representations of covering groups with multiplicity free K-types (ENGLISH)
[ 講演概要 ]
Let g be a simple Lie algebra over complex numbers. McGovern has
described an ideal J in the enveloping algebra U such that U/J, considered as a g-module under the adjoint action, is a sum of all self-dual representations of g with multiplicity one. In a joint work with Loke, we prove that all (g,K)-modules annihilated by J have multiplicity free K-types, where K is defined by the Chevalley involution.
Let g be a simple Lie algebra over complex numbers. McGovern has
described an ideal J in the enveloping algebra U such that U/J, considered as a g-module under the adjoint action, is a sum of all self-dual representations of g with multiplicity one. In a joint work with Loke, we prove that all (g,K)-modules annihilated by J have multiplicity free K-types, where K is defined by the Chevalley involution.
2014年07月11日(金)
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 123号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
小林俊行 氏 (東京大学大学院数理科学研究科)
不定値計量をもつ局所対称空間の大域幾何と解析 (JAPANESE)
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
小林俊行 氏 (東京大学大学院数理科学研究科)
不定値計量をもつ局所対称空間の大域幾何と解析 (JAPANESE)
[ 講演概要 ]
弦楽器では、弦を短くするにつれて音が高くなります。
同様に、閉リーマン面上のラプラシアンの固有値はタイヒミュラー空間上の関数
として
必ず変動することが知られています。
後者は局所的に同じ曲がり方をしたリーマン多様体(双曲幾何)を舞台にしたも
のですが、
もっと一般の不定値計量をもつ空間では何が起こるでしょうか?
そもそも、大域解析の舞台となる良い空間が存在するのでしょうか。
この談話会では、
1.(局所から大域へ)閉じた空間が存在するか?
2. (スペクトル理論)変形しても音程が変わらないことがある?
という話題をとりあげてみたいと思います。
これらの問題は多岐にわたる数学の分野が関わっていますが、例として
反ドジッター空間(局所的に同じ曲がり方をしたローレンツ多様体)を
用いて、学部の4年生でもアクセスできる形で初等的に話す予定です。
弦楽器では、弦を短くするにつれて音が高くなります。
同様に、閉リーマン面上のラプラシアンの固有値はタイヒミュラー空間上の関数
として
必ず変動することが知られています。
後者は局所的に同じ曲がり方をしたリーマン多様体(双曲幾何)を舞台にしたも
のですが、
もっと一般の不定値計量をもつ空間では何が起こるでしょうか?
そもそも、大域解析の舞台となる良い空間が存在するのでしょうか。
この談話会では、
1.(局所から大域へ)閉じた空間が存在するか?
2. (スペクトル理論)変形しても音程が変わらないことがある?
という話題をとりあげてみたいと思います。
これらの問題は多岐にわたる数学の分野が関わっていますが、例として
反ドジッター空間(局所的に同じ曲がり方をしたローレンツ多様体)を
用いて、学部の4年生でもアクセスできる形で初等的に話す予定です。
FMSPレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 270号室
Oleg Emanouilov 氏 (Colorado State Univ.)
Conditional stability estimate for the Calderon's problem in two dimensional case (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov140711.pdf
Oleg Emanouilov 氏 (Colorado State Univ.)
Conditional stability estimate for the Calderon's problem in two dimensional case (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov140711.pdf
2014年07月08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
Ingrid Irmer 氏 (JSPS, 東京大学大学院数理科学研究科)
The Johnson homomorphism and a family of curve graphs (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Ingrid Irmer 氏 (JSPS, 東京大学大学院数理科学研究科)
The Johnson homomorphism and a family of curve graphs (ENGLISH)
[ 講演概要 ]
Abstract: A family of curve graphs of an oriented surface $S_{g,1}$ will be defined on which there exists a natural orientation, coming from the orientation of subsurfaces. Distances in these graphs represent commutator lengths in $\\pi_{1}(S_{g,1})$. The displacement of vertices in the graphs under the action of the Torelli group is used to give a combinatorial description of the Johnson homomorphism."
Abstract: A family of curve graphs of an oriented surface $S_{g,1}$ will be defined on which there exists a natural orientation, coming from the orientation of subsurfaces. Distances in these graphs represent commutator lengths in $\\pi_{1}(S_{g,1})$. The displacement of vertices in the graphs under the action of the Torelli group is used to give a combinatorial description of the Johnson homomorphism."
