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Seminar information archive
Seminar information archive ～12/09｜Today's seminar 12/10 | Future seminars 12/11～
2011/11/07
GCOE lecture series
17:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
Oleg Emanouilov (Colorado State University)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
[ Abstract ]
We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).
We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Atsushi Ito (University of Tokyo)
Okounkov bodies and Seshadri constants (JAPANESE)
Atsushi Ito (University of Tokyo)
Okounkov bodies and Seshadri constants (JAPANESE)
[ Abstract ]
Okounkov bodies, which are convex bodies associated to big line bundles, have rich information of the line bundles. On the other hand, Seshadri constants are invariants which measure the positivities of line bundles. In this talk, I will explain a relation between Okounkov bodies and Seshadri constants.
Okounkov bodies, which are convex bodies associated to big line bundles, have rich information of the line bundles. On the other hand, Seshadri constants are invariants which measure the positivities of line bundles. In this talk, I will explain a relation between Okounkov bodies and Seshadri constants.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Nocuchi (University of Tokyo)
Oka's extra-zero problem and related topics (JAPANESE)
Junjiro Nocuchi (University of Tokyo)
Oka's extra-zero problem and related topics (JAPANESE)
[ Abstract ]
The main part of this talk is a joint work with my colleagues, M. Abe and S. Hamano. After the solution of Cousin II problem by K. Oka III in 1939, he thought an extra-zero problem in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. Some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was obtained. We will give a complete solution of this problem with examples and to discuss some new questions. An example on a toric variety of which idea is based on K. Stein's paper in 1941 has some special interest and will be discussed. I would like also to discuss some analytic intersections form the viewpoint of Nevanlinna theory.
The main part of this talk is a joint work with my colleagues, M. Abe and S. Hamano. After the solution of Cousin II problem by K. Oka III in 1939, he thought an extra-zero problem in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. Some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was obtained. We will give a complete solution of this problem with examples and to discuss some new questions. An example on a toric variety of which idea is based on K. Stein's paper in 1941 has some special interest and will be discussed. I would like also to discuss some analytic intersections form the viewpoint of Nevanlinna theory.
2011/11/04
Colloquium
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
KANAI Masahiko (Graduate School of Mathematical Sciences, University of Tokyo)
Cross ratio, and all that
(JAPANESE)
KANAI Masahiko (Graduate School of Mathematical Sciences, University of Tokyo)
Cross ratio, and all that
(JAPANESE)
[ Abstract ]
Although the origin of cross ratio goes back to ancient Greek mathematics, new discoveries about it has been made even in the past few decades. It seems that our understanding as to cross ratio is still limited. I am going to show you the present status and my own concerns, as well.
Although the origin of cross ratio goes back to ancient Greek mathematics, new discoveries about it has been made even in the past few decades. It seems that our understanding as to cross ratio is still limited. I am going to show you the present status and my own concerns, as well.
2011/11/02
Number Theory Seminar
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kensaku Kinjo (University of Tokyo)
Hypergeometric series and arithmetic-geometric mean over 2-adic fields (JAPANESE)
Kensaku Kinjo (University of Tokyo)
Hypergeometric series and arithmetic-geometric mean over 2-adic fields (JAPANESE)
[ Abstract ]
Dwork proved that the Gaussian hypergeometric function on p-adic numbers
can be extended to a function which takes values of the unit roots of
ordinary elliptic curves over a finite field of characteristic p>2.
We present an analogous theory in the case p=2.
As an application, we give a relation between the canonical lift
and the unit root of an elliptic curve over a finite field of
characteristic 2
by using the 2-adic arithmetic-geometric mean.
Dwork proved that the Gaussian hypergeometric function on p-adic numbers
can be extended to a function which takes values of the unit roots of
ordinary elliptic curves over a finite field of characteristic p>2.
We present an analogous theory in the case p=2.
As an application, we give a relation between the canonical lift
and the unit root of an elliptic curve over a finite field of
characteristic 2
by using the 2-adic arithmetic-geometric mean.
