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過去の記録 ～05/01｜本日 05/02 | 今後の予定 05/03～
2008年10月28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
清野 和彦 氏 (東京大学大学院数理科学研究科)
Nonsmoothable group actions on spin 4-manifolds
Tea: 16:00 - 16:30 コモンルーム
清野 和彦 氏 (東京大学大学院数理科学研究科)
Nonsmoothable group actions on spin 4-manifolds
[ 講演概要 ]
We call a locally linear group action on a topological manifold nonsmoothable
if the action is not smooth with respect to any possible smooth structure.
We show in this lecture that every closed, simply connected, spin topological 4-manifold
not homeomorphic to neither S^2\\times S^2 nor S^4 allows a nonsmoothable
group action of any cyclic group with sufficiently large prime order
which depends on the manifold.
We call a locally linear group action on a topological manifold nonsmoothable
if the action is not smooth with respect to any possible smooth structure.
We show in this lecture that every closed, simply connected, spin topological 4-manifold
not homeomorphic to neither S^2\\times S^2 nor S^4 allows a nonsmoothable
group action of any cyclic group with sufficiently large prime order
which depends on the manifold.
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
Joachim Hilgert 氏 (Paderborn University)
Chevalley's restriction theorem for supersymmetric Riemannian symmetric spaces
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Joachim Hilgert 氏 (Paderborn University)
Chevalley's restriction theorem for supersymmetric Riemannian symmetric spaces
[ 講演概要 ]
We start by explaining the concept of a supersymmetric Riemannian symmetric spaces and present the examples studied by Zirnbauer in the context of universality classes of random matrices. For these classes we then show how to formulate and prove an analog of Chevalley's restriction theorem for invariant super-functions.
This is joint work with A. Alldridge (Paderborn) and M. Zirnbauer (Cologne)
[ 参考URL ]We start by explaining the concept of a supersymmetric Riemannian symmetric spaces and present the examples studied by Zirnbauer in the context of universality classes of random matrices. For these classes we then show how to formulate and prove an analog of Chevalley's restriction theorem for invariant super-functions.
This is joint work with A. Alldridge (Paderborn) and M. Zirnbauer (Cologne)
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
解析学火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 123号室
いつもと時間、場所が異なります。またこの日から3日間連続講演となります。第2回、第3回はそれぞれ29, 30日に同じ部屋、時間帯で行われます。
Serge Alinhac 氏 (パリ大学オルセイ校)
Introduction to geometric analysis of hyperbolic equations
いつもと時間、場所が異なります。またこの日から3日間連続講演となります。第2回、第3回はそれぞれ29, 30日に同じ部屋、時間帯で行われます。
Serge Alinhac 氏 (パリ大学オルセイ校)
Introduction to geometric analysis of hyperbolic equations
2008年10月27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
松野 高典 氏 (大阪府立高専)
複素射影平面上の有限Galois分岐被覆について
松野 高典 氏 (大阪府立高専)
複素射影平面上の有限Galois分岐被覆について
GCOEレクチャーズ
16:30-17:30 数理科学研究科棟(駒場) 128号室
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of highest weight representations to Olshanskii semigroups
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of highest weight representations to Olshanskii semigroups
[ 講演概要 ]
In this lecture I will present a proof of Olshanskii's Theorem, which says that
for a simple group of Hermitean type unitarizable highest weight
representations can be holomorphically extended to contractive representations
of a complex semigroup containing the group in its boundary.
In this lecture I will present a proof of Olshanskii's Theorem, which says that
for a simple group of Hermitean type unitarizable highest weight
representations can be holomorphically extended to contractive representations
of a complex semigroup containing the group in its boundary.
2008年10月24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) 002号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
Benoit Collins 氏 (オタワ大学・東京大学大学院数理科学研究科)
On the spectral measure of the sum of elements in a finite von Neumann algebra
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
Benoit Collins 氏 (オタワ大学・東京大学大学院数理科学研究科)
On the spectral measure of the sum of elements in a finite von Neumann algebra
[ 講演概要 ]
Given two self-adjoint n×n matrices A and B with prescribed eigenvalues, the set of all possible spectral distributions for A+B has been conjectured by Horn and proved by Knutson, Tao, Klyachko and Totaro.
We address the same question when A and B have prescribed spectral measures but lie in an arbitrary II_1 factor, and we give elements of answers in terms of inequalities between the spectral measures. We explain the relation with the Connes embedding problem.
Given two self-adjoint n×n matrices A and B with prescribed eigenvalues, the set of all possible spectral distributions for A+B has been conjectured by Horn and proved by Knutson, Tao, Klyachko and Totaro.
