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Seminar information archive
Seminar information archive ～04/30｜Today's seminar 05/01 | Future seminars 05/02～
2012/05/29
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Inasa Nakamura (Gakushuin University, JSPS)
Triple linking numbers and triple point numbers
of torus-covering $T^2$-links
(JAPANESE)
Inasa Nakamura (Gakushuin University, JSPS)
Triple linking numbers and triple point numbers
of torus-covering $T^2$-links
(JAPANESE)
[ Abstract ]
The triple linking number of an oriented surface link was defined as an
analogical notion of the linking number of a classical link. A
torus-covering $T^2$-link $\\mathcal{S}_m(a,b)$ is a surface link in the
form of an unbranched covering over the standard torus, determined from
two commutative $m$-braids $a$ and $b$.
In this talk, we consider $\\mathcal{S}_m(a,b)$ when $a$, $b$ are pure
$m$-braids ($m \\geq 3$), which is a surface link with $m$-components. We
present the triple linking number of $\\mathcal{S}_m(a,b)$ by using the
linking numbers of the closures of $a$ and $b$. This gives a lower bound
of the triple point number. In some cases, we can determine the triple
point numbers, each of which is a multiple of four.
The triple linking number of an oriented surface link was defined as an
analogical notion of the linking number of a classical link. A
torus-covering $T^2$-link $\\mathcal{S}_m(a,b)$ is a surface link in the
form of an unbranched covering over the standard torus, determined from
two commutative $m$-braids $a$ and $b$.
In this talk, we consider $\\mathcal{S}_m(a,b)$ when $a$, $b$ are pure
$m$-braids ($m \\geq 3$), which is a surface link with $m$-components. We
present the triple linking number of $\\mathcal{S}_m(a,b)$ by using the
linking numbers of the closures of $a$ and $b$. This gives a lower bound
of the triple point number. In some cases, we can determine the triple
point numbers, each of which is a multiple of four.
GCOE lecture series
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (CNRS, Orsay)
Random walk on reductive groups. (ENGLISH)
Yves Benoist (CNRS, Orsay)
Random walk on reductive groups. (ENGLISH)
[ Abstract ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.
Lectures
14:50-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)
Harald Niederreiter (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html
Harald Niederreiter (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html
2012/05/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Shinichi TAJIMA (University of Tsukuba)
Local cohomology and hypersurface isolated singularities II (JAPANESE)
Shinichi TAJIMA (University of Tsukuba)
Local cohomology and hypersurface isolated singularities II (JAPANESE)
[ Abstract ]
局所コホモロジーの孤立特異点への応用として
・$\mu$-constant-deformation の Tjurina 数
・対数的ベクトル場の構造と構成法
・ニュートン非退化な超曲面に対する Kouchnirenko の公式
について述べる.
局所コホモロジーの孤立特異点への応用として
・$\mu$-constant-deformation の Tjurina 数
・対数的ベクトル場の構造と構成法
・ニュートン非退化な超曲面に対する Kouchnirenko の公式
について述べる.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Mihnea Popa (University of Illinois at Chicago)
Generic vanishing and linearity via Hodge modules (ENGLISH)
Mihnea Popa (University of Illinois at Chicago)
Generic vanishing and linearity via Hodge modules (ENGLISH)
[ Abstract ]
I will explain joint work with Christian Schnell, in which we extend the fundamental results of generic vanishing theory (for instance for the canonical bundle of a smooth projective variety) to bundles of holomorphic forms and to rank one local systems, where parts of the theory have eluded previous efforts. To achiever this, we bring all of the old and new results under the same roof by enlarging the scope of generic vanishing theory to the study of filtered D-modules associated to mixed Hodge modules. Besides Saito's vanishing and direct image theorems for Hodge modules, an important input is the Laumon-Rothstein Fourier transform for bundles with integrable connection.
I will explain joint work with Christian Schnell, in which we extend the fundamental results of generic vanishing theory (for instance for the canonical bundle of a smooth projective variety) to bundles of holomorphic forms and to rank one local systems, where parts of the theory have eluded previous efforts. To achiever this, we bring all of the old and new results under the same roof by enlarging the scope of generic vanishing theory to the study of filtered D-modules associated to mixed Hodge modules. Besides Saito's vanishing and direct image theorems for Hodge modules, an important input is the Laumon-Rothstein Fourier transform for bundles with integrable connection.
Lectures
14:50-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)
Harald Niederreiter (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (I) (ENGLISH)
https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html
Harald Niederreiter (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (I) (ENGLISH)
[ Abstract ]
This is the second of the four lectures. The first one is Colloquium talk on May 25th 16:30--17:30 at 002.
