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Seminar information archive
Seminar information archive ～01/14｜Today's seminar 01/15 | Future seminars 01/16～
Seminar on Probability and Statistics
15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
矢田 和善 (筑波大学大学院数理物質科学研究科)
HDLSSデータにおけるPCAについて
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/05.html
矢田 和善 (筑波大学大学院数理物質科学研究科)
HDLSSデータにおけるPCAについて
[ Abstract ]
マイクロアレイデータなどに見られるように,データの次元数dが標本数nよりも遥かに大きな高次元小標本(HDLSS)データが,解析対象になる場面が増えてきている.
HDLSSデータに対して従来の統計手法を用いると,次元の呪いによって解析が上手くいかない.解決策の一つとして次元縮約法があり, その一つにPCAがある.高次元における従来型のPCAの漸近的性質は,正規性もしくは同等な仮定のもとで,先行研究が多数存在する. しかしながら,これら仮定は,HDLSSを研究する上で,厳しい制約にもなっている. Yata and Aoshimaの一連の研究は,この制約条件の枠を外すことから始まった.HDLSSにおける従来型PCAの限界は何か?推測が一致性をもつための標本数nと 次元数dの関係が,オーダー条件として明らかにされる.従来型PCAの限界を超える手法は何か?一つの実用的な方法として,クロス行列と呼ばれるデータの変換行列が導入され, この行列の特異値分解に基づいた新しいPCAが提案される.
当日は,マイクロアレイデータによる実例と,シミュレーション結果も交えながら,お話します.本研究は,筑波大学数理物質科学研究科の青嶋誠先生との共同研究です.
[ Reference URL ]マイクロアレイデータなどに見られるように,データの次元数dが標本数nよりも遥かに大きな高次元小標本(HDLSS)データが,解析対象になる場面が増えてきている.
HDLSSデータに対して従来の統計手法を用いると,次元の呪いによって解析が上手くいかない.解決策の一つとして次元縮約法があり, その一つにPCAがある.高次元における従来型のPCAの漸近的性質は,正規性もしくは同等な仮定のもとで,先行研究が多数存在する. しかしながら,これら仮定は,HDLSSを研究する上で,厳しい制約にもなっている. Yata and Aoshimaの一連の研究は,この制約条件の枠を外すことから始まった.HDLSSにおける従来型PCAの限界は何か?推測が一致性をもつための標本数nと 次元数dの関係が,オーダー条件として明らかにされる.従来型PCAの限界を超える手法は何か?一つの実用的な方法として,クロス行列と呼ばれるデータの変換行列が導入され, この行列の特異値分解に基づいた新しいPCAが提案される.
当日は,マイクロアレイデータによる実例と,シミュレーション結果も交えながら,お話します.本研究は,筑波大学数理物質科学研究科の青嶋誠先生との共同研究です.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/05.html
2009/09/29
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Sergei Duzhin (Steklov Mathematical Institute, Petersburg Division)
Symbol of the Conway polynomial and Drinfeld associator
Sergei Duzhin (Steklov Mathematical Institute, Petersburg Division)
Symbol of the Conway polynomial and Drinfeld associator
[ Abstract ]
The Magnus expansion is a universal finite type invariant of pure braids
with values in the space of horizontal chord diagrams. The Conway polynomial
composed with the short circuit map from braids to knots gives rise to a
series of finite type invariants of pure braids and thus factors through
the Magnus map. We describe explicitly the resulting mapping from horizontal
chord diagrams on 3 strands to univariante polynomials and evaluate it on
the Drinfeld associator obtaining a beautiful generating function whose
coefficients are integer combinations of multple zeta values.
The Magnus expansion is a universal finite type invariant of pure braids
with values in the space of horizontal chord diagrams. The Conway polynomial
composed with the short circuit map from braids to knots gives rise to a
series of finite type invariants of pure braids and thus factors through
the Magnus map. We describe explicitly the resulting mapping from horizontal
chord diagrams on 3 strands to univariante polynomials and evaluate it on
the Drinfeld associator obtaining a beautiful generating function whose
coefficients are integer combinations of multple zeta values.
2009/09/28
GCOE lecture series
15:30-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Claudio Landim (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, I
Claudio Landim (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, I
[ Abstract ]
We present a review of recent work on the statistical mechanics of nonequilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.
We present a review of recent work on the statistical mechanics of nonequilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.