We address the same question when A and B have prescribed spectral measures but lie in an arbitrary II_1 factor, and we give elements of answers in terms of inequalities between the spectral measures. We explain the relation with the Connes embedding problem.
2008年10月23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
Emily Peters 氏 (UC Berkeley)
Planar algebras and the Haagerup subfactor
Emily Peters 氏 (UC Berkeley)
Planar algebras and the Haagerup subfactor
2008年10月22日(水)
代数学コロキウム
16:30-17:30 数理科学研究科棟(駒場) 056号室
10月から教室が056号室に変更になります.
Pierre Parent 氏 (Universite Bordeaux 1)
Serre's uniformity in the split Cartan case
10月から教室が056号室に変更になります.
Pierre Parent 氏 (Universite Bordeaux 1)
Serre's uniformity in the split Cartan case
[ 講演概要 ]
We show that, for large enough prime number p, the modular curve
X_{split}(p) has no other point with values in Q than CM points and the rational cusp. This gives a partial answer to an old question of J.-P. Serre concerning the uniform surjectivity of Galois representations associated to torsion points on elliptic curves without complex multiplication.
(Joint work with Yuri Bilu.)
We show that, for large enough prime number p, the modular curve
X_{split}(p) has no other point with values in Q than CM points and the rational cusp. This gives a partial answer to an old question of J.-P. Serre concerning the uniform surjectivity of Galois representations associated to torsion points on elliptic curves without complex multiplication.
(Joint work with Yuri Bilu.)
2008年10月21日(火)
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
いつもと開始時刻が違います。また同氏による集中講義がこの週に行われます。
落合啓之 氏 (名古屋大学)
Invitation to Atlas combinatorics
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
いつもと開始時刻が違います。また同氏による集中講義がこの週に行われます。
落合啓之 氏 (名古屋大学)
Invitation to Atlas combinatorics
[ 講演概要 ]
半単純リー群のユニタリ表現の分類を手がける Atlas project(J. Adams, D. Vogan らが主催)では、実簡約(real reductive)線形代数群の admissible 表現をパラメトライズし、それに関するいくつかのプログラムが公開されています。ウェブサイトは www.liegroups.org.
現在、そのメインとなるものは Kazhdan-Lusztig-Vogan 多項式です。リー群として複素単純リー群を実リー群と見なしたケースが、通常の Kazhdan-Lusztig 理論に一致し、それを、ある一方向に拡張したのがここで扱われる KLV 理論と考えられます。
この講演では、リー群に関する背景説明などは軽く済ませ、Atlas で公開されているプログラムにおける方言、特に入出力の読み方を通常の言葉に言い換えることで、
プログラムを使ってもらう入り口での障壁を減らしたいと考えています。
ふむ、なかなか、使えるな、自分もインストールしてみようか、と思ってもらえれば、成功です。
なお、サーベイトークなので私のオリジナルな結果は含まれていません。また、計算機を使ってデモをする予定です。京都では計算機と板書の切り替えでばたばたしたので、照準を絞って慌てないように話したいと思います。
[ 参考URL ]半単純リー群のユニタリ表現の分類を手がける Atlas project(J. Adams, D. Vogan らが主催)では、実簡約(real reductive)線形代数群の admissible 表現をパラメトライズし、それに関するいくつかのプログラムが公開されています。ウェブサイトは www.liegroups.org.
現在、そのメインとなるものは Kazhdan-Lusztig-Vogan 多項式です。リー群として複素単純リー群を実リー群と見なしたケースが、通常の Kazhdan-Lusztig 理論に一致し、それを、ある一方向に拡張したのがここで扱われる KLV 理論と考えられます。
この講演では、リー群に関する背景説明などは軽く済ませ、Atlas で公開されているプログラムにおける方言、特に入出力の読み方を通常の言葉に言い換えることで、
プログラムを使ってもらう入り口での障壁を減らしたいと考えています。
ふむ、なかなか、使えるな、自分もインストールしてみようか、と思ってもらえれば、成功です。
なお、サーベイトークなので私のオリジナルな結果は含まれていません。また、計算機を使ってデモをする予定です。京都では計算機と板書の切り替えでばたばたしたので、照準を絞って慌てないように話したいと思います。
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
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) 002号室
Tea: 16:00 - 16:30 コモンルーム
森山 哲裕 氏 (東京大学大学院数理科学研究科)
On embeddings of 3-manifolds in 6-manifolds
Tea: 16:00 - 16:30 コモンルーム
森山 哲裕 氏 (東京大学大学院数理科学研究科)
On embeddings of 3-manifolds in 6-manifolds
[ 講演概要 ]
In this talk, we give a simple axiomatic definition of an invariant of
smooth embeddings of 3-manifolds in 6-manifolds.