Abstract from Colloquium:
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo
methods in computational mathematics. QMC methods employ evenly distributed
low-discrepancy sequences instead of the random samples used in Monte Carlo methods.
For many types of computational problems, QMC methods are more efficient than
Monte Carlo methods. After a general introduction to QMC methods, the talk focuses
on the problem of constructing low-discrepancy sequences which has fascinating links
with subjects such as finite fields, error-correcting codes, and algebraic curves.
[ Reference URL ]This is the second of the four lectures. The first one is Colloquium talk on May 25th 16:30--17:30 at 002.
Abstract from Colloquium:
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo
methods in computational mathematics. QMC methods employ evenly distributed
low-discrepancy sequences instead of the random samples used in Monte Carlo methods.
For many types of computational problems, QMC methods are more efficient than
Monte Carlo methods. After a general introduction to QMC methods, the talk focuses
on the problem of constructing low-discrepancy sequences which has fascinating links
with subjects such as finite fields, error-correcting codes, and algebraic curves.
https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html
2012/05/26
Harmonic Analysis Komaba Seminar
13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kiko Kawamura (University of North Texas) 13:30-15:00
The Takagi function - a survey (JAPANESE)
Dyadic, classical and martingale harmonic analysis II (JAPANESE)
Kiko Kawamura (University of North Texas) 13:30-15:00
The Takagi function - a survey (JAPANESE)
[ Abstract ]
More than a century has passed since Takagi published his simple example of a continuous but nowhere differentiable function,
yet Takagi's function -- as it is now commonly referred
to despite repeated rediscovery
by mathematicians in the West -- continues to inspire, fascinate and puzzle researchers as never before.
In this talk, I will give not only an overview of the history and known characteristics of the function,
but also discuss some of the fascinating applications it has found -- some quite recently! -- in such diverse areas of mathematics as number theory, combinatorics, and analysis.
Yutaka Terasawa (The University of Tokyo) 15:30-17:00More than a century has passed since Takagi published his simple example of a continuous but nowhere differentiable function,
yet Takagi's function -- as it is now commonly referred
to despite repeated rediscovery
by mathematicians in the West -- continues to inspire, fascinate and puzzle researchers as never before.
In this talk, I will give not only an overview of the history and known characteristics of the function,
but also discuss some of the fascinating applications it has found -- some quite recently! -- in such diverse areas of mathematics as number theory, combinatorics, and analysis.
Dyadic, classical and martingale harmonic analysis II (JAPANESE)
[ Abstract ]
In a filtered measure space, we investigate the characterization of weights for which positive operators and maximal operators are bounded.
For this, a refinement of Carleson embedding theorem is introduced in this setting. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. If time permits, we would like to mention Hyt\\"onen-P\\'erez type sharp one-weight estimate of Doob's
maximal operator which is derived from our two-weight characterization.
This talk is based on a joint work with Professor Hitoshi Tanaka
(The University of Tokyo).
In a filtered measure space, we investigate the characterization of weights for which positive operators and maximal operators are bounded.
For this, a refinement of Carleson embedding theorem is introduced in this setting. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. If time permits, we would like to mention Hyt\\"onen-P\\'erez type sharp one-weight estimate of Doob's
maximal operator which is derived from our two-weight characterization.
This talk is based on a joint work with Professor Hitoshi Tanaka
(The University of Tokyo).
2012/05/25
Colloquium
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Harald Niederreiter (RICAM, Austrian Academy of Sciences)
Quasi-Monte Carlo methods: deterministic is often better than random (ENGLISH)
https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html
Harald Niederreiter (RICAM, Austrian Academy of Sciences)
Quasi-Monte Carlo methods: deterministic is often better than random (ENGLISH)
[ Abstract ]
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.
This talk also serves as the first talk of the four lecture series. The other three are on 5/28, 5/29, 5/30, 14:50-16:20 at room 123.
[ Reference URL ]Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.
This talk also serves as the first talk of the four lecture series. The other three are on 5/28, 5/29, 5/30, 14:50-16:20 at room 123.
https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html
GCOE lecture series
14:00-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Mihnea Popa (University of Illinois at Chicago)
Generic vanishing theory and connections with derived categories (ENGLISH)
Mihnea Popa (University of Illinois at Chicago)
Generic vanishing theory and connections with derived categories (ENGLISH)
[ Abstract ]
I will give a basic introduction to the main results regarding the cohomology of deformations of the canonical bundle, and explain a connection with certain t-structures on the derived categories of Picard varieties. (This will also serve as an introduction for the talk at AG seminar on 5/28, 15:30-17:00.)