2009/09/17
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Norayr MATEVOSYAN (ケンブリッジ大学・数理)
On a parabolic free boundary problem modelling price formation
Norayr MATEVOSYAN (ケンブリッジ大学・数理)
On a parabolic free boundary problem modelling price formation
[ Abstract ]
We will discuss existence and uniqueness of solutions for a one dimensional parabolic evolution equation with a free boundary. This problem was introduced by J.-M. Lasry and P.-L. Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in time-extension of the local solution which is intimately connected to the regularity of the free boundary.
We also present numerical results.
We will discuss existence and uniqueness of solutions for a one dimensional parabolic evolution equation with a free boundary. This problem was introduced by J.-M. Lasry and P.-L. Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in time-extension of the local solution which is intimately connected to the regularity of the free boundary.
We also present numerical results.
2009/09/15
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
打越 敬祐 (防衛大学校数学教育室)
渦層の超局所解析
打越 敬祐 (防衛大学校数学教育室)
渦層の超局所解析
[ Abstract ]
渦層とは,2次元流体が界面を境に2層に分かれて流れる状態で,今井功氏は「佐藤超関数は渦層である」と言っている.この考え方を用いると,
界面の時間変化を記述するBirkoff-Rott方程式を,擬微分方程式に書き直して解けることを説明する.
渦層とは,2次元流体が界面を境に2層に分かれて流れる状態で,今井功氏は「佐藤超関数は渦層である」と言っている.この考え方を用いると,
界面の時間変化を記述するBirkoff-Rott方程式を,擬微分方程式に書き直して解けることを説明する.
2009/09/14
Number Theory Seminar
11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Dinakar Ramakrishnan (カリフォルニア工科大学)
Modular forms and Calabi-Yau varieties
Dinakar Ramakrishnan (カリフォルニア工科大学)
Modular forms and Calabi-Yau varieties
2009/09/10
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Henrik SHAHGHOLIAN (王立工科大学・ストックホルム)
A two phase free boundary problem with applications in potential theory
Henrik SHAHGHOLIAN (王立工科大学・ストックホルム)
A two phase free boundary problem with applications in potential theory
[ Abstract ]
In this talk I will present some recent directions, still to be developed, in potential theory, that are connected to a two-phase free boundary problems. The potential theoretic topic that I will discuss is the so called Quadrature Domains.
The most simple free boundary/potential problem that we can present is the following. Given constants $a_\\pm, \\lambda_\\pm >0$ and two points $x^\\pm$ in ${\\bf R}^n$. Find a function $u$ such that
$$\\Delta u = \\left( \\lambda_+ \\chi_{\\{u>0 \\}} - a_+\\delta_{x^+}\\right) - \\left( \\lambda_- \\chi_{\\{u<0 \\}} - a_-\\delta_{x^-}\\right),$$
where $\\delta$ is the Dirac mass.
In general this problem is solvable for two Dirac masses. The requirement, somehow implicit in the above equation, is that the support of the measures (in this case the Dirac masses) is to be in included in the positivity and the negativity set (respectively).
In general this problem does not have a solution, and there some strong restrictions on the measures, in order to have some partial results.
In this talk I will present some recent directions, still to be developed, in potential theory, that are connected to a two-phase free boundary problems. The potential theoretic topic that I will discuss is the so called Quadrature Domains.
The most simple free boundary/potential problem that we can present is the following. Given constants $a_\\pm, \\lambda_\\pm >0$ and two points $x^\\pm$ in ${\\bf R}^n$. Find a function $u$ such that
$$\\Delta u = \\left( \\lambda_+ \\chi_{\\{u>0 \\}} - a_+\\delta_{x^+}\\right) - \\left( \\lambda_- \\chi_{\\{u<0 \\}} - a_-\\delta_{x^-}\\right),$$
where $\\delta$ is the Dirac mass.
In general this problem is solvable for two Dirac masses. The requirement, somehow implicit in the above equation, is that the support of the measures (in this case the Dirac masses) is to be in included in the positivity and the negativity set (respectively).
In general this problem does not have a solution, and there some strong restrictions on the measures, in order to have some partial results.
2009/09/08
GCOE Seminars
15:00-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
H.R.Thieme (Arizona State University)
Global compact attractors and their tripartition under persistence (ENGLISH)
H.R.Thieme (Arizona State University)
Global compact attractors and their tripartition under persistence (ENGLISH)
[ Abstract ]
The study of the dynamics of a semiflow (inertial manifolds, persistence) is largely facilitated if there is a global compact attractor, i.e. a compact invariant subset which attracts a sufficiently broad class of subsets of the state space.