古典解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 122号室
中園信孝 氏 (シドニー大学)
ABS equations arising from q-P((A2+A1)^{(1)}) (JAPANESE)
中園信孝 氏 (シドニー大学)
ABS equations arising from q-P((A2+A1)^{(1)}) (JAPANESE)
[ 講演概要 ]
The study of periodic reductions from ABS equations to discrete Painlevé equations have been investigated by many groups. However, there still remain open questions:
(i) How do we identify the discrete Painlevé equation that would result from applying a periodic reduction to an ABS equation?
(ii) Discrete Painlevé equations obtained by periodic reductions often have insufficient number of parameters. How do we obtain the general case with all essential parameters?
To solve these problems, we investigated the periodic reductions from the viewpoint of Painlevé systems.
In this talk, we show how to construct a lattice where ABS equations arise from relationships between $\\tau$ functions of Painlevé systems and explain how this lattice relates to a hyper cube associated with an ABS equation on each face.
In particular, we consider the $q$-Painlevé equations, which have the affine Weyl group symmetry of type $(A_2+A_1)^{(1)}$.
The study of periodic reductions from ABS equations to discrete Painlevé equations have been investigated by many groups. However, there still remain open questions:
(i) How do we identify the discrete Painlevé equation that would result from applying a periodic reduction to an ABS equation?
(ii) Discrete Painlevé equations obtained by periodic reductions often have insufficient number of parameters. How do we obtain the general case with all essential parameters?
To solve these problems, we investigated the periodic reductions from the viewpoint of Painlevé systems.
In this talk, we show how to construct a lattice where ABS equations arise from relationships between $\\tau$ functions of Painlevé systems and explain how this lattice relates to a hyper cube associated with an ABS equation on each face.
In particular, we consider the $q$-Painlevé equations, which have the affine Weyl group symmetry of type $(A_2+A_1)^{(1)}$.
2014年07月07日(月)
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
谷本翔 氏 (Rice University)
Balanced line bundles (JAPANESE)
谷本翔 氏 (Rice University)
Balanced line bundles (JAPANESE)
[ 講演概要 ]
A conjecture of Batyrev and Manin relates arithmetic properties of
varieties with big anticanonical class to geometric invariants; in
particular, counting functions defined by metrized ample line bundles
and the corresponding asymptotics of rational points of bounded height
are interpreted in terms of cones of effective divisors and certain
thresholds with respect to these cones. This framework leads to the
notion of balanced line bundles, whose counting functions, conjecturally,
capture generic distributions of rational points. We investigate
balanced line bundles in the context of the Minimal Model Program, with
special regard to the classification of Fano threefolds and Mori fiber
spaces.
This is joint work with Brian Lehmann and Yuri Tschinkel.
A conjecture of Batyrev and Manin relates arithmetic properties of
varieties with big anticanonical class to geometric invariants; in
particular, counting functions defined by metrized ample line bundles
and the corresponding asymptotics of rational points of bounded height
are interpreted in terms of cones of effective divisors and certain
thresholds with respect to these cones. This framework leads to the
notion of balanced line bundles, whose counting functions, conjecturally,
capture generic distributions of rational points. We investigate
balanced line bundles in the context of the Minimal Model Program, with
special regard to the classification of Fano threefolds and Mori fiber
spaces.
This is joint work with Brian Lehmann and Yuri Tschinkel.
