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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
GCOE lecture series
14:40-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory
, Lecture 2
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory
, Lecture 2
2008/11/26
Algebraic Geometry Seminar
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Piotr Pragacz
(Banach Institute)
Diagonal subschemes and vector bundles
Piotr Pragacz
(Banach Institute)
Diagonal subschemes and vector bundles
GCOE lecture series
14:40-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory, Lecture 1
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory, Lecture 1
[ Abstract ]
Morse theory of circle-valued functions, initiated by S. P. Novikov in 1980-1982 is now a rapidly developing domain with applications and connections to many other fields of geometry and topology such as dynamical systems, Lagrangian intersections,
knots and links in three-dimensional sphere.
We will start with the basics of the theory, discuss the construction of the Novikov complex, relations with the dynamical zeta functions, and the knot theory. We will conclude with a list of the open problems of the theory.
Morse theory of circle-valued functions, initiated by S. P. Novikov in 1980-1982 is now a rapidly developing domain with applications and connections to many other fields of geometry and topology such as dynamical systems, Lagrangian intersections,
knots and links in three-dimensional sphere.
We will start with the basics of the theory, discuss the construction of the Novikov complex, relations with the dynamical zeta functions, and the knot theory. We will conclude with a list of the open problems of the theory.
Number Theory Seminar
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
平田典子 (日本大学理工学部)
Lang's Observation in Diophantine Problems
平田典子 (日本大学理工学部)
Lang's Observation in Diophantine Problems
[ Abstract ]
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let $E$ be an elliptic curve defined over a number field $K$, and $\\varphi$ be a rational function on $E$. Then, for every point $P\\in E(K)$ where $\\varphi$ does not vanish at $P$, the logarithms of a norm of $\\varphi(P)$ is at worst linear in the logarithms of the Neron-Tate height of the point $P$.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let $E$ be an elliptic curve defined over a number field $K$, and $\\varphi$ be a rational function on $E$. Then, for every point $P\\in E(K)$ where $\\varphi$ does not vanish at $P$, the logarithms of a norm of $\\varphi(P)$ is at worst linear in the logarithms of the Neron-Tate height of the point $P$.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.
2008/11/25
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ovidiu Calin (Eastern Michigan University)
Heat kernels for subelliptic operators
Ovidiu Calin (Eastern Michigan University)
Heat kernels for subelliptic operators
[ Abstract ]
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels of
subelliptic operators. The heat kernels of subelliptic operators are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators too.
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels of
subelliptic operators. The heat kernels of subelliptic operators are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators too.
Algebraic Geometry Seminar
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Xavier Roulleau (東大)
Cotangent maps of surfaces of general type
Xavier Roulleau (東大)
Cotangent maps of surfaces of general type
[ Abstract ]
Surfaces are usualy studied and classified via the properties of the pluricanonical maps. For surfaces of general type whose cotangent sheaf is generated by global sections, we propose to study an other map, called the cotangent map, in order to obtain geometric informations on the surface. In this way, we obtain informations on the ampleness of the cotangent sheaf of such a surface. We will illustate this talk with the example of the Fano surface of lines of cubic threefolds.
Surfaces are usualy studied and classified via the properties of the pluricanonical maps. For surfaces of general type whose cotangent sheaf is generated by global sections, we propose to study an other map, called the cotangent map, in order to obtain geometric informations on the surface. In this way, we obtain informations on the ampleness of the cotangent sheaf of such a surface. We will illustate this talk with the example of the Fano surface of lines of cubic threefolds.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
吉野太郎 (東工大)
$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
吉野太郎 (東工大)
$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
[ Abstract ]
Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:
"Does the quotient topology admits a manifold structure?"
Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.
If Lipsman's conjecture were true, all of the answer should be affirmative.
But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.
As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
[ Reference URL ]Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:
"Does the quotient topology admits a manifold structure?"
Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.
If Lipsman's conjecture were true, all of the answer should be affirmative.
But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.