2011/11/01
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Kiyoshi Takeuchi (University of Tsukuba)
Motivic Milnor fibers and Jordan normal forms of monodromies (JAPANESE)
Kiyoshi Takeuchi (University of Tsukuba)
Motivic Milnor fibers and Jordan normal forms of monodromies (JAPANESE)
[ Abstract ]
We introduce a method to calculate the equivariant
Hodge-Deligne numbers of toric hypersurfaces.
Then we apply it to motivic Milnor
fibers introduced by Denef-Loeser and study the Jordan
normal forms of the local and global monodromies
of polynomials maps in various situations.
Especially we focus our attention on monodromies
at infinity studied by many people. The results will be
explicitly described by the ``convexity" of
the Newton polyhedra of polynomials. This is a joint work
with Y. Matsui and A. Esterov.
We introduce a method to calculate the equivariant
Hodge-Deligne numbers of toric hypersurfaces.
Then we apply it to motivic Milnor
fibers introduced by Denef-Loeser and study the Jordan
normal forms of the local and global monodromies
of polynomials maps in various situations.
Especially we focus our attention on monodromies
at infinity studied by many people. The results will be
explicitly described by the ``convexity" of
the Newton polyhedra of polynomials. This is a joint work
with Y. Matsui and A. Esterov.
2011/10/31
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Osamu Fujino (Kyoto University)
Minimal model theory for log surfaces (JAPANESE)
Osamu Fujino (Kyoto University)
Minimal model theory for log surfaces (JAPANESE)
[ Abstract ]
We discuss the log minimal model theory for log sur- faces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the usual framework of the log minimal model theory.
We discuss the log minimal model theory for log sur- faces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the usual framework of the log minimal model theory.
PDE Real Analysis Seminar
13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Horst Heck
(Technische Universität Darmstadt)
Stationary Weak Solutions of the Navier-Stokes Equations Past an Obstacle (ENGLISH)
Horst Heck
(Technische Universität Darmstadt)
Stationary Weak Solutions of the Navier-Stokes Equations Past an Obstacle (ENGLISH)
[ Abstract ]
Consider the stationary Navier-Stokes equations in an exterior smooth domain $\\Omega$. If the flow condition $u_\\infty$ for $u$ at infinity is non-zero and the external force $f\\in \\dot H^{-1}_2(\\Omega)$ is given Leray constructed a weak solution $u\\in \\dot H^1_2(\\Omega)$, the homogeneous Sobolev space, with $u-u_\\infty\\in L^6(\\Omega)$.
We show that if in addition $f\\in \\dot H^{-1}_q(\\Omega)$ for some $q\\in (4/3,4)$ then the weak solution has the property $u-u_\\infty\\in L^{4q/(4-q)}(\\Omega)$.
This additional integrability implies that $u$ satisfies the energy identity. Further consequences are uniqueness results for small $u_\\infty$ and $f$ and continuous dependence of the solution with respect to $u_\\infty$.
The presented results are joint work with Hyunseok Kim and Hideo Kozono.
Consider the stationary Navier-Stokes equations in an exterior smooth domain $\\Omega$. If the flow condition $u_\\infty$ for $u$ at infinity is non-zero and the external force $f\\in \\dot H^{-1}_2(\\Omega)$ is given Leray constructed a weak solution $u\\in \\dot H^1_2(\\Omega)$, the homogeneous Sobolev space, with $u-u_\\infty\\in L^6(\\Omega)$.
We show that if in addition $f\\in \\dot H^{-1}_q(\\Omega)$ for some $q\\in (4/3,4)$ then the weak solution has the property $u-u_\\infty\\in L^{4q/(4-q)}(\\Omega)$.
This additional integrability implies that $u$ satisfies the energy identity. Further consequences are uniqueness results for small $u_\\infty$ and $f$ and continuous dependence of the solution with respect to $u_\\infty$.
