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Seminar information archive
Seminar information archive ～04/03｜Today's seminar 04/04 | Future seminars 04/05～
2011/06/15
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Abe (IPMU)
Product formula for $p$-adic epsilon factors (ENGLISH)
Tomoyuki Abe (IPMU)
Product formula for $p$-adic epsilon factors (ENGLISH)
[ Abstract ]
I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.
I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.
2011/06/14
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Toshiki Mabuchi (Osaka University)
Donaldson-Tian-Yau's Conjecture (JAPANESE)
Toshiki Mabuchi (Osaka University)
Donaldson-Tian-Yau's Conjecture (JAPANESE)
[ Abstract ]
For polarized algebraic manifolds, the concept of K-stability
introduced by Tian and Donaldson is conjecturally strongly correlated
to the existence of constant scalar curvature metrics (or more
generally extremal K\\"ahler metrics) in the polarization class. This is
known as Donaldson-Tian-Yau's conjecture. Recently, a remarkable
progress has been made by many authors toward its solution. In this
talk, I'll discuss the topic mainly with emphasis on the existence
part of the conjecture.
For polarized algebraic manifolds, the concept of K-stability
introduced by Tian and Donaldson is conjecturally strongly correlated
to the existence of constant scalar curvature metrics (or more
generally extremal K\\"ahler metrics) in the polarization class. This is
known as Donaldson-Tian-Yau's conjecture. Recently, a remarkable
progress has been made by many authors toward its solution. In this
talk, I'll discuss the topic mainly with emphasis on the existence
part of the conjecture.
2011/06/13
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takeo Ohsawa (Nagoya Univeristy)
On the complement of effective divisors with semipositive normal bundle (JAPANESE)
Takeo Ohsawa (Nagoya Univeristy)
On the complement of effective divisors with semipositive normal bundle (JAPANESE)
Lectures
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
CHEN Hua (Wuhan University)
Regularity of Solutions for a Class of Degenerate Equations (ENGLISH)
CHEN Hua (Wuhan University)
Regularity of Solutions for a Class of Degenerate Equations (ENGLISH)
[ Abstract ]
In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including
(1) generalized Kolmogorov equations,
(2) Fokker-Planck equations,
(3) Landau equations and
(4) sub-elliptic Monge-Ampere equations.
In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including
(1) generalized Kolmogorov equations,
(2) Fokker-Planck equations,
(3) Landau equations and
(4) sub-elliptic Monge-Ampere equations.
2011/06/09
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Hiroaki Yoshida (Ochanomizu Univ.)
On the free Fisher information distance and the free logarithmic Sobolev inequality (JAPANESE)
Hiroaki Yoshida (Ochanomizu Univ.)
On the free Fisher information distance and the free logarithmic Sobolev inequality (JAPANESE)
Applied Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kiyoshi Mochizuki (Tokyo Metropolitan University, Emeritus Professor)
Spectral representations and scattering for Schr\\"odinger operators on star graphs (JAPANESE)
Kiyoshi Mochizuki (Tokyo Metropolitan University, Emeritus Professor)
Spectral representations and scattering for Schr\\"odinger operators on star graphs (JAPANESE)
[ Abstract ]
We consider Schr\\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.
We consider Schr\\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.
2011/06/08
Number Theory Seminar
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yuichi Hirano (University of Tokyo)
Congruences of modular forms and the Iwasawa λ-invariants (JAPANESE)
Yuichi Hirano (University of Tokyo)
Congruences of modular forms and the Iwasawa λ-invariants (JAPANESE)
2011/06/07
Algebraic Geometry Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Chenyang Xu (MIT)
Log canonical closure (ENGLISH)
Chenyang Xu (MIT)
Log canonical closure (ENGLISH)
[ Abstract ]
(joint with Christopher Hacon) In this talk, we will address the problem on given a log canonical variety, how we compactify it. Our approach is via MMP. The result has a few applications. Especially I will explain the one on the moduli of stable schemes.
If time permits, I will also talk about how a similar approach can be applied to give a proof of the existence of log canonical flips and a conjecture due to Kollár on the geometry of log centers.
(joint with Christopher Hacon) In this talk, we will address the problem on given a log canonical variety, how we compactify it. Our approach is via MMP. The result has a few applications. Especially I will explain the one on the moduli of stable schemes.
If time permits, I will also talk about how a similar approach can be applied to give a proof of the existence of log canonical flips and a conjecture due to Kollár on the geometry of log centers.