As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory for knots and links
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory for knots and links
[ Abstract ]
We will discuss several recent developments in
this theory. In the first part of the talk we prove that the Morse-Novikov number of a knot is less than or equal to twice the tunnel number of the knot, and present consequences of this result. In the second part we report on our joint project with Hiroshi Goda on the half-transversal Morse-Novikov theory for 3-manifolds.
We will discuss several recent developments in
this theory. In the first part of the talk we prove that the Morse-Novikov number of a knot is less than or equal to twice the tunnel number of the knot, and present consequences of this result. In the second part we report on our joint project with Hiroshi Goda on the half-transversal Morse-Novikov theory for 3-manifolds.
2008/11/22
Infinite Analysis Seminar Tokyo
13:30-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)
桂 法称 ((理化学研究所)
理化学研究所) 13:30-14:30
Quantum Entanglement in Exactly Solvable Models
非例外型KRクリスタルについて
桂 法称 ((理化学研究所)
理化学研究所) 13:30-14:30
Quantum Entanglement in Exactly Solvable Models
[ Abstract ]
近年、量子情報論的な観点からの量子多体問題の研究が盛んに行われている。
特に基底状態におけるentanglementのvon Neumann(entanglement) entropyなどの
指標を用いた特徴づけが盛んに議論されている。これらの研究において可解模型
は、この新しく導入された指標が量子多体系の基本性質を正しく反映しているか
をテストする一種の実験室として重要な役割を果たしてきた。セミナーでは、
先ずentanglement entropyの定義などについての簡単な説明を行い、その後私が
主に行ってきた以下の幾つかのテーマについてご紹介したい。
1. Affleck-Kennedy-Lieb-Tasaki modelのvalence bond solid基底状態におけるenta
nglementと端状態
2. Calogero-Sutherland modelにおける粒子間entanglementと排他的分数統計
3. Bethe ansatz波動関数の行列積表示
尚、本研究は初田泰之(東大理), 平野嵩明(東大工)、丸山勲(大阪大)、初貝安弘(筑
波大)、Ying Xu, Vladimir E. Korepin(SUNY at Stony Brook)各氏との共同研究に基
づくものである。
尾角正人 (阪大基礎工) 15:00-16:00近年、量子情報論的な観点からの量子多体問題の研究が盛んに行われている。
特に基底状態におけるentanglementのvon Neumann(entanglement) entropyなどの
指標を用いた特徴づけが盛んに議論されている。これらの研究において可解模型
は、この新しく導入された指標が量子多体系の基本性質を正しく反映しているか
をテストする一種の実験室として重要な役割を果たしてきた。セミナーでは、
先ずentanglement entropyの定義などについての簡単な説明を行い、その後私が
主に行ってきた以下の幾つかのテーマについてご紹介したい。
1. Affleck-Kennedy-Lieb-Tasaki modelのvalence bond solid基底状態におけるenta
nglementと端状態
2. Calogero-Sutherland modelにおける粒子間entanglementと排他的分数統計
3. Bethe ansatz波動関数の行列積表示
尚、本研究は初田泰之(東大理), 平野嵩明(東大工)、丸山勲(大阪大)、初貝安弘(筑
波大)、Ying Xu, Vladimir E. Korepin(SUNY at Stony Brook)各氏との共同研究に基
づくものである。
非例外型KRクリスタルについて
[ Abstract ]
KRクリスタルとはアフィンリー環gのディンキン図の0以外の頂点と
正整数に付随して定義される量子アフィン代数の特殊な有限次元
表現(KR加群)の結晶基底である。KRクリスタルの存在は非例外型
の場合には昨年確認された。今年になって、それらの結晶グラフの
構造が組合せ論的に具体的にわかる進展があったので、そのこと
についてgが$A_{2n-1}^{(2)}$と$C_n^{(1)}$の場合にお話したい。
また、組合せ論的に与えた結晶グラフが、なぜ表現論的に存在が
わかった結晶基底のグラフと一致するかについての証明の概略に
ついても触れたい。
KRクリスタルとはアフィンリー環gのディンキン図の0以外の頂点と
正整数に付随して定義される量子アフィン代数の特殊な有限次元
表現(KR加群)の結晶基底である。KRクリスタルの存在は非例外型
の場合には昨年確認された。今年になって、それらの結晶グラフの
構造が組合せ論的に具体的にわかる進展があったので、そのこと
についてgが$A_{2n-1}^{(2)}$と$C_n^{(1)}$の場合にお話したい。
また、組合せ論的に与えた結晶グラフが、なぜ表現論的に存在が
わかった結晶基底のグラフと一致するかについての証明の概略に
ついても触れたい。
2008/11/21
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #128 (Graduate School of Math. Sci. Bldg.)
