Text only print
Full screen print
Seminar information archive
Seminar information archive ～04/23｜Today's seminar 04/24 | Future seminars 04/25～
2014/11/14
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Manabu Akaho (Tokyo Metropolitan University)
Symplectic displacement energy for exact Lagrangian immersions
(JAPANESE)
Manabu Akaho (Tokyo Metropolitan University)
Symplectic displacement energy for exact Lagrangian immersions
(JAPANESE)
[ Abstract ]
We give an inequality of the displacement energy for exact Lagrangian immersions and the symplectic area of punctured holomorphic discs. Our approach is based on Floer homology for Lagrangian immersions and Chekanov's homotopy technique of continuations. Moreover, we discuss our inequality and the Hofer--Zehnder capacity.
We give an inequality of the displacement energy for exact Lagrangian immersions and the symplectic area of punctured holomorphic discs. Our approach is based on Floer homology for Lagrangian immersions and Chekanov's homotopy technique of continuations. Moreover, we discuss our inequality and the Hofer--Zehnder capacity.
2014/11/12
Number Theory Seminar
18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ruochuan Liu (BICMR)
Relative (φ, Γ)-modules (English)
Ruochuan Liu (BICMR)
Relative (φ, Γ)-modules (English)
[ Abstract ]
In this talk, we will introduce the theory of (φ, Γ)-modules for general adic spaces. This is a joint work with Kedlaya.
In this talk, we will introduce the theory of (φ, Γ)-modules for general adic spaces. This is a joint work with Kedlaya.
2014/11/11
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Kenneth Baker (University of Miami)
Unifying unexpected exceptional Dehn surgeries (ENGLISH)
Kenneth Baker (University of Miami)
Unifying unexpected exceptional Dehn surgeries (ENGLISH)
[ Abstract ]
This past summer Dunfield-Hoffman-Licata produced examples of asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space Dehn fillings through a search of the extended SnapPea census.
Examinations of these examples with Hoffman and Licata lead us to coincidences with other work in progress that gives a simple holistic topological approach towards producing and extending many of these families. In this talk we'll explicitly describe our construction and discuss related applications of the technique.
This past summer Dunfield-Hoffman-Licata produced examples of asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space Dehn fillings through a search of the extended SnapPea census.
Examinations of these examples with Hoffman and Licata lead us to coincidences with other work in progress that gives a simple holistic topological approach towards producing and extending many of these families. In this talk we'll explicitly describe our construction and discuss related applications of the technique.
Seminar on Probability and Statistics
16:30-17:40 Room #052 (Graduate School of Math. Sci. Bldg.)
Terada, Yoshikazu (CiNet / Center for Information and Neural Networks)
Local Ordinal Embedding
Terada, Yoshikazu (CiNet / Center for Information and Neural Networks)
Local Ordinal Embedding
2014/11/10
FMSP Lectures
17:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Alfred Ramani (Ecole Polytechnique)
Discrete Painlevé equations with periodic coefficients (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani.pdf
Alfred Ramani (Ecole Polytechnique)
Discrete Painlevé equations with periodic coefficients (ENGLISH)
[ Abstract ]
We present a series of results on discrete Painlevé equations with coefficients which are periodic functions of the independent variable. We show by explicit construction that for each affine Weyl group there exists an equation the coefficients of which have maximal periodicity. New results on equations associated to the affine Weyl group E_8 are also presented.
[ Reference URL ]We present a series of results on discrete Painlevé equations with coefficients which are periodic functions of the independent variable. We show by explicit construction that for each affine Weyl group there exists an equation the coefficients of which have maximal periodicity. New results on equations associated to the affine Weyl group E_8 are also presented.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani.pdf
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Tokyo Institute of Technology)
On a convex level set of a plurisubharmonic function and the support of the Monge-Ampere current (JAPANESE)
Yusaku Tiba (Tokyo Institute of Technology)
On a convex level set of a plurisubharmonic function and the support of the Monge-Ampere current (JAPANESE)
[ Abstract ]
In this talk, we study a geometric property of a continuous plurisubharmonic function which is a solution of the Monge-Ampere equation and has a convex level set. By using our results and Lempert's results, we show a relation between the supports of the Monge-Ampere currents and complex $k$-extreme points of closed balls for the Kobayashi distance in a bounded convex domain in $C^n$.