Unfortunately, there in no uniform use of the concept of a global compact attractor in the literature: it has been used for a compact attractor of points, compact attractor of neighborhoods of compact sets, and compact attractor of bounded sets.
Persistence theory allows to discuss the long-term survival of populations in a dynamical systems framework. There is a two-way interaction between persistence and global compact attractors. On the one hand, the existence of a compact attractor of points helps to establish the persistence of the semiflow. On the other hand, the global attractor of a uniformly persistent semiflow divides into three invariant parts: an extinction attractor, a persistence attractor, and a set of orbits that connect the extinction to the persistence attractor. The persistence attractor has further interesting properties like local stability and connectedness. Examples are presented where the persistence attractor can be used to prove the global stability of the persistence equilibrium. (joint work with Hal L. Smith)
The study of the dynamics of a semiflow (inertial manifolds, persistence) is largely facilitated if there is a global compact attractor, i.e. a compact invariant subset which attracts a sufficiently broad class of subsets of the state space.
Unfortunately, there in no uniform use of the concept of a global compact attractor in the literature: it has been used for a compact attractor of points, compact attractor of neighborhoods of compact sets, and compact attractor of bounded sets.
Persistence theory allows to discuss the long-term survival of populations in a dynamical systems framework. There is a two-way interaction between persistence and global compact attractors. On the one hand, the existence of a compact attractor of points helps to establish the persistence of the semiflow. On the other hand, the global attractor of a uniformly persistent semiflow divides into three invariant parts: an extinction attractor, a persistence attractor, and a set of orbits that connect the extinction to the persistence attractor. The persistence attractor has further interesting properties like local stability and connectedness. Examples are presented where the persistence attractor can be used to prove the global stability of the persistence equilibrium. (joint work with Hal L. Smith)
GCOE Seminars
16:15-17:15 Room #123 (Graduate School of Math. Sci. Bldg.)
Glenn Webb (Vanderbilt University)
Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)
Glenn Webb (Vanderbilt University)
Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)
[ Abstract ]
We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
2009/09/07
Operator Algebra Seminars
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Marek Bozejko (University of Wroclaw)
Generalized Gaussian field, theta function of Jacobi and functor of second quantization
Marek Bozejko (University of Wroclaw)
Generalized Gaussian field, theta function of Jacobi and functor of second quantization
2009/09/01
Algebraic Geometry Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Matthias Schuett (Leibniz University Hannover)
Arithmetic of K3 surfaces
Matthias Schuett (Leibniz University Hannover)
Arithmetic of K3 surfaces
[ Abstract ]
This talk aims to review recent developments in the arithmetic of K3 surfaces, with emphasis on singular K3 surfaces.
We will consider in particular modularity, Galois action on Neron-Severi groups and behaviour in families.
This talk aims to review recent developments in the arithmetic of K3 surfaces, with emphasis on singular K3 surfaces.
We will consider in particular modularity, Galois action on Neron-Severi groups and behaviour in families.
2009/08/12
Lie Groups and Representation Theory
10:00-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Sigurdur Helgason (MIT) 10:00-11:00
Radon Transform and some Applications
Fulton G. Gonzalez (Tufts University) 11:20-12:20
Multitemporal Wave Equations: Mean Value Solutins
Angela Pasquale (Universite Metz) 14:00-15:00
Analytic continuation of the resolvent of the Laplacian in the Euclidean settings
Decay of smooth vectors for regular representations
Sigurdur Helgason (MIT) 10:00-11:00
Radon Transform and some Applications
Fulton G. Gonzalez (Tufts University) 11:20-12:20
Multitemporal Wave Equations: Mean Value Solutins
Angela Pasquale (Universite Metz) 14:00-15:00
Analytic continuation of the resolvent of the Laplacian in the Euclidean settings
[ Abstract ]
We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting.
Henrik Schlichtkrull (University of Copenhagen) 15:30-16:30We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting.