大本 隆 (野村證券金融工学研究センター)
デリバティブ・プロダクツの価格付け II
大本 隆 (野村證券金融工学研究センター)
デリバティブ・プロダクツの価格付け II
Colloquium
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
平地健吾 (東京大学大学院数理科学研究科)
What is Q-curvature?
次回開催日は11月28日(金)(講演者:川又雄二郎 氏)です。ご注意下さい。
平地健吾 (東京大学大学院数理科学研究科)
What is Q-curvature?
[ Abstract ]
共形幾何は次元の偶奇におうじて著しく異なった性質をもちます。その多くは n次元球面の共形自己同型群SO(n+1,1)が奇数次元ならB型,偶数次元ならD型になるといことから説明できます。この講演では偶数次元にのみ現れるQ-曲率とよばれる局所不変量とその周辺に現れる共形不変量および不変作用素の理論を紹介します。Q-曲率はAdS/CFT対応にも自然に現れることもあり,最近の共形幾何の主要テーマになっていますが,その定義は簡単ではありません。Q-曲率の(短い)歴史と表現論の結果をふまえて,なっとくのできる定義を与えることを目指します。
[ Reference URL ]共形幾何は次元の偶奇におうじて著しく異なった性質をもちます。その多くは n次元球面の共形自己同型群SO(n+1,1)が奇数次元ならB型,偶数次元ならD型になるといことから説明できます。この講演では偶数次元にのみ現れるQ-曲率とよばれる局所不変量とその周辺に現れる共形不変量および不変作用素の理論を紹介します。Q-曲率はAdS/CFT対応にも自然に現れることもあり,最近の共形幾何の主要テーマになっていますが,その定義は簡単ではありません。Q-曲率の(短い)歴史と表現論の結果をふまえて,なっとくのできる定義を与えることを目指します。
次回開催日は11月28日(金)(講演者:川又雄二郎 氏)です。ご注意下さい。
2008/11/20
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Jan Haskovec
(Vienna University of Technology(オーストリア))
Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System
Jan Haskovec
(Vienna University of Technology(オーストリア))
Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System
[ Abstract ]
We construct an approximation to the measure valued, global in time solutions to the Keller-Segel model in 2D, based on systems of stochastic interacting particles. The advantage of our approach is that it reproduces the well-known dichtomy in the qualitative behavior of the system and, moreover, captures the solution even after the possible blow-up events. We present a numerical method based on this approach and show some numerical results. Moreover, we make a first step toward the convergence analysis of our scheme by proving the convergence of the stochastic particle approximation for the Keller-Segel model with a regularized interaction potential. The proof is based on a BBGKY-like approach for the corresponding particle distribution function.
We construct an approximation to the measure valued, global in time solutions to the Keller-Segel model in 2D, based on systems of stochastic interacting particles. The advantage of our approach is that it reproduces the well-known dichtomy in the qualitative behavior of the system and, moreover, captures the solution even after the possible blow-up events. We present a numerical method based on this approach and show some numerical results. Moreover, we make a first step toward the convergence analysis of our scheme by proving the convergence of the stochastic particle approximation for the Keller-Segel model with a regularized interaction potential. The proof is based on a BBGKY-like approach for the corresponding particle distribution function.
