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Seminar information archive
Seminar information archive ～04/23｜Today's seminar 04/24 | Future seminars 04/25～
2015/01/14
Number Theory Seminar
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Laurent Berger (ENS de Lyon)
Iterate extensions and relative Lubin-Tate groups
Laurent Berger (ENS de Lyon)
Iterate extensions and relative Lubin-Tate groups
[ Abstract ]
Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.
Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Zhuofeng He (Univ. Tokyo)
Canonical cyclic group actions on noncommutative tori
Zhuofeng He (Univ. Tokyo)
Canonical cyclic group actions on noncommutative tori
2015/01/13
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ken'ichi Yoshida (The University of Tokyo)
Stable presentation length of 3-manifold groups (JAPANESE)
Ken'ichi Yoshida (The University of Tokyo)
Stable presentation length of 3-manifold groups (JAPANESE)
[ Abstract ]
We will introduce the stable presentation length
of a finitely presented group, which is defined
by stabilizing the presentation length for the
finite index subgroups. The stable presentation
length of the fundamental group of a 3-manifold
is an analogue of the simplicial volume and the
stable complexity introduced by Francaviglia,
Frigerio and Martelli. We will explain some
similarities of stable presentation length with
simplicial volume and stable complexity.
We will introduce the stable presentation length
of a finitely presented group, which is defined
by stabilizing the presentation length for the
finite index subgroups. The stable presentation
length of the fundamental group of a 3-manifold
is an analogue of the simplicial volume and the
stable complexity introduced by Francaviglia,
Frigerio and Martelli. We will explain some
similarities of stable presentation length with
simplicial volume and stable complexity.
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Wojciech Zajączkowski (Institute of Mathematics Polish Academy of Sciences)
Global regular solutions to the Navier-Stokes equations which remain close to the two-dimensional solutions (English)
Wojciech Zajączkowski (Institute of Mathematics Polish Academy of Sciences)
Global regular solutions to the Navier-Stokes equations which remain close to the two-dimensional solutions (English)
[ Abstract ]
We consider the motion of the Navier-Stokes equations in a cylinder with the Navier-boundary conditions. First we prove global existence of regular two-dimensional solutions non-decaying in time. Next we show stability of these solutions. In this way we have existence of global regular solutions which remain close to the two-dimensional solutions. We prove the results for nonvanishing external force in time.
We consider the motion of the Navier-Stokes equations in a cylinder with the Navier-boundary conditions. First we prove global existence of regular two-dimensional solutions non-decaying in time. Next we show stability of these solutions. In this way we have existence of global regular solutions which remain close to the two-dimensional solutions. We prove the results for nonvanishing external force in time.
2015/01/10
Harmonic Analysis Komaba Seminar
13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Koichi Kaizuka (Gakushuin University) 13:30-15:00
Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application (JAPANESE)
Norisuke Ioku (Ehime University) 15:30-17:00
スケール不変性を持つ臨界Hardyの不等式について (JAPANESE)
Koichi Kaizuka (Gakushuin University) 13:30-15:00
Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application (JAPANESE)
Norisuke Ioku (Ehime University) 15:30-17:00
スケール不変性を持つ臨界Hardyの不等式について (JAPANESE)
2015/01/07
Number Theory Seminar
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Sandra Rozensztajn (ENS de Lyon)
Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)
Sandra Rozensztajn (ENS de Lyon)
Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)
[ Abstract ]
In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.
In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Tomohiro Hayase (Univ. Tokyo)
De Finetti theorems related to Boolean independence (English)
Tomohiro Hayase (Univ. Tokyo)
De Finetti theorems related to Boolean independence (English)
2015/01/06
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Elio Eduardo Espejo (National University of Colombia / Osaka University)
Global existence and asymptotic behavior for some Keller-Segel systems coupled with Navier-Stokes equations (英語)
Elio Eduardo Espejo (National University of Colombia / Osaka University)
Global existence and asymptotic behavior for some Keller-Segel systems coupled with Navier-Stokes equations (英語)
[ Abstract ]
There are plenty of examples in nature, where cells move in response to some chemical signal in the environment. Biologists call this phenomenon chemotaxis. In my talk I will approach the problem of describing mathematically the phenomenon of chemotaxis when it happens surrounded by a fluid. This is a new research topic bringing the attention of many scientists because it has given rise to many interesting questions having relevance in both biology and mathematics. In particular, I will present some new mathematical models arising from my current research that have given rise to Keller-Segel type systems coupled with Navier-Stokes systems. I will present some results of global existence and asymptotic behavior. Finally I will discuss some open problems.