Decay of smooth vectors for regular representations
[ Abstract ]
Let $G/H$ be a homogeneous space of a Lie group, and consider the regular representation $L$ of $G$ on $E=L^p(G/H)$. A smooth vector for $L$ is a function $f$ in $E$ such that $g$ mapsto $L(g)f$ is smooth, $G$ to $E$. We investigate circumstances under which all such functions decay at infinity (jt with B. Krotz)
Let $G/H$ be a homogeneous space of a Lie group, and consider the regular representation $L$ of $G$ on $E=L^p(G/H)$. A smooth vector for $L$ is a function $f$ in $E$ such that $g$ mapsto $L(g)f$ is smooth, $G$ to $E$. We investigate circumstances under which all such functions decay at infinity (jt with B. Krotz)
2009/08/07
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Fabien Trihan (Nottingham大学)
On the $p$-parity conjecture in the function field case
Fabien Trihan (Nottingham大学)
On the $p$-parity conjecture in the function field case
[ Abstract ]
Let $F$ be a function field in one variable with field of constant a finite field of characteristic $p>0$. Let $E/F$ be an elliptic curve over $F$. We show that the order of the Hasse-Weil $L$-function of $E/F$ at $s=1$ and the corank of the $p$-Selmer group of $E/F$ have the same parity (joint work with C. Wuthrich).
Let $F$ be a function field in one variable with field of constant a finite field of characteristic $p>0$. Let $E/F$ be an elliptic curve over $F$. We show that the order of the Hasse-Weil $L$-function of $E/F$ at $s=1$ and the corank of the $p$-Selmer group of $E/F$ have the same parity (joint work with C. Wuthrich).
2009/07/30
GCOE lecture series
11:00-15:45 Room #002 (Graduate School of Math. Sci. Bldg.)
水町 徹 (九州大学) 11:00-12:00
長波長近似モデルと孤立波の安定性Ⅱ
Frank Merle (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅤ
Frank Merle (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅥ
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
水町 徹 (九州大学) 11:00-12:00
長波長近似モデルと孤立波の安定性Ⅱ
Frank Merle (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅤ
Frank Merle (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅥ
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
2009/07/29
GCOE lecture series
11:00-17:15 Room #002 (Graduate School of Math. Sci. Bldg.)
水町 徹 (京都大学) 11:00-12:00
長波長近似モデルと孤立波の安定性Ⅰ
Dynamics of solitons in non-integrable systemsⅢ
Frank Merle (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅣ
中西 賢次 (九州大学) 16:15-17:15
シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅡ
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
水町 徹 (京都大学) 11:00-12:00
長波長近似モデルと孤立波の安定性Ⅰ
[ Abstract ]
KdV方程式をはじめとする長波長近似の非線形分散型方程式は,水面波の運動やプラズマ中のイオンの運動を記述することで知られている. KdV方程式のソリトン解は安定的に伝播することが知られていたが,近年変分法に基づいたアプローチで非可積分系のモデルの場合にもソリトン解とよく似た解が安定的に存在することが証明された.第1回目の講演ではに変分原理に基づいた安定性の結果について概説し,次にFermi-Pasta-Ulam格子やある種の流体のbidirectional modelなど変分原理から安定性がうまく説明できないモデルの場合について述べる.
Frank Merle (Cergy Pontoise 大学/IHES) 13:30-14:30KdV方程式をはじめとする長波長近似の非線形分散型方程式は,水面波の運動やプラズマ中のイオンの運動を記述することで知られている. KdV方程式のソリトン解は安定的に伝播することが知られていたが,近年変分法に基づいたアプローチで非可積分系のモデルの場合にもソリトン解とよく似た解が安定的に存在することが証明された.第1回目の講演ではに変分原理に基づいた安定性の結果について概説し,次にFermi-Pasta-Ulam格子やある種の流体のbidirectional modelなど変分原理から安定性がうまく説明できないモデルの場合について述べる.
Dynamics of solitons in non-integrable systemsⅢ
Frank Merle (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅣ
中西 賢次 (九州大学) 16:15-17:15
シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅡ
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
2009/07/28
GCOE lecture series
13:30-17:15 Room #002 (Graduate School of Math. Sci. Bldg.)