The presented results are joint work with Hyunseok Kim and Hideo Kozono.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Nobuhiro Honda (Tohoku Univeristy)
Classification of Moishezon twistor spaces on 4CP^2 (JAPANESE)
Nobuhiro Honda (Tohoku Univeristy)
Classification of Moishezon twistor spaces on 4CP^2 (JAPANESE)
2011/10/29
Infinite Analysis Seminar Tokyo
11:00-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Alexander Orlov (Nonlinear Wave Processes Laboratory, Oceanology Institute (Moscow)) 11:00-12:00
CKP Hierarchy, Bosonic Tau Function, Bosonization Formulae and Orthogonal Polynomials both in Odd and Even Variables
(based on a joint work with Johan van de Leur and Takahiro Shiota) (ENGLISH)
Kernel function identities associated with van Diejen's $q$-difference operators
and transformation formulas for multiple $q$-hypergeometric series (JAPANESE)
Alexander Orlov (Nonlinear Wave Processes Laboratory, Oceanology Institute (Moscow)) 11:00-12:00
CKP Hierarchy, Bosonic Tau Function, Bosonization Formulae and Orthogonal Polynomials both in Odd and Even Variables
(based on a joint work with Johan van de Leur and Takahiro Shiota) (ENGLISH)
[ Abstract ]
We develop the theory of CKP hierarchy introduced in the papers of Kyoto school where the CKP tau function is written as a vacuum expectation value in terms of free bosons. We show that a sort of odd currents naturaly appear. We consider bosonization formulae which relate bosonic Fock vectors to polynomials in even and odd Grassmannian variables, where both sets play a role of higher times.
Yasuho Masuda (Kobe Univ. ) 13:30-14:30We develop the theory of CKP hierarchy introduced in the papers of Kyoto school where the CKP tau function is written as a vacuum expectation value in terms of free bosons. We show that a sort of odd currents naturaly appear. We consider bosonization formulae which relate bosonic Fock vectors to polynomials in even and odd Grassmannian variables, where both sets play a role of higher times.
Kernel function identities associated with van Diejen's $q$-difference operators
and transformation formulas for multiple $q$-hypergeometric series (JAPANESE)
2011/10/26
Seminar on Probability and Statistics
15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)
SEI, Tomonari (Department of Mathematics, Keio University)
Statistical models constructed by optimal stationary coupling (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html
SEI, Tomonari (Department of Mathematics, Keio University)
Statistical models constructed by optimal stationary coupling (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html
2011/10/25
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes, Univ. of Tokyo)
Circle-valued Morse theory for complex hyperplane arrangements (ENGLISH)
Andrei Pajitnov (Univ. de Nantes, Univ. of Tokyo)
Circle-valued Morse theory for complex hyperplane arrangements (ENGLISH)
[ Abstract ]
Let A be a complex hyperplane arrangement
in an n-dimensional complex vector space V.
Denote by H the union of the hyperplanes
and by M the complement to H in V.
We develop the real-valued and circle-valued Morse
theory on M. We prove that if A is essential then
M has the homotopy type of a space
obtained from a finite n-dimensional
CW complex fibered over a circle,
by attaching several cells of dimension n.
We compute the Novikov homology of M and show
that its structure is similar to the
homology with generic local coefficients:
it vanishes for all dimensions except n.
This is a joint work with Toshitake Kohno.
Let A be a complex hyperplane arrangement
in an n-dimensional complex vector space V.
Denote by H the union of the hyperplanes
and by M the complement to H in V.
We develop the real-valued and circle-valued Morse
theory on M. We prove that if A is essential then
M has the homotopy type of a space
obtained from a finite n-dimensional
CW complex fibered over a circle,
by attaching several cells of dimension n.
We compute the Novikov homology of M and show
that its structure is similar to the
homology with generic local coefficients:
it vanishes for all dimensions except n.
This is a joint work with Toshitake Kohno.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshiki Oshima (Graduate School of Mathematical Sciences, the University of Tokyo)
Localization of Cohomological Induction (ENGLISH)
Yoshiki Oshima (Graduate School of Mathematical Sciences, the University of Tokyo)
Localization of Cohomological Induction (ENGLISH)
[ Abstract ]
Cohomological induction is defined for (g,K)-modules in an algebraic way and construct important representations such as (Harish-Chandra modules of) discrete series representations,
principal series representations and Zuckerman's modules of
semisimple Lie groups.