There are plenty of examples in nature, where cells move in response to some chemical signal in the environment. Biologists call this phenomenon chemotaxis. In my talk I will approach the problem of describing mathematically the phenomenon of chemotaxis when it happens surrounded by a fluid. This is a new research topic bringing the attention of many scientists because it has given rise to many interesting questions having relevance in both biology and mathematics. In particular, I will present some new mathematical models arising from my current research that have given rise to Keller-Segel type systems coupled with Navier-Stokes systems. I will present some results of global existence and asymptotic behavior. Finally I will discuss some open problems.
2014/12/22
Mathematical Biology Seminar
15:00-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)
Don Yueping (Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo)
Estimating the seroincidence of pertussis in Japan
Don Yueping (Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo)
Estimating the seroincidence of pertussis in Japan
[ Abstract ]
Despite relatively high vaccination coverage of pertussis for decades, the disease keeps circulating among both vaccinated and unvaccinated individuals and a periodic large epidemic is observed every 4 years. To understand the transmission dynamics, specific immunoglobulin G (IgG) antibodies against pertussis toxin (PT) have been routinely measured in Japan. Using the cross-sectional serological survey data with a known decay rate of antibody titres as a function of time since infection, we estimate the age-dependent seroincidence of pertussis. The estimated incidence of pertussis declined with age, the shape of which will be extremely useful for reconstructing the transmission dynamics and considering effective countermeasures.
Despite relatively high vaccination coverage of pertussis for decades, the disease keeps circulating among both vaccinated and unvaccinated individuals and a periodic large epidemic is observed every 4 years. To understand the transmission dynamics, specific immunoglobulin G (IgG) antibodies against pertussis toxin (PT) have been routinely measured in Japan. Using the cross-sectional serological survey data with a known decay rate of antibody titres as a function of time since infection, we estimate the age-dependent seroincidence of pertussis. The estimated incidence of pertussis declined with age, the shape of which will be extremely useful for reconstructing the transmission dynamics and considering effective countermeasures.
2014/12/19
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Yuichi KABAYA (Kyoto University)
Exotic components in linear slices of quasi-Fuchsian groups
Yuichi KABAYA (Kyoto University)
Exotic components in linear slices of quasi-Fuchsian groups
[ Abstract ]
The linear slice of quasi-Fuchsian punctured torus groups is defined by fixing the length of some simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks, and it has one `standard' component containing Fuchsian groups. Komori-Yamashita proved that there exist non-standard components if the length is sufficiently large. In this talk, I give another proof based on the theory of complex projective structures. If time permits, I will talk about a refined statement and a generalization to other surfaces.
The linear slice of quasi-Fuchsian punctured torus groups is defined by fixing the length of some simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks, and it has one `standard' component containing Fuchsian groups. Komori-Yamashita proved that there exist non-standard components if the length is sufficiently large. In this talk, I give another proof based on the theory of complex projective structures. If time permits, I will talk about a refined statement and a generalization to other surfaces.
2014/12/17
Number Theory Seminar
18:00-19:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Konstantin Ardakov (University of Oxford)
Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces
(English)
Konstantin Ardakov (University of Oxford)
Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces
(English)
[ Abstract ]
Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.
Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Valentin Zagrebnov (Univ. d'Aix-Marseille)
Dynamics of an Open Quantum System with Repeated Harmonic Perturbation (with Hiroshi Tamura) (English)
Valentin Zagrebnov (Univ. d'Aix-Marseille)
Dynamics of an Open Quantum System with Repeated Harmonic Perturbation (with Hiroshi Tamura) (English)
Mathematical Biology Seminar
14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)
Yumi YAHAGI (Tokyo City University)
A probabilistic interpretation of an evolution model of slime bacteria
(JAPANESE)
Yumi YAHAGI (Tokyo City University)
A probabilistic interpretation of an evolution model of slime bacteria
(JAPANESE)
2014/12/16
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Haruya Mizutani (Graduate School of Science, Osaka University)
Global Strichartz estimates for Schr¥”odinger equations on
asymptotically conic manifolds (Japanese)
Haruya Mizutani (Graduate School of Science, Osaka University)
Global Strichartz estimates for Schr¥”odinger equations on
asymptotically conic manifolds (Japanese)
Tuesday Seminar on Topology
17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)
Norio Iwase (Kyushu University)
Differential forms in diffeological spaces (JAPANESE)
Norio Iwase (Kyushu University)
Differential forms in diffeological spaces (JAPANESE)
[ Abstract ]
The idea of a space with smooth structure is first introduced by K. T. Chen in his study of a loop space to employ the idea of iterated path integrals.
