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Seminar information archive
Seminar information archive ～04/25｜Today's seminar 04/26 | Future seminars 04/27～
2008/06/19
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
David Kerr (Texas A&M University)
Turbulence, representations, and trace-preserving actions
David Kerr (Texas A&M University)
Turbulence, representations, and trace-preserving actions
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
谷口 雅治 (東京工業大学大学院情報理工学研究科)
Allen-Cahn方程式における角錐型進行波の一意性と安定性
(The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations)
谷口 雅治 (東京工業大学大学院情報理工学研究科)
Allen-Cahn方程式における角錐型進行波の一意性と安定性
(The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations)
[ Abstract ]
We study the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity. For this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces. Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waves on the edges. This characterization also uniquely determines a pyramidal traveling front.
We study the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity. For this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces. Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waves on the edges. This characterization also uniquely determines a pyramidal traveling front.
Lectures
16:20-17:50 Room #052 (Graduate School of Math. Sci. Bldg.)
伊藤 高一 (IRI-DNL)
インターネットにおける数理科学的手法と実際「DNSとWebアクセス」
https://www.ms.u-tokyo.ac.jp/lecture/2008/inet/index.html
伊藤 高一 (IRI-DNL)
インターネットにおける数理科学的手法と実際「DNSとWebアクセス」
[ Abstract ]
テーマごとに個別の企業活動を紹介し、第一線で活躍する企業研究者を招聘し、現場レポートを聴き、議論を行うことで、インターネット数理科学の原理とその応用の実際を紹介する。
[ Reference URL ]テーマごとに個別の企業活動を紹介し、第一線で活躍する企業研究者を招聘し、現場レポートを聴き、議論を行うことで、インターネット数理科学の原理とその応用の実際を紹介する。
https://www.ms.u-tokyo.ac.jp/lecture/2008/inet/index.html
2008/06/18
Number Theory Seminar
16:30-18:45 Room #117 (Graduate School of Math. Sci. Bldg.)
服部 新 (北海道大学大学院理学研究院) 16:30-17:30
On a ramification bound of semi-stable torsion representations over a local field
朝倉 政典 (北海道大学大学院理学研究院) 17:45-18:45
Beilinson-Tate予想と楕円曲面のK_1の不分解元
服部 新 (北海道大学大学院理学研究院) 16:30-17:30
On a ramification bound of semi-stable torsion representations over a local field
朝倉 政典 (北海道大学大学院理学研究院) 17:45-18:45
Beilinson-Tate予想と楕円曲面のK_1の不分解元
[ Abstract ]
(佐藤周友氏との共同研究)
代数サイクルのTate予想のK理論における類似であるBeilinson-Tate予想について、
楕円曲面の場合にそれが成り立つ非自明な例を構成する。
これは、p進レギュレーターの非消滅と関係しており、
応用としてK_1の不分解元であって整数環上のモデルからくるようなものを構成する。
(佐藤周友氏との共同研究)
代数サイクルのTate予想のK理論における類似であるBeilinson-Tate予想について、
楕円曲面の場合にそれが成り立つ非自明な例を構成する。
これは、p進レギュレーターの非消滅と関係しており、
応用としてK_1の不分解元であって整数環上のモデルからくるようなものを構成する。
Mathematical Finance
17:30-19:00 Room #122 (Graduate School of Math. Sci. Bldg.)
塩谷 匡介 (日本銀行)
経済学と金融工学 ―Financial Economics入門―」(講義)
+M. Piazzesi and E. Swanson, "Futures Prices as Risk-Adjusted Forecasts
of Monetary Policy", Journal of Monetary Economics (2008)
塩谷 匡介 (日本銀行)
経済学と金融工学 ―Financial Economics入門―」(講義)
+M. Piazzesi and E. Swanson, "Futures Prices as Risk-Adjusted Forecasts
of Monetary Policy", Journal of Monetary Economics (2008)
2008/06/17
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
佐野 友二 (東京大学IPMU)
Multiplier ideal sheaves and Futaki invariant on toric Fano manifolds.
佐野 友二 (東京大学IPMU)
Multiplier ideal sheaves and Futaki invariant on toric Fano manifolds.
[ Abstract ]
I would like to discuss the subvarieties cut off by the multiplier
ideal sheaves (MIS) and Futaki invariant on toric Fano manifolds.
Futaki invariant is one of the necessary conditions for the existence
of Kahler-Einstein metrics on Fano manifolds,
on the other hand MIS is one of the sufficient conditions introduced by Nadel.
Especially I would like to focus on the MIS related to the Monge-Ampere equation
for Kahler-Einstein metrics on non-KE toric Fano manifolds.
The motivation of this work comes from the investigation of the
relationship with slope stability
of polarized manifolds introduced by Ross and Thomas.
This talk will be based on a part of the joint work with Akito Futaki
(arXiv:0711.0614).
I would like to discuss the subvarieties cut off by the multiplier
ideal sheaves (MIS) and Futaki invariant on toric Fano manifolds.