Hecht, Milicic, Schmid, and Wolf proved that modules induced from
one-dimensional representations of Borel subalgebra can be realized as D-modules on the flag variety.
In this talk, we show a similar result for modules induced from
more general representations.
Cohomological induction is defined for (g,K)-modules in an algebraic way and construct important representations such as (Harish-Chandra modules of) discrete series representations,
principal series representations and Zuckerman's modules of
semisimple Lie groups.
Hecht, Milicic, Schmid, and Wolf proved that modules induced from
one-dimensional representations of Borel subalgebra can be realized as D-modules on the flag variety.
In this talk, we show a similar result for modules induced from
more general representations.
2011/10/22
Infinite Analysis Seminar Tokyo
13:30-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Leonid Rybnikov (IITP, and State University Higher School of Economics,
Department of Mathematics) 13:30-14:30
Quantization of Quasimaps' Spaces (joint work with M. Finkelberg) (ENGLISH)
Instituteof Biochemical Physics) 15:00-16:00
Quantum integrable models with elliptic R-matrices
and elliptic hypergeometric series (ENGLISH)
Leonid Rybnikov (IITP, and State University Higher School of Economics,
Department of Mathematics) 13:30-14:30
Quantization of Quasimaps' Spaces (joint work with M. Finkelberg) (ENGLISH)
[ Abstract ]
Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a
remarkable compactification of the space of based degree d maps from
the projective line to the flag variety of type A. The space Z_d has a
natural Poisson structure,
which goes back to Atiyah and Hitchin. We describe
the Quasimaps' space as some quiver variety, and define the
Atiyah-Hitchin Poisson structure in quiver terms.
This gives a natural way to quantize this Poisson structure.
The quantization of the coordinate ring of the Quasimaps' space turns
to be some natural subquotient of the Yangian of type A.
I will also discuss some generalization of this result to the BCD types.
Anton Zabrodin ( Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a
remarkable compactification of the space of based degree d maps from
the projective line to the flag variety of type A. The space Z_d has a
natural Poisson structure,
which goes back to Atiyah and Hitchin. We describe
the Quasimaps' space as some quiver variety, and define the
Atiyah-Hitchin Poisson structure in quiver terms.
This gives a natural way to quantize this Poisson structure.
The quantization of the coordinate ring of the Quasimaps' space turns
to be some natural subquotient of the Yangian of type A.
I will also discuss some generalization of this result to the BCD types.
Instituteof Biochemical Physics) 15:00-16:00
Quantum integrable models with elliptic R-matrices
and elliptic hypergeometric series (ENGLISH)
[ Abstract ]
Intertwining operators for infinite-dimensional representations of the
Sklyanin algebra with spins l and -l-1 are constructed using the technique of
intertwining vectors for elliptic L-operator. They are expressed in
terms of
elliptic hypergeometric series with operator argument. The intertwining
operators obtained (W-operators) serve as building blocks for the
elliptic R-matrix
which intertwines tensor product of two L-operators taken in
infinite-dimensional
representations of the Sklyanin algebra with arbitrary spin. The
Yang-Baxter equation
for this R-matrix follows from simpler equations of the star-triangle
type for the
W-operators. A natural graphic representation of the objects and
equations involved
in the construction is used.
Intertwining operators for infinite-dimensional representations of the
Sklyanin algebra with spins l and -l-1 are constructed using the technique of
intertwining vectors for elliptic L-operator. They are expressed in
terms of
elliptic hypergeometric series with operator argument. The intertwining
operators obtained (W-operators) serve as building blocks for the
elliptic R-matrix
which intertwines tensor product of two L-operators taken in
infinite-dimensional
representations of the Sklyanin algebra with arbitrary spin. The
Yang-Baxter equation
for this R-matrix follows from simpler equations of the star-triangle
type for the
W-operators. A natural graphic representation of the objects and
equations involved
in the construction is used.
2011/10/20
GCOE Seminars
16:30-18:00 Room #270 (Graduate School of Math. Sci. Bldg.)