Frank Merle (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅠ
Dynamics of solitons in non-integrable systemsⅡ
中西 賢次 (京都大学) 16:15-17:15
シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅠ
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
Frank Merle (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅠ
[ Abstract ]
完全可積分系であるKdV方程式においては,多重ソリトン解の構造はすでに詳しく解明されており,ソリトンどうしが衝突した後,各ソリトンの形状がすぐに元通りに復元するなどの性質もよく知られている.しかし方程式中の指数を変えて得られる一般化KdV方程式の場合は,非可積分系であるため,多重ソリトン解の便利な表示式は存在せず,ソリトンどうしの衝突後に何が起こるのか,理論的には未解明であった.Merle氏は,最近Yvon Martel氏と共同でこの問題を解決し,衝突後にわずかな欠損が生じるもののソリトンの形状が見事に復元することを証明するとともに,大きなソリトンが微小なソリトンと衝突した際に生じる位相(phase)のズレに関して, KdV方程式の場合と全く違う現象が起こることも明らかにした.
Frank Merle (Cergy Pontoise 大学/IHES) 14:45-15:45完全可積分系であるKdV方程式においては,多重ソリトン解の構造はすでに詳しく解明されており,ソリトンどうしが衝突した後,各ソリトンの形状がすぐに元通りに復元するなどの性質もよく知られている.しかし方程式中の指数を変えて得られる一般化KdV方程式の場合は,非可積分系であるため,多重ソリトン解の便利な表示式は存在せず,ソリトンどうしの衝突後に何が起こるのか,理論的には未解明であった.Merle氏は,最近Yvon Martel氏と共同でこの問題を解決し,衝突後にわずかな欠損が生じるもののソリトンの形状が見事に復元することを証明するとともに,大きなソリトンが微小なソリトンと衝突した際に生じる位相(phase)のズレに関して, KdV方程式の場合と全く違う現象が起こることも明らかにした.
Dynamics of solitons in non-integrable systemsⅡ
中西 賢次 (京都大学) 16:15-17:15
シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅠ
[ Abstract ]
平面から球面への調和写像をシュレディンガーや熱流で時間発展させたときの漸近安定性を回転対称下で調べる.この問題は,調和写像の写像度が低いほど摂動部との空間遠方相互作用が大きくなる所が難しく,実際写像度2の熱流では初期摂動に応じて非自明な時間漸近挙動が現れる.この講演では,非線形シュディンガー方程式の場合をモデルとして比較しながら、漸近安定性を示す一般的な手続きとそこからの変更点,必要となる線形評価などについて解説する.
[ Reference URL ]平面から球面への調和写像をシュレディンガーや熱流で時間発展させたときの漸近安定性を回転対称下で調べる.この問題は,調和写像の写像度が低いほど摂動部との空間遠方相互作用が大きくなる所が難しく,実際写像度2の熱流では初期摂動に応じて非自明な時間漸近挙動が現れる.この講演では,非線形シュディンガー方程式の場合をモデルとして比較しながら、漸近安定性を示す一般的な手続きとそこからの変更点,必要となる線形評価などについて解説する.
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
2009/07/27
thesis presentations
14:00-15:15 Room #123 (Graduate School of Math. Sci. Bldg.)
野澤 啓 (東京大学大学院数理科学研究科)
『Five dimensional K-contact Manifolds of rank 2(階数2の5次元K接触多様体について)』
野澤 啓 (東京大学大学院数理科学研究科)
『Five dimensional K-contact Manifolds of rank 2(階数2の5次元K接触多様体について)』
Kavli IPMU Komaba Seminar
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Misha Verbitsky (ITEP Moscow/IPMU)
Mapping class group for hyperkaehler manifolds
Misha Verbitsky (ITEP Moscow/IPMU)
Mapping class group for hyperkaehler manifolds
[ Abstract ]
A mapping class group is a group of orientation-preserving
diffeomorphisms up to isotopy. I explain how to compute a
mapping class group of a hyperkaehler manifold. It is
commensurable to an arithmetic lattice in a Lie group
$SO(n-3,3)$. This makes it possible to state and prove a
new version of Torelli theorem.
A mapping class group is a group of orientation-preserving
diffeomorphisms up to isotopy. I explain how to compute a
mapping class group of a hyperkaehler manifold. It is
commensurable to an arithmetic lattice in a Lie group
$SO(n-3,3)$. This makes it possible to state and prove a
new version of Torelli theorem.
2009/07/24
Colloquium
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Carlos Simpson (CNRS, University of Nice)
Differential equations and the topology of algebraic varieties
Carlos Simpson (CNRS, University of Nice)
Differential equations and the topology of algebraic varieties
[ Abstract ]
The study of the topology of complex algebraic varieties makes use of differential equations in several different ways. The classical notion of variation of Hodge structure contains, on the one hand, the Gauss-Manin differential equations, on the other hand Hodge metric data which satisfy harmonic bundle equations. These two aspects persist in the study of arbitrary representations of the fundamental group. Combining them leads to a notion of ``Hodge structure'' on the space of representations. This can be extended to the higher homotopical structure of a variety, by using ideas of ``shape'' and nonabelian cohomology.