The axiom is expressed in terms of some cobordisms of pairs of manifolds of
dimensions 6 and 3 (equipped with some cohomology class of the complement) and
the signature of 4-manifolds.
We then show that our invariant gives a unified framework for some classical
invariants in low-dimensions (Haefliger invariant, Milnor's triple
linking number, Rokhlin invariant, Casson invariant,
Takase's invariant, Skopenkov's invariants).
In this talk, we give a simple axiomatic definition of an invariant of
smooth embeddings of 3-manifolds in 6-manifolds.
The axiom is expressed in terms of some cobordisms of pairs of manifolds of
dimensions 6 and 3 (equipped with some cohomology class of the complement) and
the signature of 4-manifolds.
We then show that our invariant gives a unified framework for some classical
invariants in low-dimensions (Haefliger invariant, Milnor's triple
linking number, Rokhlin invariant, Casson invariant,
Takase's invariant, Skopenkov's invariants).
2008年10月20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
岩崎 克則 氏 (九大数理)
パンルヴェ方程式と複素力学系
岩崎 克則 氏 (九大数理)
パンルヴェ方程式と複素力学系
2008年10月17日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 128号室
岩根 和郎 氏 (岩根研究所)
岩根研究所に於ける画像処理技術の紹介Ⅱ; CV技術による空間認識と対象物認識、及び人工知能
岩根 和郎 氏 (岩根研究所)
岩根研究所に於ける画像処理技術の紹介Ⅱ; CV技術による空間認識と対象物認識、及び人工知能
講演会
15:00-16:00 数理科学研究科棟(駒場) 570号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その4 "Applications and open problems"
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その4 "Applications and open problems"
[ 講演概要 ]
In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krotz-Stanton), random matrices (Huckleberry-Puttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
[ 参考URL ]In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krotz-Stanton), random matrices (Huckleberry-Puttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
代数幾何学セミナー
13:00-14:30 数理科学研究科棟(駒場) 128号室
Yongnam Lee 氏 (Sogang U.)
Construction of surfaces of general type with pg=0 via
Q-Gorenstein smoothing
Yongnam Lee 氏 (Sogang U.)
Construction of surfaces of general type with pg=0 via
Q-Gorenstein smoothing
GCOEレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 118号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その4 Applications and open problems
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その4 Applications and open problems
[ 講演概要 ]
In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krötz-Stanton), random matrices (Huckleberry-Püttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
[ 参考URL ]In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krötz-Stanton), random matrices (Huckleberry-Püttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
2008年10月16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
Scott Morrison 氏 (UC Santa Barbara)
The $D_{2n}$ planar algebras
Scott Morrison 氏 (UC Santa Barbara)
The $D_{2n}$ planar algebras
講演会
15:00-16:00 数理科学研究科棟(駒場) 570号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その3 "Highest weight representations"
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その3 "Highest weight representations"
[ 講演概要 ]
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
[ 参考URL ]In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
Joseph F. Grotowski 氏 (University of Queensland)
Two-dimensional harmonic map heat flow versus four-dimensional Yang-Mills heat flow
Joseph F. Grotowski 氏 (University of Queensland)
Two-dimensional harmonic map heat flow versus four-dimensional Yang-Mills heat flow
[ 講演概要 ]
Harmonic map heat flow and Yang-Mills heat flow are the gradient flows associated to particular energy functionals. In the considered dimension, (i.e. dimension two for the harmonic map heat flow, dimension four for the Yang-Mills heat flow), the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. This leads to a number of interesting phenomena when considering both the functionals and the associated flows. In this talk we discuss qualitative similarities and differences between the flows.
Harmonic map heat flow and Yang-Mills heat flow are the gradient flows associated to particular energy functionals. In the considered dimension, (i.e. dimension two for the harmonic map heat flow, dimension four for the Yang-Mills heat flow), the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. This leads to a number of interesting phenomena when considering both the functionals and the associated flows. In this talk we discuss qualitative similarities and differences between the flows.
GCOEレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 123号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その3 Highest weight representations
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その3 Highest weight representations
[ 講演概要 ]
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
[ 参考URL ]In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
2008年10月15日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
八木厚志 氏 (大阪大学)
Asymptotic behavior of solutions for BCF model describing crystal surface growth
八木厚志 氏 (大阪大学)
Asymptotic behavior of solutions for BCF model describing crystal surface growth
[ 講演概要 ]
This talk is concerned with the initial-boundary value problem for a nonlinear parabolic equation which was presented Johnson et al. for describing the process of growth of a crystal surface on the
basis of the BCF theory. We will investigate asymptotic behavior of solutions by construct exponential attractors and a Lyapunov function and by examining a structure of the $\\omega$ limit set.