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Takashi Nakazawa (Okayama University)
Linear stability analyses of flow fields driven by propellers on
the water surface for water quality improvement
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Takashi Nakazawa (Okayama University)
Linear stability analyses of flow fields driven by propellers on
the water surface for water quality improvement
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Lie Groups and Representation Theory
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Masahiko Kanai (the University of Tokyo)
Rigidity of group actions via invariant geometric structures
(JAPANESE)
Masahiko Kanai (the University of Tokyo)
Rigidity of group actions via invariant geometric structures
(JAPANESE)
[ Abstract ]
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Masahiko Kanai (The University of Tokyo)
Rigidity of group actions via invariant geometric structures (JAPANESE)
Masahiko Kanai (The University of Tokyo)
Rigidity of group actions via invariant geometric structures (JAPANESE)
[ Abstract ]
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
2011/06/06
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoko Shinohara (Tokyo Metropolitan College of Industrial Technology)
An invariant surface of a fixed indeterminate point for rational mappings (JAPANESE)
Tomoko Shinohara (Tokyo Metropolitan College of Industrial Technology)
An invariant surface of a fixed indeterminate point for rational mappings (JAPANESE)
Algebraic Geometry Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Shihoko Ishii (University of Tokyo)
Multiplier ideals via Mather discrepancies (JAPANESE)
Shihoko Ishii (University of Tokyo)
Multiplier ideals via Mather discrepancies (JAPANESE)
[ Abstract ]
For an arbitrary variety we define a multiplier ideal by using Mather discrepancy.
This ideal coincides with the usual multiplier ideal if the variety is normal and complete intersection.
In the talk I will show a local vanishing theorem for this ideal and as corollaries we obtain restriction theorem, subadditivity theorem, Skoda type theorem, and Briancon-Skoda type theorem.
For an arbitrary variety we define a multiplier ideal by using Mather discrepancy.
This ideal coincides with the usual multiplier ideal if the variety is normal and complete intersection.
In the talk I will show a local vanishing theorem for this ideal and as corollaries we obtain restriction theorem, subadditivity theorem, Skoda type theorem, and Briancon-Skoda type theorem.
2011/06/02
Infinite Analysis Seminar Tokyo
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshihisa Saito (Graduate School of Mathematical Sciences, Univ. of Tokyo)
On the module category of $¥overline{U}_q(¥mathfrak{sl}_2)$ (JAPANESE)
Yoshihisa Saito (Graduate School of Mathematical Sciences, Univ. of Tokyo)
On the module category of $¥overline{U}_q(¥mathfrak{sl}_2)$ (JAPANESE)
[ Abstract ]
In the representation theory of quantum groups at roots of unity, it is
often assumed that the parameter $q$ is a primitive $n$-th root of unity
where $n$ is a odd prime number. However, there has recently been
increasing interest in the the cases where $n$ is an even integer ---
for example, in the study of logarithmic conformal field theories, or in
knot invariants. In this talk,
we work out a fairly detailed study on the category of finite
dimensional
modules of the restricted quantum $¥overline{U}_q(¥mathfrak{sl}_2)$
where
$q$ is a $2p$-th root of unity, $p¥ge2$.
In the representation theory of quantum groups at roots of unity, it is
often assumed that the parameter $q$ is a primitive $n$-th root of unity
where $n$ is a odd prime number. However, there has recently been
increasing interest in the the cases where $n$ is an even integer ---
for example, in the study of logarithmic conformal field theories, or in
knot invariants. In this talk,
we work out a fairly detailed study on the category of finite
dimensional
modules of the restricted quantum $¥overline{U}_q(¥mathfrak{sl}_2)$
where
$q$ is a $2p$-th root of unity, $p¥ge2$.
2011/05/31
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takehiko Morita (Osaka University)
Measures with maximum total exponent and generic properties of $C^
{1}$ expanding maps (JAPANESE)
Takehiko Morita (Osaka University)
Measures with maximum total exponent and generic properties of $C^
{1}$ expanding maps (JAPANESE)
[ Abstract ]
This is a joint work with Yusuke Tokunaga. Let $M$ be an $N$
dimensional compact connected smooth Riemannian manifold without
boundary and let $\\mathcal{E}^{r}(M,M)$ be the space of $C^{r}$
expandig maps endowed with $C^{r}$ topology. We show that
each of the following properties for element $T$ in $\\mathcal{E}
^{1}(M,M)$ is generic.
\\begin{itemize}
\\item[(1)] $T$ has a unique measure with maximum total exponent.
\\item[(2)] Any measure with maximum total exponent for $T$ has
zero entropy.
\\item[(3)] Any measure with maximum total exponent for $T$ is
fully supported.