The study of the topology of complex algebraic varieties makes use of differential equations in several different ways. The classical notion of variation of Hodge structure contains, on the one hand, the Gauss-Manin differential equations, on the other hand Hodge metric data which satisfy harmonic bundle equations. These two aspects persist in the study of arbitrary representations of the fundamental group. Combining them leads to a notion of ``Hodge structure'' on the space of representations. This can be extended to the higher homotopical structure of a variety, by using ideas of ``shape'' and nonabelian cohomology.
Infinite Analysis Seminar Tokyo
13:00-15:30 Room #056 (Graduate School of Math. Sci. Bldg.)
武部尚志 (Faculty of Math, Higher School of Economics, Moscow) 13:00-14:00
On recursion relation of the KP hierarchy
球面のフルビッツ数とKP・戸田階層の特殊解
武部尚志 (Faculty of Math, Higher School of Economics, Moscow) 13:00-14:00
On recursion relation of the KP hierarchy
[ Abstract ]
This talk is based on an ongoing project in collaboration with Takasaki and Tsuchiya. Our goal is to reconstruct and generalise results by Eynard et al. from the standpoint of the integrable systems. Eynard, Orantin and their collaborators found "topological recursion formulae" to describe partition functions and correlation functions of the matrix models, topological string theories etc., using simple algebro-geometric data called "spectral curves". On the other hand, it is well known that the partition functions of those theories are tau functions of integrable hierarchies.
We have found that any solution of the KP hierarchy (with an asymptotic expansion parameter h) can be recovered by recursion relations from its "dispersionless" part (which corresponds to the genus zero part in topological theories) and a quantised contact transformation (which corresponds to the string equations) specifying the solution.
高崎金久 (京大人間) 14:30-15:30This talk is based on an ongoing project in collaboration with Takasaki and Tsuchiya. Our goal is to reconstruct and generalise results by Eynard et al. from the standpoint of the integrable systems. Eynard, Orantin and their collaborators found "topological recursion formulae" to describe partition functions and correlation functions of the matrix models, topological string theories etc., using simple algebro-geometric data called "spectral curves". On the other hand, it is well known that the partition functions of those theories are tau functions of integrable hierarchies.
We have found that any solution of the KP hierarchy (with an asymptotic expansion parameter h) can be recovered by recursion relations from its "dispersionless" part (which corresponds to the genus zero part in topological theories) and a quantised contact transformation (which corresponds to the string equations) specifying the solution.
球面のフルビッツ数とKP・戸田階層の特殊解
[ Abstract ]
球面の1点を指定し、その上方で任意被覆型の分岐点
をもち、それ以外では単純分岐点のみもつような n 次分岐被覆を考える。
このような分岐被覆の位相的同型類の個数は単純フルビッツ数と呼ばれる。
1点の代わりに2点を指定して同様に定義されるものは2重フルビッツ数である。
これらのフルビッツ数にシューア函数を乗じて総和したものはそれぞれ
KP階層および戸田階層のτ函数になることが知られている。この講演では
これらの特殊解においてラックス作用素とオルロフ・シュルマン作用素が
満たす関係式 (拘束条件) を紹介し、そこから導かれる帰結を探る。
球面の1点を指定し、その上方で任意被覆型の分岐点
をもち、それ以外では単純分岐点のみもつような n 次分岐被覆を考える。
このような分岐被覆の位相的同型類の個数は単純フルビッツ数と呼ばれる。
1点の代わりに2点を指定して同様に定義されるものは2重フルビッツ数である。
これらのフルビッツ数にシューア函数を乗じて総和したものはそれぞれ
KP階層および戸田階層のτ函数になることが知られている。この講演では
これらの特殊解においてラックス作用素とオルロフ・シュルマン作用素が
満たす関係式 (拘束条件) を紹介し、そこから導かれる帰結を探る。
2009/07/23
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Catherine Oikonomides (慶応大理工)
Cyclic cohomology and the Novikov conjecture
Catherine Oikonomides (慶応大理工)
Cyclic cohomology and the Novikov conjecture
2009/07/21
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Georgi Raikov (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
Georgi Raikov (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
[ Abstract ]
In my talk, I will consider the 3D Pauli operator with non-constant magnetic field of constant direction,
perturbed by a matrix-valued electric potential which decays fast enough at infinity. I will discuss
the low-energy asymptotics of the associated spectral shift function which is proportional to the eigenvalue
counting function at negative energies, and to the scattering phase at positive energies.