In this talk, we study a geometric property of a continuous plurisubharmonic function which is a solution of the Monge-Ampere equation and has a convex level set. By using our results and Lempert's results, we show a relation between the supports of the Monge-Ampere currents and complex $k$-extreme points of closed balls for the Kobayashi distance in a bounded convex domain in $C^n$.
Classical Analysis
16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre RAMIS (Toulouse)
DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY OF DYNAMICAL SYSTEMS
Jean-Pierre RAMIS (Toulouse)
DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY OF DYNAMICAL SYSTEMS
[ Abstract ]
We will explain how to get obstructions to the integrability of analytic Hamiltonian Systems (in the classical Liouville sense) using Differential Galois Theory (introduced by Emile Picard at the end of XIX-th century). It is the so-called Morales-Ramis theory. Even if this sounds abstract, there exist efficient algorithms allowing to apply the theory and a lot of applications in various domains.
Firstly I will present basics on Hamiltonian Systems and integrability on one side and on Differential Galois Theory on the other side. Then I will state the main theorems. Afterwards I will describe some applications.
We will explain how to get obstructions to the integrability of analytic Hamiltonian Systems (in the classical Liouville sense) using Differential Galois Theory (introduced by Emile Picard at the end of XIX-th century). It is the so-called Morales-Ramis theory. Even if this sounds abstract, there exist efficient algorithms allowing to apply the theory and a lot of applications in various domains.
Firstly I will present basics on Hamiltonian Systems and integrability on one side and on Differential Galois Theory on the other side. Then I will state the main theorems. Afterwards I will describe some applications.
2014/11/07
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Shinpei KOBAYASHI (Hokkaido University)
Harmonic maps into the hyperbolic plane and their applications to surface theory (Japanese)
Shinpei KOBAYASHI (Hokkaido University)
Harmonic maps into the hyperbolic plane and their applications to surface theory (Japanese)
[ Abstract ]
Harmonic maps from two-dimensional Riemannian manifolds into the hyperbolic plane have been well studied. Since constant mean curvature surfaces in the Minkowski space have harmonic Gauss maps into the hyperbolic plane, there exist applications to surface theory.
In 1998, Dorfmeister, Pedit and Wu established the construction method of harmonic maps into symmetric spaces via loop group method. Recently, harmonic maps into the hyperbolic plane appear in various classes of surfaces, e.g., minimal surfaces in the Heisenberg group,
maximal surfaces in the anti-de Sitter space or constant Gaussian curvature surfaces in the hyperbolic space. In this talk I will talk about the general construction method of harmonic maps from surfaces into symmetric spaces via loop group method and the case of the hyperbolic plane in details.
Harmonic maps from two-dimensional Riemannian manifolds into the hyperbolic plane have been well studied. Since constant mean curvature surfaces in the Minkowski space have harmonic Gauss maps into the hyperbolic plane, there exist applications to surface theory.
In 1998, Dorfmeister, Pedit and Wu established the construction method of harmonic maps into symmetric spaces via loop group method. Recently, harmonic maps into the hyperbolic plane appear in various classes of surfaces, e.g., minimal surfaces in the Heisenberg group,
maximal surfaces in the anti-de Sitter space or constant Gaussian curvature surfaces in the hyperbolic space. In this talk I will talk about the general construction method of harmonic maps from surfaces into symmetric spaces via loop group method and the case of the hyperbolic plane in details.
2014/11/05
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Hiroshi Ando (Univ. Copenhagen)
On the noncommutativity of the central sequence $C^*$-algebra $F(A)$ (ENGLISH)
Hiroshi Ando (Univ. Copenhagen)
On the noncommutativity of the central sequence $C^*$-algebra $F(A)$ (ENGLISH)
Mathematical Biology Seminar
14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)
Mayuko Nakamaru (Department of Value and Decision Science, Tokyo Institute of Technology)
Ecological conditions favoring budding in colonial organisms under environmental disturbance (JAPANESE)
[ Reference URL ]
https://sites.google.com/site/mayukonakamarulab/
Mayuko Nakamaru (Department of Value and Decision Science, Tokyo Institute of Technology)
Ecological conditions favoring budding in colonial organisms under environmental disturbance (JAPANESE)
[ Reference URL ]
https://sites.google.com/site/mayukonakamarulab/
2014/11/04
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Brian Bowditch (University of Warwick)
The coarse geometry of Teichmuller space. (ENGLISH)
Brian Bowditch (University of Warwick)
The coarse geometry of Teichmuller space. (ENGLISH)
[ Abstract ]
We describe some results regarding the coarse geometry of the
Teichmuller space
of a compact surface. In particular, we describe when the Teichmuller
space admits quasi-isometric embeddings of euclidean spaces and
half-spaces.