2008/11/19
Number Theory Seminar
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Olivier Fouquet (大阪大学)
Dihedral Iwasawa theory of ordinary modular forms
Olivier Fouquet (大阪大学)
Dihedral Iwasawa theory of ordinary modular forms
[ Abstract ]
According to Hida theory, the Galois representation attached to a nearly-ordinary Hilbert eigencuspform belongs to a p-adic analytic family of Galois representations parametrized by varying weights. After restricting it to the absolute Galois group of a quadratic totally complex extension, it also belongs to a p-adic family coming from classical dihedral Iwasawa theory. We will explain the proofs of part of the main conjecture in Iwasawa theory in these situations, i.e divisibilities of characteristic ideals when equalities are actually expected.
According to Hida theory, the Galois representation attached to a nearly-ordinary Hilbert eigencuspform belongs to a p-adic analytic family of Galois representations parametrized by varying weights. After restricting it to the absolute Galois group of a quadratic totally complex extension, it also belongs to a p-adic family coming from classical dihedral Iwasawa theory. We will explain the proofs of part of the main conjecture in Iwasawa theory in these situations, i.e divisibilities of characteristic ideals when equalities are actually expected.
2008/11/18
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jorge Vargas (FAMAF-CIEM, C\'ordoba)
Liouville measures and multiplicity formulae for admissible restriction of Discrete Series
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Jorge Vargas (FAMAF-CIEM, C\'ordoba)
Liouville measures and multiplicity formulae for admissible restriction of Discrete Series
[ Abstract ]
Let $H \\subset G$ be reductive matrix Lie groups. We fix a square integrable irreducible representation $\\pi$ of $G.$
Let $\\Omega $ denote the coadjoint orbit of the Harish-Chandra parameter of $\\pi.$
Assume $\\pi$ restricted to $H$ is admissible. In joint work with Michel Duflo, by means of "discrete" and "continuos" Heaviside functions we relate the multiplicity of each irreducible $H-$factor of $\\pi$ restricted to $H$ and push forward to $\\mathfrak h^\\star$ of the Liouville measure for $\\Omega.$ This generalizes work of Duflo-Heckman-Vergne.
[ Reference URL ]Let $H \\subset G$ be reductive matrix Lie groups. We fix a square integrable irreducible representation $\\pi$ of $G.$
Let $\\Omega $ denote the coadjoint orbit of the Harish-Chandra parameter of $\\pi.$
Assume $\\pi$ restricted to $H$ is admissible. In joint work with Michel Duflo, by means of "discrete" and "continuos" Heaviside functions we relate the multiplicity of each irreducible $H-$factor of $\\pi$ restricted to $H$ and push forward to $\\mathfrak h^\\star$ of the Liouville measure for $\\Omega.$ This generalizes work of Duflo-Heckman-Vergne.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
宍倉 光広 (京都大学大学院理学研究科)
複素力学系のくりこみと剛性
宍倉 光広 (京都大学大学院理学研究科)
複素力学系のくりこみと剛性
[ Abstract ]
無限に分岐が集積しているような
ある種の力学系においては、相空間やパラメータ空間の
微細構造が取り上げる個々の力学系の族に寄らない
普遍的構造をもったりすることが知られており、
ある意味で剛性の問題とつながっている。この現象の説明には、
ある部分集合への再帰写像の構成から得られる、あるクラスの
力学系全体の空間で定義されるメタ力学系としての
くりこみ作用素の考え方が重要である。これに関して、
講演者と稲生啓行による中立的不動点をもつ複素力学系の
近放物型くりこみの話を中心に解説する。
無限に分岐が集積しているような
ある種の力学系においては、相空間やパラメータ空間の
微細構造が取り上げる個々の力学系の族に寄らない
普遍的構造をもったりすることが知られており、
ある意味で剛性の問題とつながっている。この現象の説明には、
ある部分集合への再帰写像の構成から得られる、あるクラスの
力学系全体の空間で定義されるメタ力学系としての
くりこみ作用素の考え方が重要である。これに関して、
講演者と稲生啓行による中立的不動点をもつ複素力学系の
近放物型くりこみの話を中心に解説する。
2008/11/17
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
野沢 啓 (東大数理)
Deformation of Sasakian metrics
野沢 啓 (東大数理)
Deformation of Sasakian metrics
2008/11/14
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #128 (Graduate School of Math. Sci. Bldg.)