2014年07月03日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
石毛 和弘 氏 (東北大学大学院理学研究科)
放物型冪凸と放物型境界値問題 (JAPANESE)
石毛 和弘 氏 (東北大学大学院理学研究科)
放物型冪凸と放物型境界値問題 (JAPANESE)
[ 講演概要 ]
本研究内容はフィレンツェ大学の Paolo Salani 氏との共同研究によるものである。偏微分方程式の解の凸性の研究は Brascamp-Lieb, Korevaar,Kennington らの研究により1970年代後半以降多いに進展してきた。
しかし、放物型方程式に関しては時間変数を固定した上での空間変数に関する解の凸性の研究が専らであった。本講演では、放物型冪凸という概念を導入し、冪凸非斉次項をもつ熱方程式の解の時空間変数による凸性について、最近の研究成果を含めて述べる。
本研究内容はフィレンツェ大学の Paolo Salani 氏との共同研究によるものである。偏微分方程式の解の凸性の研究は Brascamp-Lieb, Korevaar,Kennington らの研究により1970年代後半以降多いに進展してきた。
しかし、放物型方程式に関しては時間変数を固定した上での空間変数に関する解の凸性の研究が専らであった。本講演では、放物型冪凸という概念を導入し、冪凸非斉次項をもつ熱方程式の解の時空間変数による凸性について、最近の研究成果を含めて述べる。
FMSPレクチャーズ
16:00-18:00 数理科学研究科棟(駒場) 470号室
Gordan Savin 氏 (Univ. of Utah)
Structure of rational orbits in prehomogeneous spaces. (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Savin.pdf
Gordan Savin 氏 (Univ. of Utah)
Structure of rational orbits in prehomogeneous spaces. (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Savin.pdf
2014年07月01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
今城 洋亮 氏 (Kavli IPMU)
Singularities of special Lagrangian submanifolds (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
今城 洋亮 氏 (Kavli IPMU)
Singularities of special Lagrangian submanifolds (JAPANESE)
[ 講演概要 ]
There are interesting invariants defined by "counting" geometric
objects, such as instantons in dimension 4 and pseudo-holomorphic curves
in symplectic manifolds. To do the counting in a sensible way, however,
we have to care about singularities of the geometric objects. Special
Lagrangian submanifolds seem very difficult to "count" as their
singularities may be very complicated. I'll talk about simple
singularities for which we can make an analogy with instantons in
dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do
it I'll use some techniques from geometric measure theory and Lagrangian
Floer theory, and the Floer-theoretic part is a joint work with Dominic
Joyce and Oliveira dos Santos.
There are interesting invariants defined by "counting" geometric
objects, such as instantons in dimension 4 and pseudo-holomorphic curves
in symplectic manifolds. To do the counting in a sensible way, however,
we have to care about singularities of the geometric objects. Special
Lagrangian submanifolds seem very difficult to "count" as their
singularities may be very complicated. I'll talk about simple
singularities for which we can make an analogy with instantons in
dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do
it I'll use some techniques from geometric measure theory and Lagrangian
Floer theory, and the Floer-theoretic part is a joint work with Dominic
Joyce and Oliveira dos Santos.
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Pablo Ramacher
氏 (Marburg University)
WONDERFUL VARIETIES. REGULARIZED TRACES AND CHARACTERS (ENGLISH)
Pablo Ramacher
氏 (Marburg University)
WONDERFUL VARIETIES. REGULARIZED TRACES AND CHARACTERS (ENGLISH)
[ 講演概要 ]
Let G be a connected reductive complex algebraic group with split real form $G^\\sigma$.
In this talk, we introduce a distribution character for the regular representation of $G^\\sigma$ on the real locus of a strict wonderful G-variety X, showing that on a certain open subset of $G^\\sigma$ of transversal elements it is locally integrable, and given by a sum over fixed points.
Let G be a connected reductive complex algebraic group with split real form $G^\\sigma$.
In this talk, we introduce a distribution character for the regular representation of $G^\\sigma$ on the real locus of a strict wonderful G-variety X, showing that on a certain open subset of $G^\\sigma$ of transversal elements it is locally integrable, and given by a sum over fixed points.
2014年06月30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) 126号室
小木曽啓示 氏 (大阪大学)
Primitive automorphisms of positive entropy of rational and Calabi-Yau threefolds (JAPANESE)
小木曽啓示 氏 (大阪大学)
Primitive automorphisms of positive entropy of rational and Calabi-Yau threefolds (JAPANESE)
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
三内顕義 氏 (東京大学数理科学研究科)
Invariant subrings of the Cox rings of K3surfaces by automorphism groups (JAPANESE)
三内顕義 氏 (東京大学数理科学研究科)
Invariant subrings of the Cox rings of K3surfaces by automorphism groups (JAPANESE)
[ 講演概要 ]
Cox rings were introduced by D.Cox and are important rings which appeared in algebraic geometry. One of the main topic related with Cox rings is the finite generation of them. In this talk, we consider the Cox rings of K3 surfaces and answer the following question asked by D. Huybrechts; Are the invariant subrings of the Cox rings of K3 surfaces by automorphism groups finitely generated in general?
Cox rings were introduced by D.Cox and are important rings which appeared in algebraic geometry. One of the main topic related with Cox rings is the finite generation of them. In this talk, we consider the Cox rings of K3 surfaces and answer the following question asked by D. Huybrechts; Are the invariant subrings of the Cox rings of K3 surfaces by automorphism groups finitely generated in general?