Following the pattern established by Chen, J. M. Souriau introduced his version of a space with smooth structure which is now called diffeology and become one of the most exciting topics in Algebraic Topology. Following Souriau, P. I.-Zenmour presented de Rham theory associated to a diffeology of a space. However, if one tries to show a version of de Rham theorem for a general diffeological space, he must encounter a difficulty to show the existence of a partition of unity and thus the exactness of the Mayer-Vietoris sequence. To resolve such difficulties, we introduce a new definition of differential forms.
The idea of a space with smooth structure is first introduced by K. T. Chen in his study of a loop space to employ the idea of iterated path integrals.
Following the pattern established by Chen, J. M. Souriau introduced his version of a space with smooth structure which is now called diffeology and become one of the most exciting topics in Algebraic Topology. Following Souriau, P. I.-Zenmour presented de Rham theory associated to a diffeology of a space. However, if one tries to show a version of de Rham theorem for a general diffeological space, he must encounter a difficulty to show the existence of a partition of unity and thus the exactness of the Mayer-Vietoris sequence. To resolve such difficulties, we introduce a new definition of differential forms.
2014/12/15
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Hajime Tsuji (Sophia University)
The limits of Kähler-Ricci flows
Hajime Tsuji (Sophia University)
The limits of Kähler-Ricci flows
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Akiyoshi Sannai (University of Tokyo)
A characterization of ordinary abelian varieties in positive characteristic (JAPANESE)
Akiyoshi Sannai (University of Tokyo)
A characterization of ordinary abelian varieties in positive characteristic (JAPANESE)
[ Abstract ]
This is joint work with Hiromu Tanaka. In this talk, we study F^e_*O_X on a projective variety over the algebraic closed field of positive characteristic. For an ordinary abelian variety X, F^e_*O_X is decomposed into line bundles for every positive integer e. Conversely, if a smooth projective variety X satisfies this property and its Kodaira dimension is non-negative, then X is an ordinary abelian variety.
This is joint work with Hiromu Tanaka. In this talk, we study F^e_*O_X on a projective variety over the algebraic closed field of positive characteristic. For an ordinary abelian variety X, F^e_*O_X is decomposed into line bundles for every positive integer e. Conversely, if a smooth projective variety X satisfies this property and its Kodaira dimension is non-negative, then X is an ordinary abelian variety.
2014/12/11
Infinite Analysis Seminar Tokyo
15:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Yohei Kashima (Graduate School of Mathematical Sciences, the University of Tokyo) 15:00-16:30
Renormalization group method for many-electron systems (JAPANESE)
Unitary transformations and multivariate special
orthogonal polynomials (JAPANESE)
Yohei Kashima (Graduate School of Mathematical Sciences, the University of Tokyo) 15:00-16:30
Renormalization group method for many-electron systems (JAPANESE)
[ Abstract ]
We consider quantum many-body systems of electrons
hopping and interacting on a lattice at positive temperature.
As it is possible to write down each order term rigorously in
principle, the perturbation series expansion with the coupling
constant between electrons is thought as a valid method to
compute physical quantities. By directly estimating each term,
one can prove that the perturbation series is convergent if the
coupling constant is less than some power of temperature. This is,
however, a serious constraint for models of interacting electrons
in low temperature. In order to ensure the analyticity of physical
quantities of many-electron systems with the coupling constant in
low temperature, renormalization group methods have been developed
in recent years. As one progress in this direction, we construct a
renormalization group method for the half-filled Hubbard model on a
square lattice, which is a typical model of many-electron, and prove
the following. If the system contains the magnetic flux pi (mod 2 pi)
per plaquette, the free energy density of the system is analytic with
the coupling constant in a neighborhood of the origin and it uniformly
converges to the infinite-volume, zero-temperature limit. It is known
that the flux pi condition is sufficient for the free energy density
to be minimum. Thus, it follows that the same analyticity and the
convergent property hold for the minimum free energy density of the
system.
Genki Shibukawa (Institute of Mathematics for Industory, Kyushu University) 17:00-18:30We consider quantum many-body systems of electrons
hopping and interacting on a lattice at positive temperature.