I will give a basic introduction to the main results regarding the cohomology of deformations of the canonical bundle, and explain a connection with certain t-structures on the derived categories of Picard varieties. (This will also serve as an introduction for the talk at AG seminar on 5/28, 15:30-17:00.)
2012/05/23
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Xingfei Xiang (East China Normal University)
$L^p$ Estimates of the Vector Fields and their Applications (ENGLISH)
Xingfei Xiang (East China Normal University)
$L^p$ Estimates of the Vector Fields and their Applications (ENGLISH)
[ Abstract ]
For $1< p < \\infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \\infty$. As an application of the $L^p$ estimates, the Global $\\dv-\\curl$ lemma in Sobolev spaces of negative indices is given.
For $1< p < \\infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \\infty$. As an application of the $L^p$ estimates, the Global $\\dv-\\curl$ lemma in Sobolev spaces of negative indices is given.
Number Theory Seminar
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Kentaro Mitsui (University of Tokyo)
Simply connected elliptic surfaces (JAPANESE)
Kentaro Mitsui (University of Tokyo)
Simply connected elliptic surfaces (JAPANESE)
[ Abstract ]
We characterize simply connected elliptic surfaces by their singular fibers in any characteristic case. To this end, we study orbifolds of curves, local canonical bundle formula, and resolutions of multiple fibers. The result was known for the complex analytic case. Our method can be applied to the rigid analytic case.
We characterize simply connected elliptic surfaces by their singular fibers in any characteristic case. To this end, we study orbifolds of curves, local canonical bundle formula, and resolutions of multiple fibers. The result was known for the complex analytic case. Our method can be applied to the rigid analytic case.
2012/05/22
Tuesday Seminar of Analysis
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Norbert Pozar (Graduate School of Mathematical Sciences, The University of Tokyo)
Viscosity solutions for nonlinear elliptic-parabolic problems (ENGLISH)
Norbert Pozar (Graduate School of Mathematical Sciences, The University of Tokyo)
Viscosity solutions for nonlinear elliptic-parabolic problems (ENGLISH)
[ Abstract ]
We introduce a notion of viscosity solutions for a general class of
elliptic-parabolic phase transition problems. These include the
Richards equation, which is a classical model in filtration theory.
Existence and uniqueness results are proved via the comparison
principle. In particular, we show existence and stability properties
of maximal and minimal viscosity solutions for a general class of
initial data. These results are new even in the linear case, where we
also show that viscosity solutions coincide with the regular weak
solutions introduced in [Alt&Luckhaus 1983]. This talk is based on a
recent work with Inwon Kim.
We introduce a notion of viscosity solutions for a general class of
elliptic-parabolic phase transition problems. These include the
Richards equation, which is a classical model in filtration theory.
Existence and uniqueness results are proved via the comparison
principle. In particular, we show existence and stability properties
of maximal and minimal viscosity solutions for a general class of
initial data. These results are new even in the linear case, where we
also show that viscosity solutions coincide with the regular weak
solutions introduced in [Alt&Luckhaus 1983]. This talk is based on a
recent work with Inwon Kim.
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Daisuke Koyama (The University of Electro-Communications)
The DtN finite element method and the Schwarz method for multiple scattering problems (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Daisuke Koyama (The University of Electro-Communications)
The DtN finite element method and the Schwarz method for multiple scattering problems (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Tuesday Seminar on Topology
17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)
Hiroshi Iritani (Kyoto University)
Gamma Integral Structure in Gromov-Witten theory (JAPANESE)
Hiroshi Iritani (Kyoto University)
Gamma Integral Structure in Gromov-Witten theory (JAPANESE)
[ Abstract ]
The quantum cohomology of a symplectic
manifold undelies a certain integral local system
defined by the Gamma characteristic class.
This local system originates from the natural integral
local sysmem on the B-side under mirror symmetry.
In this talk, I will explain its relationships to the problem
of analytic continuation of Gromov-Witten theoy (potentials),
including crepant resolution conjecture, LG/CY correspondence,
modularity in higher genus theory.
The quantum cohomology of a symplectic
manifold undelies a certain integral local system
defined by the Gamma characteristic class.
This local system originates from the natural integral
local sysmem on the B-side under mirror symmetry.
In this talk, I will explain its relationships to the problem
of analytic continuation of Gromov-Witten theoy (potentials),
including crepant resolution conjecture, LG/CY correspondence,
modularity in higher genus theory.