Kavli IPMU Komaba Seminar
16:30-18:00 数理科学研究科棟(駒場) 002号室
Anatol Kirillov 氏 (RIMS, Kyoto University)
On some quadratic algebras with applications to Topology,
Algebra, Combinatorics, Schubert Calculus and Integrable Systems. (ENGLISH)
Anatol Kirillov 氏 (RIMS, Kyoto University)
On some quadratic algebras with applications to Topology,
Algebra, Combinatorics, Schubert Calculus and Integrable Systems. (ENGLISH)
[ 講演概要 ]
The main purpose of my talk is to draw attention of the
participants of the seminar to a certain family of quadratic algebras
which has a wide range of applications to the subject mentioned in the
title of my talk.
The main purpose of my talk is to draw attention of the
participants of the seminar to a certain family of quadratic algebras
which has a wide range of applications to the subject mentioned in the
title of my talk.
2014年06月28日(土)
調和解析駒場セミナー
13:30-17:00 数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
Neal Bez 氏 (埼玉大学) 13:30-15:00
On the multilinear restriction problem (ENGLISH)
John-Nirenberg lemmas for a doubling measure (ENGLISH)
このセミナーは,月に1度程度,不定期に開催されます.
Neal Bez 氏 (埼玉大学) 13:30-15:00
On the multilinear restriction problem (ENGLISH)
[ 講演概要 ]
I will discuss the multilinear restriction problem for the Fourier transform. This will include an overview of the pioneering work of Bennett, Carbery and Tao on this problem and the very losely connected multilinear Kakeya problem. I will also discuss some of my own work in this area which is connected to nonlinear Brascamp-Lieb inequalities (joint work with Jonathan Bennett).
Hong Yue 氏 (Georgia College and State University) 15:30-17:00I will discuss the multilinear restriction problem for the Fourier transform. This will include an overview of the pioneering work of Bennett, Carbery and Tao on this problem and the very losely connected multilinear Kakeya problem. I will also discuss some of my own work in this area which is connected to nonlinear Brascamp-Lieb inequalities (joint work with Jonathan Bennett).
John-Nirenberg lemmas for a doubling measure (ENGLISH)
[ 講演概要 ]
We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.
We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.
2014年06月26日(木)
幾何コロキウム
10:00-11:30 数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
桑田和正 氏 (東京工業大学)
Entropic curvature-dimension condition and Bochner’s inequality (JAPANESE)
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
桑田和正 氏 (東京工業大学)
Entropic curvature-dimension condition and Bochner’s inequality (JAPANESE)
[ 講演概要 ]
As a characterization of "lower Ricci curvature bound and upper dimension bound”, there appear several conditions which make sense even on singular spaces. In this talk we show the equivalence in complete generality between two major conditions: a reduced version of curvature-dimension bounds of Sturm-Lott-Villani via entropy and optimal transport and Bakry–¥'Emery's one via Markov generator or the associated heat semigroup. More precisely, it holds for metric measure spaces where Cheeger's L^2-energy functional is a quadratic form. In particular, we establish the full Bochner inequality, which originally comes from the Bochner-Weitzenb¥"ock formula, on such spaces. This talk is based on a joint work with M. Erbar and K.-T. Sturm (Bonn).
As a characterization of "lower Ricci curvature bound and upper dimension bound”, there appear several conditions which make sense even on singular spaces. In this talk we show the equivalence in complete generality between two major conditions: a reduced version of curvature-dimension bounds of Sturm-Lott-Villani via entropy and optimal transport and Bakry–¥'Emery's one via Markov generator or the associated heat semigroup. More precisely, it holds for metric measure spaces where Cheeger's L^2-energy functional is a quadratic form. In particular, we establish the full Bochner inequality, which originally comes from the Bochner-Weitzenb¥"ock formula, on such spaces. This talk is based on a joint work with M. Erbar and K.-T. Sturm (Bonn).
2014年06月25日(水)
作用素環セミナー
16:45-18:00 数理科学研究科棟(駒場) 122号室
守屋創 氏 (芝浦工大)
Supersymmetric C*-dynamical systems (JAPANESE)
守屋創 氏 (芝浦工大)
Supersymmetric C*-dynamical systems (JAPANESE)
< 前へ 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185 次へ >