As it is possible to write down each order term rigorously in
principle, the perturbation series expansion with the coupling
constant between electrons is thought as a valid method to
compute physical quantities. By directly estimating each term,
one can prove that the perturbation series is convergent if the
coupling constant is less than some power of temperature. This is,
however, a serious constraint for models of interacting electrons
in low temperature. In order to ensure the analyticity of physical
quantities of many-electron systems with the coupling constant in
low temperature, renormalization group methods have been developed
in recent years. As one progress in this direction, we construct a
renormalization group method for the half-filled Hubbard model on a
square lattice, which is a typical model of many-electron, and prove
the following. If the system contains the magnetic flux pi (mod 2 pi)
per plaquette, the free energy density of the system is analytic with
the coupling constant in a neighborhood of the origin and it uniformly
converges to the infinite-volume, zero-temperature limit. It is known
that the flux pi condition is sufficient for the free energy density
to be minimum. Thus, it follows that the same analyticity and the
convergent property hold for the minimum free energy density of the
system.
Unitary transformations and multivariate special
orthogonal polynomials (JAPANESE)
[ Abstract ]
Investigations into special orthogonal function systems by
using unitary transformations have a long history.
This is, by calculating an image of some unitary transform (e.g. Fourier
trans.) of a known orthogonal system, we derive a new orthogonal system
and obtain its fundamental properties.
This basic concept and technique have been known since ancient times for
a single variable case, and recently these multivariate analogue has
been studied by Davidson, Olafsson, Zhang, Faraut, Wakayama et.al..
In our talk, we introduce the unitary picture for the circular Jacobi
polynomials obtained by Shen, further give a multivariate analogue of
the results of Shen.
These polynomials, which we call multivariate circular Jacobi (MCJ)
polynomials, are generalizations (2-parameter deformation) of the
spherical (zonal) polynomials that are different from the Jack or
Macdonald polynomials, which are well known as an extension of spherical
polynomials.
We also remark that the weight function of their orthogonality relation
coincides with the circular Jacobi ensemble defined by Bourgade,et,al.,
and the modified Cayley transform of the MCJ polynomials satisfy with
some quasi differential equation.
In addition, we can give a generalization of MCJ polynomials as
including the Jack polynomials.
For this generalized MCJ polynomials, we would like to present some
conjectures and problems.
If we have time, we also describe a unitary picture of Meixner,
Charlier and Krawtchouk polynomials which are typical examples of
discrete orthogonal systems, and mention their multivariate analogue.
Investigations into special orthogonal function systems by
using unitary transformations have a long history.
This is, by calculating an image of some unitary transform (e.g. Fourier
trans.) of a known orthogonal system, we derive a new orthogonal system
and obtain its fundamental properties.
This basic concept and technique have been known since ancient times for
a single variable case, and recently these multivariate analogue has
been studied by Davidson, Olafsson, Zhang, Faraut, Wakayama et.al..
In our talk, we introduce the unitary picture for the circular Jacobi
polynomials obtained by Shen, further give a multivariate analogue of
the results of Shen.
These polynomials, which we call multivariate circular Jacobi (MCJ)
polynomials, are generalizations (2-parameter deformation) of the
spherical (zonal) polynomials that are different from the Jack or
Macdonald polynomials, which are well known as an extension of spherical
polynomials.
We also remark that the weight function of their orthogonality relation
coincides with the circular Jacobi ensemble defined by Bourgade,et,al.,
and the modified Cayley transform of the MCJ polynomials satisfy with
some quasi differential equation.
In addition, we can give a generalization of MCJ polynomials as
including the Jack polynomials.
For this generalized MCJ polynomials, we would like to present some
conjectures and problems.
If we have time, we also describe a unitary picture of Meixner,
Charlier and Krawtchouk polynomials which are typical examples of
discrete orthogonal systems, and mention their multivariate analogue.
2014/12/10
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Akitaka Kishimoto (Hokkaido Univ.)
Approximately inner flows on $C^*$-algebras (English)
Akitaka Kishimoto (Hokkaido Univ.)
Approximately inner flows on $C^*$-algebras (English)
FMSP Lectures
16:00-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / Univ. Paris-Sud)
Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium
Danielle Hilhorst (CNRS / Univ. Paris-Sud)
Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium
[ Abstract ]
This talk is concerned with a mathematical model for the storage of radioactive waste. The model which we study deals with the diffusion of chemical species transported by water, with possible dissolution or precipitation and for a rather general kinetics law. In this talk, we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by the combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case. This is joint work with Hideki Murakawa.
This talk is concerned with a mathematical model for the storage of radioactive waste. The model which we study deals with the diffusion of chemical species transported by water, with possible dissolution or precipitation and for a rather general kinetics law. In this talk, we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by the combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case. This is joint work with Hideki Murakawa.