Futaki invariant is one of the necessary conditions for the existence
of Kahler-Einstein metrics on Fano manifolds,
on the other hand MIS is one of the sufficient conditions introduced by Nadel.
Especially I would like to focus on the MIS related to the Monge-Ampere equation
for Kahler-Einstein metrics on non-KE toric Fano manifolds.
The motivation of this work comes from the investigation of the
relationship with slope stability
of polarized manifolds introduced by Ross and Thomas.
This talk will be based on a part of the joint work with Akito Futaki
(arXiv:0711.0614).
2008/06/16
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
山ノ井 克俊 (熊本大自然)
有理型関数の高階導関数の零点について
山ノ井 克俊 (熊本大自然)
有理型関数の高階導関数の零点について
2008/06/14
Infinite Analysis Seminar Tokyo
13:30-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)
孫 娟娟 (東大数理) 13:30-14:30
Confluent KZ equations for $sl_2$ and quantization of monodromy preserving deformation
Exact Solution and Physical Combinatorics of Critical Dense
Polymers
孫 娟娟 (東大数理) 13:30-14:30
Confluent KZ equations for $sl_2$ and quantization of monodromy preserving deformation
[ Abstract ]
We obtain a system of confluent Knizhnik-Zamolodchikov (KZ) equations which generalizes that of KZ equations for $sl_2$,
and give integral solutions of the system. We also study the relation between the system and monodromy preserving deformation theory,
and recover quantizations of Painlev\\'e equations P_I-P_V with affine Weyl group symmetry which are introduced by H.Nagoya.
Paul A. Pearce (Univ. of Melbourne) 15:00-16:00We obtain a system of confluent Knizhnik-Zamolodchikov (KZ) equations which generalizes that of KZ equations for $sl_2$,
and give integral solutions of the system. We also study the relation between the system and monodromy preserving deformation theory,
and recover quantizations of Painlev\\'e equations P_I-P_V with affine Weyl group symmetry which are introduced by H.Nagoya.
Exact Solution and Physical Combinatorics of Critical Dense
Polymers
[ Abstract ]
A Yang-Baxter integrable model of critical dense polymers on the
square lattice
is introduced corresponding to the first member ${\\cal LM}(1,2)$ of a
family of logarithmic
minimal models. The model has no local degrees of freedom, only non-
local degrees
of freedom in the form of extended polymers. The model is built
diagrammatically using the
planar Temperley-Lieb algebra and solved exactly on finite width
strips using transfer matrix
techniques. The bulk and boundary free energies and finite-size
corrections are
obtained from the Euler-Maclaurin formula. The spectra are classified
by selection rules and
the physical combinatorics of the eigenvalue patterns of zeros in the
complex
spectral-parameter plane. This yields explicit finitized conformal
characters.
In particular, in the scaling limit, we confirm the central charge
$c=-2$ and conformal weights
$\\Delta_{1,s}=\\frac{(2-s)^2-1}{8}$ for $s=1,2,3,\\ldots$ where $s-1$ is
the number
of defects.
A Yang-Baxter integrable model of critical dense polymers on the
square lattice
is introduced corresponding to the first member ${\\cal LM}(1,2)$ of a
family of logarithmic
minimal models. The model has no local degrees of freedom, only non-
local degrees
of freedom in the form of extended polymers. The model is built
diagrammatically using the
planar Temperley-Lieb algebra and solved exactly on finite width
strips using transfer matrix
techniques. The bulk and boundary free energies and finite-size
corrections are
obtained from the Euler-Maclaurin formula. The spectra are classified
by selection rules and
the physical combinatorics of the eigenvalue patterns of zeros in the
complex
spectral-parameter plane. This yields explicit finitized conformal
characters.
In particular, in the scaling limit, we confirm the central charge
$c=-2$ and conformal weights
$\\Delta_{1,s}=\\frac{(2-s)^2-1}{8}$ for $s=1,2,3,\\ldots$ where $s-1$ is
the number
of defects.
2008/06/12
Operator Algebra Seminars
16:30-18:00 Room #156 (Graduate School of Math. Sci. Bldg.)