O. Emanouilov (Colorado State University)
On reconstruction of Lame coefficients from partial Cauchy data (ENGLISH)
O. Emanouilov (Colorado State University)
On reconstruction of Lame coefficients from partial Cauchy data (ENGLISH)
[ Abstract ]
For the isotropic Lame system, we prove that if the Lame coefficient ¥mu is a positive constant, then both Lame coefficients can be recovered from the partial Cauchy data.
For the isotropic Lame system, we prove that if the Lame coefficient ¥mu is a positive constant, then both Lame coefficients can be recovered from the partial Cauchy data.
2011/10/19
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Suslin (Northwestern University)
K_2 of the biquaternion algebra (ENGLISH)
[ Reference URL ]
http://www.ihes.fr/~abbes/SGA/suslin.pdf
Andrei Suslin (Northwestern University)
K_2 of the biquaternion algebra (ENGLISH)
[ Reference URL ]
http://www.ihes.fr/~abbes/SGA/suslin.pdf
2011/10/17
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshinobu Kamishima (Tokyo Metropolitan University)
Compact locally homogeneous Kähler manifolds $\Gamma\backslash G/K$ (JAPANESE)
Yoshinobu Kamishima (Tokyo Metropolitan University)
Compact locally homogeneous Kähler manifolds $\Gamma\backslash G/K$ (JAPANESE)
2011/10/12
Seminar on Probability and Statistics
15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)
SUZUKI, Taiji (University of Tokyo)
On Convergence Rate of Multiple Kernel Learning with Various Regularization Types (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html
SUZUKI, Taiji (University of Tokyo)
On Convergence Rate of Multiple Kernel Learning with Various Regularization Types (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html
2011/10/11
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Gael Meigniez (Univ. de Bretagne-Sud, Chuo Univ.)
Making foliations of codimension one,
thirty years after Thurston's works
(ENGLISH)
Gael Meigniez (Univ. de Bretagne-Sud, Chuo Univ.)
Making foliations of codimension one,
thirty years after Thurston's works
(ENGLISH)
[ Abstract ]
In 1976 Thurston proved that every closed manifold M whose
Euler characteristic is null carries a smooth foliation F of codimension
one. He actually established a h-principle allowing the regularization of
Haefliger structures through homotopy. I shall give some accounts of a new,
simpler proof of Thurston's result, not using Mather's homology equivalence; and also show that this proof allows to make F have dense leaves if dim M is at least 4. The emphasis will be put on the high dimensions.
In 1976 Thurston proved that every closed manifold M whose
Euler characteristic is null carries a smooth foliation F of codimension
one. He actually established a h-principle allowing the regularization of
Haefliger structures through homotopy. I shall give some accounts of a new,
simpler proof of Thurston's result, not using Mather's homology equivalence; and also show that this proof allows to make F have dense leaves if dim M is at least 4. The emphasis will be put on the high dimensions.
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hidemitsu Wadade (Waseda University (JSPS-PD))
On the best constant of the weighted Trudinger-Moser
type inequality (JAPANESE)
Hidemitsu Wadade (Waseda University (JSPS-PD))
On the best constant of the weighted Trudinger-Moser
type inequality (JAPANESE)
2011/10/07
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Takeshi Katsura (Keio University)
Towards the classification of non-simple $C^*$-algebras of real rank zero (ENGLISH)
Takeshi Katsura (Keio University)
Towards the classification of non-simple $C^*$-algebras of real rank zero (ENGLISH)
2011/10/05
Seminar on Mathematics for various disciplines
10:00-11:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Chun Liu (University of Tokyo / Pennsylvania State University)
Energetic Variational Approaches for Ionic Fluids (ENGLISH)
Chun Liu (University of Tokyo / Pennsylvania State University)
Energetic Variational Approaches for Ionic Fluids (ENGLISH)
[ Abstract ]
In this talk, I will present our recent study on the ionic transport through ion channels in cell membranes. Motivated by our earlier work on energetic variational approaches, developed for various complex fluids, especially electrorheological (ER) fluids (Phys. Rev. Lett. 101, 194503 (2008)), we derived/proposed a coupled system for ionic solutions, which takes into account of the solvent water, the diffusion and electro-static interaction of different ions. In particular, I will emphasize on the selectivity effects of the ion channels, under the simplest geometric and molecular structures.