We also give some partial results regarding the quasi-isometric rigidity
of Teichmuller space. These results are based on the fact that Teichmuller
space admits a ternary operation, natural up to bounded distance
which endows it with the structure of a coarse median space.
We describe some results regarding the coarse geometry of the
Teichmuller space
of a compact surface. In particular, we describe when the Teichmuller
space admits quasi-isometric embeddings of euclidean spaces and
half-spaces.
We also give some partial results regarding the quasi-isometric rigidity
of Teichmuller space. These results are based on the fact that Teichmuller
space admits a ternary operation, natural up to bounded distance
which endows it with the structure of a coarse median space.
Seminar on Probability and Statistics
16:30-17:40 Room #052 (Graduate School of Math. Sci. Bldg.)
YANAGIHARA, Hirokazu (Graduate School of Science, Hiroshima University)
Conditions for consistency of a log-likelihood-based information criterion in normal multivariate linear regression models under the violation of normality assumption
YANAGIHARA, Hirokazu (Graduate School of Science, Hiroshima University)
Conditions for consistency of a log-likelihood-based information criterion in normal multivariate linear regression models under the violation of normality assumption
2014/10/29
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Sven Raum (RIMS, Kyoto Univ.)
The classification of easy quantum groups (ENGLISH)
Sven Raum (RIMS, Kyoto Univ.)
The classification of easy quantum groups (ENGLISH)
Lie Groups and Representation Theory
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Patrick Delorme (UER Scientifique de Luminy Universite d'Aix-Marseille II )
Harmonic analysis on reductive p-adic symmetric spaces. (ENGLISH)
Patrick Delorme (UER Scientifique de Luminy Universite d'Aix-Marseille II )
Harmonic analysis on reductive p-adic symmetric spaces. (ENGLISH)
[ Abstract ]
In this lecture we will review the Plancherel formula that
we got by looking to neighborhoods at infinity of the
symmetric spaces and then using the method of Sakellaridis-Venkatesh
for spherical varieties for a split group. For us the group
is not necessarily split. We will try to show what questions
are raised by this work for real spherical varieties.
We will present in the last part a joint work with Pascale
Harinck and Yiannis Sakellaridis in which we prove Paley-Wiener
theorems for symmetric spaces.
In this lecture we will review the Plancherel formula that
we got by looking to neighborhoods at infinity of the
symmetric spaces and then using the method of Sakellaridis-Venkatesh
for spherical varieties for a split group. For us the group
is not necessarily split. We will try to show what questions
are raised by this work for real spherical varieties.
We will present in the last part a joint work with Pascale
Harinck and Yiannis Sakellaridis in which we prove Paley-Wiener
theorems for symmetric spaces.
Classical Analysis
16:00-17:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Eric Stade (University of Colorado Boulder)
Whittaker functions and Barnes-Type Lemmas (ENGLISH)
Eric Stade (University of Colorado Boulder)
Whittaker functions and Barnes-Type Lemmas (ENGLISH)
[ Abstract ]
In the theory of automorphic forms on GL(n,R), which concerns harmonic analysis and representation theory of this group, certain special functions known as GL(n,R) Whittaker functions play an important role. These Whittaker functions are generalizations of classical Whittaker (or, more specifically, Bessel) functions.
Mellin transforms of products of GL(n,R) Whittaker functions may be expressed as certain Barnes type integrals, or equivalently, as hypergeometric series of unit argument. The general theory of automorphic forms predicts that these Mellin transforms reduce, in certain cases, to products of gamma functions. That this does in fact occur amounts to a whole family of generalizations of the so-called Barnes' Lemma and Barnes' Second Lemma, from the theory of hypergeometric series. We will explore these generalizations in this talk.