\\end{itemize}
On the contrary, we show that for $r\\ge 2$, a generic element
in $\\mathcal{E}^{r}(M,M)$ has no fully supported measures with
maximum total exponent.
This is a joint work with Yusuke Tokunaga. Let $M$ be an $N$
dimensional compact connected smooth Riemannian manifold without
boundary and let $\\mathcal{E}^{r}(M,M)$ be the space of $C^{r}$
expandig maps endowed with $C^{r}$ topology. We show that
each of the following properties for element $T$ in $\\mathcal{E}
^{1}(M,M)$ is generic.
\\begin{itemize}
\\item[(1)] $T$ has a unique measure with maximum total exponent.
\\item[(2)] Any measure with maximum total exponent for $T$ has
zero entropy.
\\item[(3)] Any measure with maximum total exponent for $T$ is
fully supported.
\\end{itemize}
On the contrary, we show that for $r\\ge 2$, a generic element
in $\\mathcal{E}^{r}(M,M)$ has no fully supported measures with
maximum total exponent.
Lie Groups and Representation Theory
16:30-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Hirotake Kurihara (Tohoku University)
On character tables of association schemes based on attenuated
spaces (JAPANESE)
Hirotake Kurihara (Tohoku University)
On character tables of association schemes based on attenuated
spaces (JAPANESE)
[ Abstract ]
An association scheme is a pair of a finite set $X$
and a set of relations $\\{R_i\\}_{0\\le i\\le d}$
on $X$ which satisfies several axioms of regularity.
The notion of association schemes is viewed as some axiomatized
properties of transitive permutation groups in terms of combinatorics, and also the notion of association schemes is regarded as a generalization of the subring of the group ring spanned by the conjugacy classes of finite groups.
Thus, the theory of association schemes had been developed in the
study of finite permutation groups and representation theory.
To determine the character tables of association schemes is an
important first step to a systematic study of association schemes, and is helpful toward the classification of those schemes.
In this talk, we determine the character tables of association schemes based on attenuated spaces.
These association schemes are obtained from subspaces of a given
dimension in attenuated spaces.
An association scheme is a pair of a finite set $X$
and a set of relations $\\{R_i\\}_{0\\le i\\le d}$
on $X$ which satisfies several axioms of regularity.
The notion of association schemes is viewed as some axiomatized
properties of transitive permutation groups in terms of combinatorics, and also the notion of association schemes is regarded as a generalization of the subring of the group ring spanned by the conjugacy classes of finite groups.
Thus, the theory of association schemes had been developed in the
study of finite permutation groups and representation theory.
To determine the character tables of association schemes is an
important first step to a systematic study of association schemes, and is helpful toward the classification of those schemes.
In this talk, we determine the character tables of association schemes based on attenuated spaces.
These association schemes are obtained from subspaces of a given
dimension in attenuated spaces.
2011/05/30
Algebraic Geometry Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jungkai Alfred Chen (National Taiwan University and RIMS)
Kodaira Dimension of Irregular Varieties (ENGLISH)
Jungkai Alfred Chen (National Taiwan University and RIMS)
Kodaira Dimension of Irregular Varieties (ENGLISH)
[ Abstract ]
$f:X\\to Y$ be an algebraic fiber space with generic geometric fiber $F$, $\\dim X=n$ and $\\dim Y=m$. Then Iitaka's $C_{n,m}$ conjecture states $$\\kappa (X)\\geq \\kappa (Y)+\\kappa (F).$$ In particular, if $X$ is a variety with $\\kappa(X)=0$ and $f: X \\to Y$ is the Albanese map, then Ueno conjecture that $\\kappa(F)=0$. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and $C_{n,m}$ conjecture holds when $Y$ is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
$f:X\\to Y$ be an algebraic fiber space with generic geometric fiber $F$, $\\dim X=n$ and $\\dim Y=m$. Then Iitaka's $C_{n,m}$ conjecture states $$\\kappa (X)\\geq \\kappa (Y)+\\kappa (F).$$ In particular, if $X$ is a variety with $\\kappa(X)=0$ and $f: X \\to Y$ is the Albanese map, then Ueno conjecture that $\\kappa(F)=0$. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and $C_{n,m}$ conjecture holds when $Y$ is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atusi Yamamori (Meiji University)
On the Forelli-Rudin construction and explicit formulas of the Bergman kernels (JAPANESE)
Atusi Yamamori (Meiji University)
On the Forelli-Rudin construction and explicit formulas of the Bergman kernels (JAPANESE)
2011/05/26
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Takeshi Fukao (Kyoto University of Education)
Obstacle problem of Navier-Stokes equations in thermohydraulics (JAPANESE)
Takeshi Fukao (Kyoto University of Education)
Obstacle problem of Navier-Stokes equations in thermohydraulics (JAPANESE)
[ Abstract ]
In this talk, we consider the well-posedness of a variational inequality for the Navier-Stokes equations in 2 or 3 space dimension with time dependent constraints. This problem is motivated by an initial-boundary value problem for a thermohydraulics model. The velocity field is constrained by a prescribed function,
depending on the space and time variables, so this is called the obstacle problem. The abstract theory of nonlinear evolution equations governed by subdifferentials of time dependent convex functionals is quite useful for showing their well-posedness. In their mathematical treatment one of the key is to specify the class of time-dependence of convex functionals. We shall discuss the existence and uniqueness questions for Navier-Stokes variational inequalities, in which a bounded constraint is imposed on the velocity field, in higher space dimensions. Especially, the uniqueness of a solution is due to the advantage of the prescribed constraint to the velocity fields.