In this talk, I will present our recent study on the ionic transport through ion channels in cell membranes. Motivated by our earlier work on energetic variational approaches, developed for various complex fluids, especially electrorheological (ER) fluids (Phys. Rev. Lett. 101, 194503 (2008)), we derived/proposed a coupled system for ionic solutions, which takes into account of the solvent water, the diffusion and electro-static interaction of different ions. In particular, I will emphasize on the selectivity effects of the ion channels, under the simplest geometric and molecular structures.
2011/10/04
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshifumi Matsuda (The University of Tokyo)
Relatively quasiconvex subgroups of relatively hyperbolic groups (JAPANESE)
Yoshifumi Matsuda (The University of Tokyo)
Relatively quasiconvex subgroups of relatively hyperbolic groups (JAPANESE)
[ Abstract ]
Relative hyperbolicity of groups was introduced by Gromov as a
generalization of word hyperbolicity. Motivating examples of relatively
hyperbolic groups are fundamental groups of noncompact complete
hyperbolic manifolds of finite volume. The class of relatively
quasiconvex subgroups of a realtively hyperbolic group is defined as a
genaralization of that of quasicovex subgroups of a word hyperbolic
group. The notion of hyperbolically embedded subgroups of a relatively
hyperbolic group was introduced by Osin and such groups are
characterized as relatively quasiconvex subgroups with additional
algebraic properties. In this talk I will present an introduction to
relatively quasiconvex subgroups and discuss recent joint work with Shin
-ichi Oguni and Saeko Yamagata on hyperbolically embedded subgroups.
Relative hyperbolicity of groups was introduced by Gromov as a
generalization of word hyperbolicity. Motivating examples of relatively
hyperbolic groups are fundamental groups of noncompact complete
hyperbolic manifolds of finite volume. The class of relatively
quasiconvex subgroups of a realtively hyperbolic group is defined as a
genaralization of that of quasicovex subgroups of a word hyperbolic
group. The notion of hyperbolically embedded subgroups of a relatively
hyperbolic group was introduced by Osin and such groups are
characterized as relatively quasiconvex subgroups with additional
algebraic properties. In this talk I will present an introduction to
relatively quasiconvex subgroups and discuss recent joint work with Shin
-ichi Oguni and Saeko Yamagata on hyperbolically embedded subgroups.
2011/09/20
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Clara Loeh (Univ. Regensburg)
Functorial semi-norms on singular homology (ENGLISH)
Clara Loeh (Univ. Regensburg)
Functorial semi-norms on singular homology (ENGLISH)
[ Abstract ]
Functorial semi-norms on singular homology add metric information to
homology classes that is compatible with continuous maps. In particular,
functorial semi-norms give rise to degree theorems for certain classes
of manifolds; an invariant fitting into this context is Gromov's
simplicial volume. On the other hand, knowledge about mapping degrees
allows to construct functorial semi-norms with interesting properties;
for example, so-called inflexible simply connected manifolds give rise
to functorial semi-norms that are non-trivial on certain simply connected
spaces.
Functorial semi-norms on singular homology add metric information to
homology classes that is compatible with continuous maps. In particular,
functorial semi-norms give rise to degree theorems for certain classes
of manifolds; an invariant fitting into this context is Gromov's
simplicial volume. On the other hand, knowledge about mapping degrees
allows to construct functorial semi-norms with interesting properties;
for example, so-called inflexible simply connected manifolds give rise
to functorial semi-norms that are non-trivial on certain simply connected
spaces.
2011/08/12
GCOE Seminars
16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)
Benny Hon (Department of Mathematics City University of Hong Kong)
Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations (ENGLISH)
Benny Hon (Department of Mathematics City University of Hong Kong)
Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations (ENGLISH)
[ Abstract ]
In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green’s functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.
In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green’s functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.
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