This talk will not require any specific knowledge of automorphic forms.
In the theory of automorphic forms on GL(n,R), which concerns harmonic analysis and representation theory of this group, certain special functions known as GL(n,R) Whittaker functions play an important role. These Whittaker functions are generalizations of classical Whittaker (or, more specifically, Bessel) functions.
Mellin transforms of products of GL(n,R) Whittaker functions may be expressed as certain Barnes type integrals, or equivalently, as hypergeometric series of unit argument. The general theory of automorphic forms predicts that these Mellin transforms reduce, in certain cases, to products of gamma functions. That this does in fact occur amounts to a whole family of generalizations of the so-called Barnes' Lemma and Barnes' Second Lemma, from the theory of hypergeometric series. We will explore these generalizations in this talk.
This talk will not require any specific knowledge of automorphic forms.
2014/10/28
Number Theory Seminar
16:40-18:50 Room #002 (Graduate School of Math. Sci. Bldg.)
Judith Ludwig (Imperial college) 16:40-17:40
A p-adic Labesse-Langlands transfer (English)
Plectic cohomology (English)
Judith Ludwig (Imperial college) 16:40-17:40
A p-adic Labesse-Langlands transfer (English)
[ Abstract ]
Let B be a definite quaternion algebra over the rationals, G the algebraic group defined by the units in B and H the subgroup of G of norm one elements. Then the classical transfer of automorphic representations from G to H is well understood thanks to Labesse and Langlands, who proved formulas for the multiplicity of irreducible admissible representations of H(adeles) in the discrete automorphic spectrum.
The goal of this talk is to prove a p-adic version of this transfer. By this we mean an extension of the classical transfer to p-adic families of automorphic forms as parametrized by certain rigid analytic spaces called eigenvarieties. We will prove the p-adic transfer by constructing a morphism between eigenvarieties, which agrees with the classical transfer on points corresponding to classical automorphic representations.
Jan Nekovar (Université Paris 6) 17:50-18:50Let B be a definite quaternion algebra over the rationals, G the algebraic group defined by the units in B and H the subgroup of G of norm one elements. Then the classical transfer of automorphic representations from G to H is well understood thanks to Labesse and Langlands, who proved formulas for the multiplicity of irreducible admissible representations of H(adeles) in the discrete automorphic spectrum.
The goal of this talk is to prove a p-adic version of this transfer. By this we mean an extension of the classical transfer to p-adic families of automorphic forms as parametrized by certain rigid analytic spaces called eigenvarieties. We will prove the p-adic transfer by constructing a morphism between eigenvarieties, which agrees with the classical transfer on points corresponding to classical automorphic representations.
Plectic cohomology (English)
2014/10/27
Algebraic Geometry Seminar
14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)
Meng Chen (Fudan University)
On projective varieties with very large canonical volume (ENGLISH)
Meng Chen (Fudan University)
On projective varieties with very large canonical volume (ENGLISH)
[ Abstract ]
For any positive integer n>0, a theorem of Hacon-McKernan, Takayama and Tsuji says that there is a constant c(n) so that the m-canonical map is birational onto its image for all smooth projective n-folds and all m>=c(n). We are interested in the following problem "P(n)": is there a constant M(n) so that, for all smooth projective n-fold X with Vol(X)>M(n), the m-canonical map of X is birational for all m>=c(n-1). The answer to “P_n" is positive due to Bombieri when $n=2$ and to Todorov when $n=3$. The aim of this talk is to introduce my joint work with Zhi Jiang from Universite Paris-Sud. We give a positive answer in dimensions 4 and 5.