This talk is concerned with the initial-boundary value problem for a nonlinear parabolic equation which was presented Johnson et al. for describing the process of growth of a crystal surface on the
basis of the BCF theory. We will investigate asymptotic behavior of solutions by construct exponential attractors and a Lyapunov function and by examining a structure of the $\\omega$ limit set.
講演会
16:00-17:30 数理科学研究科棟(駒場) 002号室
George Sell 氏 (ミネソタ大学)
連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その2 The role of the 2D limit problem
George Sell 氏 (ミネソタ大学)
連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その2 The role of the 2D limit problem
[ 講演概要 ]
In both lectures we will examine a new topic of the thin
3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness
of strong solutions and the related theory of global
attractors.
In the second lecture, which will include a brief summary
of the first lecture, we will examine the role played by the
2D Limit Problem. These issues are a special challenge for
analysis because the 2D Limit Problem is NOT imbedded the
3D problem.
These lectures are based on joint work with Genevieve Raugel,Dragos Iftimie, and Luan Hoang.
In both lectures we will examine a new topic of the thin
3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness
of strong solutions and the related theory of global
attractors.
In the second lecture, which will include a brief summary
of the first lecture, we will examine the role played by the
2D Limit Problem. These issues are a special challenge for
analysis because the 2D Limit Problem is NOT imbedded the
3D problem.
These lectures are based on joint work with Genevieve Raugel,Dragos Iftimie, and Luan Hoang.
講演会
15:00-16:00 数理科学研究科棟(駒場) 570号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その2 "Geometric Background"
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その2 "Geometric Background"
[ 講演概要 ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ 参考URL ]In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
GCOEレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 122号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その2 Geometric background
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その2 Geometric background
[ 講演概要 ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ 参考URL ]In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert
2008年10月14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
Jeffrey Herschel Giansiracusa 氏 (Oxford University)
Pontrjagin-Thom maps and the Deligne-Mumford compactification
Tea: 16:00 - 16:30 コモンルーム
Jeffrey Herschel Giansiracusa 氏 (Oxford University)
Pontrjagin-Thom maps and the Deligne-Mumford compactification
[ 講演概要 ]
An embedding f: M -> N produces, via a construction of Pontrjagin-Thom, a map from N to the Thom space of the normal bundle over M. If f is an arbitrary map then one instead gets a map from N to the infinite loop space of the Thom spectrum of the normal bundle of f. We extend this Pontrjagin-Thom construction of wrong-way maps to differentiable stacks and use it to produce interesting maps from the Deligne-Mumford compactification of the moduli space of curves to certain infinite loop spaces. We show that these maps are surjective on mod p homology in a range of degrees. We thus produce large new families of torsion cohomology classes on the Deligne-Mumford compactification.
An embedding f: M -> N produces, via a construction of Pontrjagin-Thom, a map from N to the Thom space of the normal bundle over M. If f is an arbitrary map then one instead gets a map from N to the infinite loop space of the Thom spectrum of the normal bundle of f. We extend this Pontrjagin-Thom construction of wrong-way maps to differentiable stacks and use it to produce interesting maps from the Deligne-Mumford compactification of the moduli space of curves to certain infinite loop spaces. We show that these maps are surjective on mod p homology in a range of degrees. We thus produce large new families of torsion cohomology classes on the Deligne-Mumford compactification.
講演会
16:00-17:30 数理科学研究科棟(駒場) 002号室
George Sell 氏 (ミネソタ大学)
連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その1
Ultimate boundedness of solutions with large data and global attractors
George Sell 氏 (ミネソタ大学)
連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その1
Ultimate boundedness of solutions with large data and global attractors
[ 講演概要 ]
In both lectures we will examine a new topic of the thin 3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness of strong solutions and the related theory of global attractors.
In the second lecture, which will include a brief summary of the first lecture, we will examine the role played by the 2D Limit Problem. These issues are a special challenge for analysis because the 2D Limit Problem is NOT imbedded the 3D problem.
These lectures are based on joint work with Genevieve Raugel, Dragos Iftimie, and Luan Hoang.
In both lectures we will examine a new topic of the thin 3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness of strong solutions and the related theory of global attractors.
In the second lecture, which will include a brief summary of the first lecture, we will examine the role played by the 2D Limit Problem. These issues are a special challenge for analysis because the 2D Limit Problem is NOT imbedded the 3D problem.
These lectures are based on joint work with Genevieve Raugel, Dragos Iftimie, and Luan Hoang.
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