2012/05/21
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Taku Suzuki (Waseda University)
Characterizations of projective spaces and hyperquadrics
(JAPANESE)
Taku Suzuki (Waseda University)
Characterizations of projective spaces and hyperquadrics
(JAPANESE)
[ Abstract ]
After Mori's works on Hartshorne's conjecture, many results to
characterize projective spaces and hyperquadrics in terms of
positivity properties of the tangent bundle have been provided.
Kov\\'acs' conjecture states that smooth complex projective
varieties are projective spaces or hyperquadrics if the $p$-th
exterior product of their tangent bundle contains the $p$-th
exterior product of an ample vector bundle. This conjecture is
the generalization of many preceding results. In this talk, I will
explain the idea of the proof of Kov\\'acs' conjecture for varieties
with Picard number one by using a method of slope-stabilities
of sheaves.
After Mori's works on Hartshorne's conjecture, many results to
characterize projective spaces and hyperquadrics in terms of
positivity properties of the tangent bundle have been provided.
Kov\\'acs' conjecture states that smooth complex projective
varieties are projective spaces or hyperquadrics if the $p$-th
exterior product of their tangent bundle contains the $p$-th
exterior product of an ample vector bundle. This conjecture is
the generalization of many preceding results. In this talk, I will
explain the idea of the proof of Kov\\'acs' conjecture for varieties
with Picard number one by using a method of slope-stabilities
of sheaves.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Shinichi TAJIMA (University of Tsukuba)
Local cohomology and hypersurface isolated singularities I (JAPANESE)
Shinichi TAJIMA (University of Tsukuba)
Local cohomology and hypersurface isolated singularities I (JAPANESE)
Kavli IPMU Komaba Seminar
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Emanuel Scheidegger (The University of Freiburg)
Topological Strings on Elliptic Fibrations (ENGLISH)
Emanuel Scheidegger (The University of Freiburg)
Topological Strings on Elliptic Fibrations (ENGLISH)
[ Abstract ]
We will explain a conjecture that expresses the BPS invariants
(Gopakumar-Vafa invariants) for elliptically fibered Calabi-Yau
threefolds in terms of modular forms. In particular, there is a
recursion relation which governs these modular forms. Evidence comes
from the polynomial formulation of the higher genus topological string
amplitudes with insertions.
We will explain a conjecture that expresses the BPS invariants
(Gopakumar-Vafa invariants) for elliptically fibered Calabi-Yau
threefolds in terms of modular forms. In particular, there is a
recursion relation which governs these modular forms. Evidence comes
from the polynomial formulation of the higher genus topological string
amplitudes with insertions.
2012/05/19
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Takashi Taniguchi (Kobe Univeristy) 13:30-14:30
TBA (JAPANESE)
Masao Tsuzuki (Sophia University) 15:00-16:00
TBA (JAPANESE)
Takashi Taniguchi (Kobe Univeristy) 13:30-14:30
TBA (JAPANESE)
Masao Tsuzuki (Sophia University) 15:00-16:00
TBA (JAPANESE)
2012/05/18
Seminar on Probability and Statistics
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
SUZUKI, Taiji (University of Tokyo)
PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additive Model (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/04.html
SUZUKI, Taiji (University of Tokyo)
PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additive Model (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/04.html
2012/05/16
Number Theory Seminar
16:40-17:40 Room #002 (Graduate School of Math. Sci. Bldg.)
Naoya Umezaki (University of Tokyo)
On uniform bound of the maximal subgroup of the inertia group acting unipotently on $¥ell$-adic cohomology (JAPANESE)
Naoya Umezaki (University of Tokyo)
On uniform bound of the maximal subgroup of the inertia group acting unipotently on $¥ell$-adic cohomology (JAPANESE)
[ Abstract ]
For a smooth projective variety over a local field,
the action of the inertia group on the $¥ell$-adic cohomology group is
unipotent if it is restricted to some open subgroup.
In this talk, we give a uniform bound of the index of the maximal open
subgroup satisfying this property.
This bound depends only on the Betti numbers of $X$ and certain Chern
numbers depending on a projective embedding of $X$.
For a smooth projective variety over a local field,
the action of the inertia group on the $¥ell$-adic cohomology group is
unipotent if it is restricted to some open subgroup.
In this talk, we give a uniform bound of the index of the maximal open
subgroup satisfying this property.
This bound depends only on the Betti numbers of $X$ and certain Chern
numbers depending on a projective embedding of $X$.