For any positive integer n>0, a theorem of Hacon-McKernan, Takayama and Tsuji says that there is a constant c(n) so that the m-canonical map is birational onto its image for all smooth projective n-folds and all m>=c(n). We are interested in the following problem "P(n)": is there a constant M(n) so that, for all smooth projective n-fold X with Vol(X)>M(n), the m-canonical map of X is birational for all m>=c(n-1). The answer to “P_n" is positive due to Bombieri when $n=2$ and to Todorov when $n=3$. The aim of this talk is to introduce my joint work with Zhi Jiang from Universite Paris-Sud. We give a positive answer in dimensions 4 and 5.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (University of Tokyo)
On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles (JAPANESE)
Takayuki Koike (University of Tokyo)
On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles (JAPANESE)
[ Abstract ]
We apply Ueda theory to a study of singular Hermitian metrics of a (strictly) nef line bundle $L$. Especially we study minimal singular metrics of $L$, metrics of $L$ with the mildest singularities among singular Hermitian metrics of $L$ whose local weights are plurisubharmonic. In some situations, we determine a minimal singular metric of $L$. As an application, we give new examples of (strictly) nef line bundles which admit no smooth Hermitian metric with semi-positive curvature.
We apply Ueda theory to a study of singular Hermitian metrics of a (strictly) nef line bundle $L$. Especially we study minimal singular metrics of $L$, metrics of $L$ with the mildest singularities among singular Hermitian metrics of $L$ whose local weights are plurisubharmonic. In some situations, we determine a minimal singular metric of $L$. As an application, we give new examples of (strictly) nef line bundles which admit no smooth Hermitian metric with semi-positive curvature.
2014/10/25
Harmonic Analysis Komaba Seminar
13:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Sawano (Tokyo Metropolitan University) 13:30-14:30
Approximation in Banach space by linear positive operators (JAPANESE)
Local ill-posedness of the Euler equations in a critical Besov space (JAPANESE)
Yoshihiro Sawano (Tokyo Metropolitan University) 13:30-14:30
Approximation in Banach space by linear positive operators (JAPANESE)
[ Abstract ]
We obtain a sufficient condition for the
convergence of positive linear operators in Banach
function spaces on Rn and derive a Korovkin type
theorem for these spaces. Also, we generalized
this result via statistical sense. This is a joint
work with Professor Arash Ghorbanalizadeh.
Tsuyoshi Yoneda (Tokyo Institute of Technology) 15:00-16:30We obtain a sufficient condition for the
convergence of positive linear operators in Banach
function spaces on Rn and derive a Korovkin type
theorem for these spaces. Also, we generalized
this result via statistical sense. This is a joint
work with Professor Arash Ghorbanalizadeh.
Local ill-posedness of the Euler equations in a critical Besov space (JAPANESE)
2014/10/22
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yusuke Isono (Kyoto Univ.)
Free independence in ultraproduct von Neumann algebras and applications (ENGLISH)
Yusuke Isono (Kyoto Univ.)
Free independence in ultraproduct von Neumann algebras and applications (ENGLISH)
Mathematical Biology Seminar
14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)
Harunori Monobe (Meiji Institute for Advanced Study of Mathematical Sciences)
Fast reaction limit of a system with different reaction terms (JAPANESE)
Harunori Monobe (Meiji Institute for Advanced Study of Mathematical Sciences)
Fast reaction limit of a system with different reaction terms (JAPANESE)
2014/10/21
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Toshiyuki Akita (Hokkaido University)
Vanishing theorems for p-local homology of Coxeter groups and their alternating subgroups (JAPANESE)
Toshiyuki Akita (Hokkaido University)
Vanishing theorems for p-local homology of Coxeter groups and their alternating subgroups (JAPANESE)
[ Abstract ]
Given a prime number $p$, we estimate vanishing ranges of $p$-local homology groups of Coxeter groups (of possibly infinite order) and alternating subgroups of finite reflection groups. Our results generalize those by Nakaoka for symmetric groups and Kleshchev-Nakano and Burichenko for alternating groups. The key ingredient is the equivariant homology of Coxeter complexes.
Given a prime number $p$, we estimate vanishing ranges of $p$-local homology groups of Coxeter groups (of possibly infinite order) and alternating subgroups of finite reflection groups. Our results generalize those by Nakaoka for symmetric groups and Kleshchev-Nakano and Burichenko for alternating groups. The key ingredient is the equivariant homology of Coxeter complexes.