中川 淳一 (新日本製鐵先端技術研究所)
製鐵プロセスの数学Ⅰ
中川 淳一 (新日本製鐵先端技術研究所)
製鐵プロセスの数学Ⅰ
2008/11/13
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
杉山 由恵 (津田塾大学・学芸学部・数学科)
Aronson-Benilan type estimate and the optimal Hoelder continuity of weak solutions for the 1D degenerate Keller-Segel systems
杉山 由恵 (津田塾大学・学芸学部・数学科)
Aronson-Benilan type estimate and the optimal Hoelder continuity of weak solutions for the 1D degenerate Keller-Segel systems
[ Abstract ]
We consider the Cauchy problem for the 1D Keller-Segel system of degenerate
type (KS)_m with $m>1$:
u_t= \\partial_x^2 u^m - \\partial_x (u^{q-2} \\partial_x v),
-\\partial_x^2 v + v - u=0.
We establish a uniform estimate from below of $\\partial_x^2 u^{m-1}$.
The corresponding estimate to the porous medium equation is well-known
as an Aronson-Benilan type.
As an application of our Aronson-Benilan type estimate,
we prove the optimal Hoelder continuity of the weak solution $u$ of (KS)_m.
In addition, we find that the positive region $D(t):=\\{x \\in \\R; u(x,t)>0\\}$
of $u$ is monotonically non-decreasing with respect to the time $t$.
We consider the Cauchy problem for the 1D Keller-Segel system of degenerate
type (KS)_m with $m>1$:
u_t= \\partial_x^2 u^m - \\partial_x (u^{q-2} \\partial_x v),
-\\partial_x^2 v + v - u=0.
We establish a uniform estimate from below of $\\partial_x^2 u^{m-1}$.
The corresponding estimate to the porous medium equation is well-known
as an Aronson-Benilan type.
As an application of our Aronson-Benilan type estimate,
we prove the optimal Hoelder continuity of the weak solution $u$ of (KS)_m.
In addition, we find that the positive region $D(t):=\\{x \\in \\R; u(x,t)>0\\}$
of $u$ is monotonically non-decreasing with respect to the time $t$.
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (IPMU)
Groups of friezes and property RD
Mikael Pichot (IPMU)
Groups of friezes and property RD
2008/11/11
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
新國 裕昭 (首都大学東京)
Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians
新國 裕昭 (首都大学東京)
Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Andrew Putman (MIT)
The second rational homology group of the moduli space of curves
with level structures
Thomas Andrew Putman (MIT)
The second rational homology group of the moduli space of curves
with level structures
[ Abstract ]
Let $\\Gamma$ be a finite-index subgroup of the mapping class
group of a closed genus $g$ surface that contains the Torelli group. For
instance, $\\Gamma$ can be the level $L$ subgroup or the spin mapping class
group. We show that $H_2(\\Gamma;\\Q) \\cong \\Q$ for $g \\geq 5$. A corollary
of this is that the rational Picard groups of the associated finite covers
of the moduli space of curves are equal to $\\Q$. We also prove analogous
results for surface with punctures and boundary components.
Let $\\Gamma$ be a finite-index subgroup of the mapping class
group of a closed genus $g$ surface that contains the Torelli group. For
instance, $\\Gamma$ can be the level $L$ subgroup or the spin mapping class
group. We show that $H_2(\\Gamma;\\Q) \\cong \\Q$ for $g \\geq 5$. A corollary
of this is that the rational Picard groups of the associated finite covers
of the moduli space of curves are equal to $\\Q$. We also prove analogous
results for surface with punctures and boundary components.
2008/11/10
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
川口 周 (阪大理)
射影空間の射に関する高さ関数の力学系的性質
川口 周 (阪大理)
射影空間の射に関する高さ関数の力学系的性質
2008/11/07
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #128 (Graduate School of Math. Sci. Bldg.)