2014/12/09
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Koji Fujiwara (Kyoto University)
Stable commutator length on mapping class groups (JAPANESE)
Koji Fujiwara (Kyoto University)
Stable commutator length on mapping class groups (JAPANESE)
[ Abstract ]
Let MCG(S) be the mapping class group of a closed orientable surface S.
We give a precise condition (in terms of the Nielsen-Thurston
decomposition) when an element
in MCG(S) has positive stable commutator length.
Stable commutator length tends to be positive if there is "negative
curvature".
The proofs use our earlier construction in the paper "Constructing group
actions on quasi-trees and applications to mapping class groups" of
group actions on quasi-trees.
This is a joint work with Bestvina and Bromberg.
Let MCG(S) be the mapping class group of a closed orientable surface S.
We give a precise condition (in terms of the Nielsen-Thurston
decomposition) when an element
in MCG(S) has positive stable commutator length.
Stable commutator length tends to be positive if there is "negative
curvature".
The proofs use our earlier construction in the paper "Constructing group
actions on quasi-trees and applications to mapping class groups" of
group actions on quasi-trees.
This is a joint work with Bestvina and Bromberg.
2014/12/08
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Masatake Tomari (Nihon University)
On maximal ideal cycle and fundamental cycle of normal two-dimensional quasi-homogeneous singularities, and singularities with star-shaped resolution (JAPANESE)
Masatake Tomari (Nihon University)
On maximal ideal cycle and fundamental cycle of normal two-dimensional quasi-homogeneous singularities, and singularities with star-shaped resolution (JAPANESE)
2014/12/04
Geometry Colloquium
17:00-18:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Ryushi Goto (Osaka University)
Deformations and the moduli spaces of generalized complex manifolds (JAPANESE)
Ryushi Goto (Osaka University)
Deformations and the moduli spaces of generalized complex manifolds (JAPANESE)
2014/12/03
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yuki Arano (Univ. Tokyo)
Central property (T) for $SU_q(2n+1)$
(English)
Yuki Arano (Univ. Tokyo)
Central property (T) for $SU_q(2n+1)$
(English)
Lectures
16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Xavier Cabre (ICREA and UPC, Barcelona)
New isoperimetric inequalities with densities, part II: Detailed proofs and related works (ENGLISH)
Xavier Cabre (ICREA and UPC, Barcelona)
New isoperimetric inequalities with densities, part II: Detailed proofs and related works (ENGLISH)
[ Abstract ]
This is a sequel to the Tuesday Analysis Seminar on December 2 by the same speaker.
In joint works with X. Ros-Oton and J. Serra, the study of the regularity of stable solutions to reaction-diffusion problems has led us to certain Sobolev and isoperimetric inequalities with weights. We will present our results in these new isoperimetric inequalities with the best constant, that we establish via the ABP method.
More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (or densities) in open convex cones of R^n. Our results apply to all nonnegative homogeneous weights satisfying a concavity condition in the cone. Surprisingly, even that our weights are not radially symmetric, Euclidean balls centered at the origin (intersected with the cone) minimize the weighted isoperimetric quotient. As a particular case of our results, we provide with new proofs of classical results such as the Wulff inequality and the isoperimetric inequality in convex cones of Lions and Pacella. Furthermore, we also study the anisotropic isoperimetric problem for the same class of weights and we prove that the Wulff shape always minimizes the anisotropic weighted perimeter under the weighted volume constraint.
This is a sequel to the Tuesday Analysis Seminar on December 2 by the same speaker.
In joint works with X. Ros-Oton and J. Serra, the study of the regularity of stable solutions to reaction-diffusion problems has led us to certain Sobolev and isoperimetric inequalities with weights. We will present our results in these new isoperimetric inequalities with the best constant, that we establish via the ABP method.
More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (or densities) in open convex cones of R^n. Our results apply to all nonnegative homogeneous weights satisfying a concavity condition in the cone. Surprisingly, even that our weights are not radially symmetric, Euclidean balls centered at the origin (intersected with the cone) minimize the weighted isoperimetric quotient. As a particular case of our results, we provide with new proofs of classical results such as the Wulff inequality and the isoperimetric inequality in convex cones of Lions and Pacella. Furthermore, we also study the anisotropic isoperimetric problem for the same class of weights and we prove that the Wulff shape always minimizes the anisotropic weighted perimeter under the weighted volume constraint.
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