In this talk, we consider the well-posedness of a variational inequality for the Navier-Stokes equations in 2 or 3 space dimension with time dependent constraints. This problem is motivated by an initial-boundary value problem for a thermohydraulics model. The velocity field is constrained by a prescribed function,
depending on the space and time variables, so this is called the obstacle problem. The abstract theory of nonlinear evolution equations governed by subdifferentials of time dependent convex functionals is quite useful for showing their well-posedness. In their mathematical treatment one of the key is to specify the class of time-dependence of convex functionals. We shall discuss the existence and uniqueness questions for Navier-Stokes variational inequalities, in which a bounded constraint is imposed on the velocity field, in higher space dimensions. Especially, the uniqueness of a solution is due to the advantage of the prescribed constraint to the velocity fields.
2011/05/25
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yuya Matsumoto (University of Tokyo)
On good reduction of some K3 surfaces (JAPANESE)
Yuya Matsumoto (University of Tokyo)
On good reduction of some K3 surfaces (JAPANESE)
2011/05/24
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Daisuke Murai (Nagoya University)
Error analysis of a solution to topology optimization problem of density type
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Daisuke Murai (Nagoya University)
Error analysis of a solution to topology optimization problem of density type
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Masahiko Yoshinaga (Kyoto University)
Minimal Stratifications for Line Arrangements (JAPANESE)
Masahiko Yoshinaga (Kyoto University)
Minimal Stratifications for Line Arrangements (JAPANESE)
[ Abstract ]
The homotopy type of complements of complex
hyperplane arrangements have a special property,
so called minimality (Dimca-Papadima and Randell,
around 2000). Since then several approaches based
on (continuous, discrete) Morse theory have appeared.
In this talk, we introduce the "dual" object, which we
call minimal stratification for real two dimensional cases.
A merit is that the minimal stratification can be explicitly
described in terms of semi-algebraic sets.
We also see associated presentation of the fundamental group.
The homotopy type of complements of complex
hyperplane arrangements have a special property,
so called minimality (Dimca-Papadima and Randell,
around 2000). Since then several approaches based
on (continuous, discrete) Morse theory have appeared.
In this talk, we introduce the "dual" object, which we
call minimal stratification for real two dimensional cases.
A merit is that the minimal stratification can be explicitly
described in terms of semi-algebraic sets.
We also see associated presentation of the fundamental group.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jun-ichi Mukuno (Nagoya University)
Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)
Jun-ichi Mukuno (Nagoya University)
Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)
[ Abstract ]
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.
thesis presentations
13:15-14:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Koichiro TAKAOKA (Graduate School of Mathematical Sciences University of Tokyo)
Martingale theory (JAPANESE)
Koichiro TAKAOKA (Graduate School of Mathematical Sciences University of Tokyo)
Martingale theory (JAPANESE)
2011/05/23
Algebraic Geometry Seminar
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Yuji Sano (Kumamoto University)
Alpha invariant and K-stability of Fano varieties (JAPANESE)
Yuji Sano (Kumamoto University)
Alpha invariant and K-stability of Fano varieties (JAPANESE)
[ Abstract ]
From the results of Tian, it is proved that the lower bounds of alpha invariant implies K-stability of Fano manifolds via the existence of Kähler-Einstein metrics. In this talk, I will give a direct proof of this relation in algebro-geometric way without using Kähler-Einstein metrics. This is joint work with Yuji Odaka (RIMS).
From the results of Tian, it is proved that the lower bounds of alpha invariant implies K-stability of Fano manifolds via the existence of Kähler-Einstein metrics. In this talk, I will give a direct proof of this relation in algebro-geometric way without using Kähler-Einstein metrics. This is joint work with Yuji Odaka (RIMS).
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