2012/05/15
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
MIZUTANI, Haruya (Research Institute for Mathematical Sciences, Kyoto University)
Strichartz estimates for Schr\\"odinger equations with variable coefficients and unbounded electromagnetic potentials (JAPANESE)
MIZUTANI, Haruya (Research Institute for Mathematical Sciences, Kyoto University)
Strichartz estimates for Schr\\"odinger equations with variable coefficients and unbounded electromagnetic potentials (JAPANESE)
[ Abstract ]
In this talk we consider the Cauchy problem for Schr\\"odinger equations with variable coefficients and unbounded potentials. Under the assumption that the Hamiltonian is a long-range perturbation of the free Schr\\"odinger operator, we construct an outgoing parametrix for the propagator near infinity, and give applications to sharp Strichartz estimates. The basic idea is to combine the standard approximation by using a time dependent modifier, which is not in the semiclassical regime, with the semiclassical approximation of Isozaki-Kitada type. We also show near sharp Strichartz estimates without asymptotic conditions by using local smoothing effects.
In this talk we consider the Cauchy problem for Schr\\"odinger equations with variable coefficients and unbounded potentials. Under the assumption that the Hamiltonian is a long-range perturbation of the free Schr\\"odinger operator, we construct an outgoing parametrix for the propagator near infinity, and give applications to sharp Strichartz estimates. The basic idea is to combine the standard approximation by using a time dependent modifier, which is not in the semiclassical regime, with the semiclassical approximation of Isozaki-Kitada type. We also show near sharp Strichartz estimates without asymptotic conditions by using local smoothing effects.
2012/05/14
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Hiroshi KANEKO (Tokyo University of Science)
Duality in the unit circle and the ring of p-adic intergers and van der Corput series (JAPANESE)
Hiroshi KANEKO (Tokyo University of Science)
Duality in the unit circle and the ring of p-adic intergers and van der Corput series (JAPANESE)
2012/05/11
Colloquium
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
SAKASAI Takuya (University of Tokyo)
Moduli spaces and symplectic derivation Lie algebras (JAPANESE)
SAKASAI Takuya (University of Tokyo)
Moduli spaces and symplectic derivation Lie algebras (JAPANESE)
[ Abstract ]
First we overview Kontsevich's theorem describing a deep connection between homology of certain infinite dimensional Lie algebras (symplectic derivation Lie algebras) and cohomology of various moduli spaces. Then we discuss some computational results on the Lie algebras together with their applications (joint work with Shigeyuki Morita and Masaaki Suzuki).
First we overview Kontsevich's theorem describing a deep connection between homology of certain infinite dimensional Lie algebras (symplectic derivation Lie algebras) and cohomology of various moduli spaces. Then we discuss some computational results on the Lie algebras together with their applications (joint work with Shigeyuki Morita and Masaaki Suzuki).
Seminar on Probability and Statistics
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
FUKASAWA, Masaaki (Department of Mathematics, Osaka University)
Efficient Discretization of Stochastic Integrals (JAPANESE)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/03.html
FUKASAWA, Masaaki (Department of Mathematics, Osaka University)
Efficient Discretization of Stochastic Integrals (JAPANESE)
[ Abstract ]
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.
[ Reference URL ]Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/03.html
2012/05/08
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Tadashi Ishibe (The University of Tokyo, JSPS)
Infinite examples of non-Garside monoids having fundamental elements (JAPANESE)
Tadashi Ishibe (The University of Tokyo, JSPS)
Infinite examples of non-Garside monoids having fundamental elements (JAPANESE)
[ Abstract ]
The Garside group, as a generalization of Artin groups,
is defined as the group of fractions of a Garside monoid.
To understand the elliptic Artin groups, which are the fundamental
groups of the complement of discriminant divisors of the semi-versal
deformation of the simply elliptic singularities E_6~, E_7~ and E_8~,
we need to consider another generalization of Artin groups.
In this talk, we will study the presentations of fundamental groups
of the complement of complexified real affine line arrangements
and consider the associated monoids.
It turns out that, in some cases, they are not Garside monoids.
Nevertheless, we will show that they satisfy the cancellation condition
and carry certain particular elements similar to the fundamental elements
in Artin monoids.
As a result, we will show that the word problem can be solved
and the center of them are determined.
The Garside group, as a generalization of Artin groups,
is defined as the group of fractions of a Garside monoid.
To understand the elliptic Artin groups, which are the fundamental
groups of the complement of discriminant divisors of the semi-versal
deformation of the simply elliptic singularities E_6~, E_7~ and E_8~,
we need to consider another generalization of Artin groups.
In this talk, we will study the presentations of fundamental groups
of the complement of complexified real affine line arrangements
and consider the associated monoids.
It turns out that, in some cases, they are not Garside monoids.
Nevertheless, we will show that they satisfy the cancellation condition
and carry certain particular elements similar to the fundamental elements
in Artin monoids.
As a result, we will show that the word problem can be solved
and the center of them are determined.
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