大本 隆 (野村證券金融工学研究センター)
デリバティブ・プロダクツの価格付け I
大本 隆 (野村證券金融工学研究センター)
デリバティブ・プロダクツの価格付け I
Algebraic Geometry Seminar
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Misha Verbitsky (ITEP and IPMU)
Hyperkaehler SYZ conjecture and stability
Misha Verbitsky (ITEP and IPMU)
Hyperkaehler SYZ conjecture and stability
[ Abstract ]
Let L be a nef bundle on a hyperkaehler manifold. A Hyperkaehler SYZ conjecture postulates that L is semi-ample. As shown by Matsushita, this implies existence of holomorphic Lagrangian fibrations on hyperkaehler manifolds. It was conjectured by many
people, most recently by Tschinkel, Hassett, Huybrechts and Sawon. We prove that a sufficiently big power of L is effective, assuming that L admits a semi-positive metric. A multiplier ideal version of this argument would give effectivity of L^N for any nef L. The proof uses stability and Boucksom's divisorial
Zariski decomposition.
Let L be a nef bundle on a hyperkaehler manifold. A Hyperkaehler SYZ conjecture postulates that L is semi-ample. As shown by Matsushita, this implies existence of holomorphic Lagrangian fibrations on hyperkaehler manifolds. It was conjectured by many
people, most recently by Tschinkel, Hassett, Huybrechts and Sawon. We prove that a sufficiently big power of L is effective, assuming that L admits a semi-positive metric. A multiplier ideal version of this argument would give effectivity of L^N for any nef L. The proof uses stability and Boucksom's divisorial
Zariski decomposition.
2008/11/05
Geometry Seminar
14:45-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
二木昌宏 (東京大学大学院数理科学研究科) 14:45-16:15
Directed Fukaya category の安定化について
四元数ケーラー構造の剛性定理
二木昌宏 (東京大学大学院数理科学研究科) 14:45-16:15
Directed Fukaya category の安定化について
[ Abstract ]
有向深谷圏(Directed Fukaya category)はホモロジー的ミラー対称性を Fano 多様体に拡張する目的で Kontsevich により提案され,Seidel により定式化された.これはシンプレクティック多様体の深谷圏の類似であり,exact Lefschetz fibration に対して定義される.有向深谷圏には幾つかの計算可能な例が知られているが,その構造については分かっていないことが多い.本講演では有向深谷圏の定義から始め,exact Lefschetz fibration の安定化(stabilization)と言われる操作での挙動に関する研究について報告する.Auroux-Katzarkov-Orlov の研究との関係にも触れる予定である.
服部広大 (東京大学大学院数理科学研究科) 16:30-18:00有向深谷圏(Directed Fukaya category)はホモロジー的ミラー対称性を Fano 多様体に拡張する目的で Kontsevich により提案され,Seidel により定式化された.これはシンプレクティック多様体の深谷圏の類似であり,exact Lefschetz fibration に対して定義される.有向深谷圏には幾つかの計算可能な例が知られているが,その構造については分かっていないことが多い.本講演では有向深谷圏の定義から始め,exact Lefschetz fibration の安定化(stabilization)と言われる操作での挙動に関する研究について報告する.Auroux-Katzarkov-Orlov の研究との関係にも触れる予定である.
四元数ケーラー構造の剛性定理
[ Abstract ]
四元数ケーラー構造とは,特殊なホロノミー群をもつリーマン計量の一種である.コンパクト多様体上では,四元数ケーラー構造の非自明な変形が存在しないこと(剛性定理)が,ツイスター理論を用いることで証明されている.今回は,ツイスター理論を使わない剛性定理の証明について説明する.
四元数ケーラー構造とは,特殊なホロノミー群をもつリーマン計量の一種である.コンパクト多様体上では,四元数ケーラー構造の非自明な変形が存在しないこと(剛性定理)が,ツイスター理論を用いることで証明されている.今回は,ツイスター理論を使わない剛性定理の証明について説明する.
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