In my talk, I will consider the 3D Pauli operator with non-constant magnetic field of constant direction,
perturbed by a matrix-valued electric potential which decays fast enough at infinity. I will discuss
the low-energy asymptotics of the associated spectral shift function which is proportional to the eigenvalue
counting function at negative energies, and to the scattering phase at positive energies.
2009/07/18
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
大石亮子 (高エネルギー加速器研究機構(KEK)) 13:30-14:30
On some algebraic properties of CM-types of CM-fileds and their reflexs
織田孝幸 (東京大学数理科学研究科) 15:00-16:00
仮題:GL(n)のWhittaker関数に関連する今後の問題
大石亮子 (高エネルギー加速器研究機構(KEK)) 13:30-14:30
On some algebraic properties of CM-types of CM-fileds and their reflexs
織田孝幸 (東京大学数理科学研究科) 15:00-16:00
仮題:GL(n)のWhittaker関数に関連する今後の問題
[ Abstract ]
今回は、普段から言及している、未解決の問題をできればなるべくきちんと定式化したい。「GL(n)上の保型形式論は終わった」という愚かな愚かな人たちもいるが、実は彼らにも新たな研究手法が必要であることを指摘したい。実際、現状ではカスプ形式の存在論に関しては、ほとんど何も分かっていない。
今回は、普段から言及している、未解決の問題をできればなるべくきちんと定式化したい。「GL(n)上の保型形式論は終わった」という愚かな愚かな人たちもいるが、実は彼らにも新たな研究手法が必要であることを指摘したい。実際、現状ではカスプ形式の存在論に関しては、ほとんど何も分かっていない。
2009/07/17
Colloquium
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Universite Paris-Sud)
Holomorphic dynamics in several variables: equidistribution problems and statistical properties
Nessim Sibony (Universite Paris-Sud)
Holomorphic dynamics in several variables: equidistribution problems and statistical properties
[ Abstract ]
The main problem in the dynamical study of a map is to understand the long term behavior of orbits. The abstract theory of non uniformly hyperbolic systems is well understood but it is very difficult to decide when a given system is non uniformly hyperbolic and to study it's sharp ergodic properties.
Holomorphic dynamics in several variables provide large classes of examples of non uniformly hyperbolic systems. One can compute the entropy, construct a measure of maximal entropy and study the sharp statistical properties: central limit theorem, large deviations and exponential decay of correlations. It is also possible to prove sharp equidistribution results for preimages of analytic sets of arbitrary dimension. The main tools are: pluripotential theory, analytic geometry, and good estimates from PDE.
These systems appear naturally if we apply Newton's method to localise the common zeros of of polynomial equations in several variables. In the study of polynomial automorphisms of complex Euclidean spaces, or automorphisms of compact K\\"ahler manifolds.
The main problem in the dynamical study of a map is to understand the long term behavior of orbits. The abstract theory of non uniformly hyperbolic systems is well understood but it is very difficult to decide when a given system is non uniformly hyperbolic and to study it's sharp ergodic properties.
Holomorphic dynamics in several variables provide large classes of examples of non uniformly hyperbolic systems. One can compute the entropy, construct a measure of maximal entropy and study the sharp statistical properties: central limit theorem, large deviations and exponential decay of correlations. It is also possible to prove sharp equidistribution results for preimages of analytic sets of arbitrary dimension. The main tools are: pluripotential theory, analytic geometry, and good estimates from PDE.
These systems appear naturally if we apply Newton's method to localise the common zeros of of polynomial equations in several variables. In the study of polynomial automorphisms of complex Euclidean spaces, or automorphisms of compact K\\"ahler manifolds.
Seminar on Geometric Complex Analysis
13:45-14:45 Room #128 (Graduate School of Math. Sci. Bldg.)
Karl Oeljeklaus (University of Provence)
Logarthmic
Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)
Karl Oeljeklaus (University of Provence)
Logarthmic
Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)
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