2014/10/20
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Shouhei Ma (Tokyo Institute of Technology)
Kodaira dimension of modular variety of type IV (JAPANESE)
Shouhei Ma (Tokyo Institute of Technology)
Kodaira dimension of modular variety of type IV (JAPANESE)
Numerical Analysis Seminar
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Guanyu Zhou (The University of Tokyo)
Finite element method with various types of penalty on domain/boundary (ENGLISH)
Guanyu Zhou (The University of Tokyo)
Finite element method with various types of penalty on domain/boundary (ENGLISH)
[ Abstract ]
We are concerned with several penalty methods (on domain/boundary)
combining with finite element method to solve some partial differential equations. The penalty methods are very useful and widely applied to various problems. For example, to solve the Navier-Stokes equations in moving boundary domain, the finite element method requires to construct the boundary fitted mesh at every times step, which is very time-consuming. The fictitious domain method is proposed to tackle this problem. It is to reformulate the equation to a larger fixed domain, called the fictitious domain, to which we can take a uniform mesh independent on the original moving boundary. The reformulation is based on a penalty method on do- main. Some penalty methods are proposed to approximate the boundary conditions which are not easy to handle with general FEM, such as the slip boundary condition to Stokes/Navier-Stokes equations, the unilateral boundary condition of Signorini’s type to Stokes equations, and so on. It is known that the variational crimes occurs if the finite element spaces or the implementation methods are not chosen properly for slip boundary condition. By introducing a penalty term to the normal component of velocity on slip boundary, we can solve the equations in FEM easily. For the boundary of Signorini’s type, the variational form is an inequality, to which the FEM is not easy to applied. However, we can approximate the variational inequality by a variation equation with penalty term, which can be solve by FEM directly. In above, we introduced several penalty methods with finite element approximation. In this work, we investigate the well-posedness of those penalty method, and obtain the error estimates of penalty; moreover, we consider the penalty methods combining with finite element approximation and show the error estimates.
We are concerned with several penalty methods (on domain/boundary)
combining with finite element method to solve some partial differential equations. The penalty methods are very useful and widely applied to various problems. For example, to solve the Navier-Stokes equations in moving boundary domain, the finite element method requires to construct the boundary fitted mesh at every times step, which is very time-consuming. The fictitious domain method is proposed to tackle this problem. It is to reformulate the equation to a larger fixed domain, called the fictitious domain, to which we can take a uniform mesh independent on the original moving boundary. The reformulation is based on a penalty method on do- main. Some penalty methods are proposed to approximate the boundary conditions which are not easy to handle with general FEM, such as the slip boundary condition to Stokes/Navier-Stokes equations, the unilateral boundary condition of Signorini’s type to Stokes equations, and so on. It is known that the variational crimes occurs if the finite element spaces or the implementation methods are not chosen properly for slip boundary condition. By introducing a penalty term to the normal component of velocity on slip boundary, we can solve the equations in FEM easily. For the boundary of Signorini’s type, the variational form is an inequality, to which the FEM is not easy to applied. However, we can approximate the variational inequality by a variation equation with penalty term, which can be solve by FEM directly. In above, we introduced several penalty methods with finite element approximation. In this work, we investigate the well-posedness of those penalty method, and obtain the error estimates of penalty; moreover, we consider the penalty methods combining with finite element approximation and show the error estimates.
2014/10/17
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Yu Kitabeppu (Kyoto University)
A finite diameter theorem on RCD spaces (JAPANESE)
Yu Kitabeppu (Kyoto University)
A finite diameter theorem on RCD spaces (JAPANESE)
[ Abstract ]
I will talk about a finite diameter theorem on RCD spaces of (possibly) infinite dimension. An RCD space is a generalization of a concept of a manifold with bounded Ricci curvature. Savar¥'e proves the "self-improving property" on RCD spaces via the Gamma calculus. Because of his work and Kuwada’s duality argument, we are able to get the L^{¥infty}-contraction of heat kernels. I will show the main result by combining the contraction property and a simple lemma.
I will talk about a finite diameter theorem on RCD spaces of (possibly) infinite dimension. An RCD space is a generalization of a concept of a manifold with bounded Ricci curvature. Savar¥'e proves the "self-improving property" on RCD spaces via the Gamma calculus. Because of his work and Kuwada’s duality argument, we are able to get the L^{¥infty}-contraction of heat kernels. I will show the main result by combining the contraction property and a simple lemma.
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185 Next >