見村万佐人 (東大数理)
On Lubotzky's property $(\\tau)$ and expander graphs
見村万佐人 (東大数理)
On Lubotzky's property $(\\tau)$ and expander graphs
Seminar on Probability and Statistics
16:20-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
福水 健次 (統計数理研究所)
再生核による指数分布族の構成とその統計的推定への応用
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/03.html
福水 健次 (統計数理研究所)
再生核による指数分布族の構成とその統計的推定への応用
[ Abstract ]
再生核ヒルベルト空間を用いて、ヒルベルト多様体として指数分布族を 構成する方法について述べる。無限次元指数分布族に関しては、Orlicz 空間を用いたPistone & Sempi (1995) の構成法が知られているが、 有限サンプルによる推定を考える場合、尤度関数が多様体上の連続汎関 数にならない点が問題となる。本講演の構成では、再生核ヒルベルト空 間を用いることにより尤度関数は連続となり、統計的推定の議論が容易 となる。再生核ヒルベルト空間が有限次元の場合は通常の有限次元指数 分布族の推定理論と一致し、無限次元の場合はその自然な拡張を与える。 本講演では、統計的推定への応用として、正則化最尤推定法と、特異点 を持つモデルの漸近理論に関して述べる。
[ Reference URL ]再生核ヒルベルト空間を用いて、ヒルベルト多様体として指数分布族を 構成する方法について述べる。無限次元指数分布族に関しては、Orlicz 空間を用いたPistone & Sempi (1995) の構成法が知られているが、 有限サンプルによる推定を考える場合、尤度関数が多様体上の連続汎関 数にならない点が問題となる。本講演の構成では、再生核ヒルベルト空 間を用いることにより尤度関数は連続となり、統計的推定の議論が容易 となる。再生核ヒルベルト空間が有限次元の場合は通常の有限次元指数 分布族の推定理論と一致し、無限次元の場合はその自然な拡張を与える。 本講演では、統計的推定への応用として、正則化最尤推定法と、特異点 を持つモデルの漸近理論に関して述べる。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/03.html
2008/06/09
Mathematical Biology Seminar
16:30-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
中岡 慎治 (東京大学大学院数理科学研究科)
幼生の行動変化が個体群動態に及ぼす影響の数理モデル
中岡 慎治 (東京大学大学院数理科学研究科)
幼生の行動変化が個体群動態に及ぼす影響の数理モデル
[ Abstract ]
動物の行動変化は個体群動態に影響を及ぼし得る。群生はもっとも良く知られた
動物行動の一つで、凝集することによって捕食者から狙われるリスクを回避する
ような効果(たとえば希釈効果)などがある。、たとえば幼生は成体に比べて一般に
捕食に会うリスクが高いため、個体の成長は行動を決める上で非常に重要な要因
である。
本研究では捕食者にステージ構造を考慮した捕食者被食者数理モデルを
構築し、動物の行動変化が個体群動態に及ぼす影響を調べた。もし種内で資源を
めぐる競争が激しい場合、上位の捕食者による捕食リスクが増えるにつれて
凝集して群生することは必ずしもメリットとはならず、Allee 効果による突然の
群生消滅が生じる可能性があることを数理モデルの解析・シミュレーションに
よって明らかにした。
動物の行動変化は個体群動態に影響を及ぼし得る。群生はもっとも良く知られた
動物行動の一つで、凝集することによって捕食者から狙われるリスクを回避する
ような効果(たとえば希釈効果)などがある。、たとえば幼生は成体に比べて一般に
捕食に会うリスクが高いため、個体の成長は行動を決める上で非常に重要な要因
である。
本研究では捕食者にステージ構造を考慮した捕食者被食者数理モデルを
構築し、動物の行動変化が個体群動態に及ぼす影響を調べた。もし種内で資源を
めぐる競争が激しい場合、上位の捕食者による捕食リスクが増えるにつれて
凝集して群生することは必ずしもメリットとはならず、Allee 効果による突然の
群生消滅が生じる可能性があることを数理モデルの解析・シミュレーションに
よって明らかにした。
Lectures
16:30-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)
W. Rundell (Texas A&M Univ.)
Some Unsolved Inverse Spectral Problems
W. Rundell (Texas A&M Univ.)
Some Unsolved Inverse Spectral Problems
[ Abstract ]
Perhaps the first well-studied inverse problem
was the determination of the potential $q(x)$ in
$-u'' + q(x) u = \\lambda_n u$ given the eigenvalues
$\\{\\lambda_n\\}$. Despite its venerable age and
the fact that a considerable literature is still being published,
there are several major outstanding problems;
some are quite simple to state.
This seminar will outline some of these.
We will try to show why the problems are hard,
but leave it to the audience to attempt solutions.
Perhaps the first well-studied inverse problem
was the determination of the potential $q(x)$ in
$-u'' + q(x) u = \\lambda_n u$ given the eigenvalues
$\\{\\lambda_n\\}$. Despite its venerable age and
the fact that a considerable literature is still being published,
there are several major outstanding problems;
some are quite simple to state.
This seminar will outline some of these.
We will try to show why the problems are hard,
but leave it to the audience to attempt solutions.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
相原 義弘 (沼津高専)
Deficiencies of holomorphic curves in algebraic manifolds
相原 義弘 (沼津高専)
Deficiencies of holomorphic curves in algebraic manifolds
2008/06/05
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
谷本溶 (東大数理)
Another analogue of the Borel-Weil theory on loop groups
谷本溶 (東大数理)
Another analogue of the Borel-Weil theory on loop groups
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
齊藤 宣一 (東京大学大学院数理科学研究科)
Keller-Segel系に対する離散化手法
齊藤 宣一 (東京大学大学院数理科学研究科)
Keller-Segel系に対する離散化手法
[ Abstract ]
細胞性粘菌の凝集現象を記述するモデルとして広く知られるKeller-Segel(KS)系に対して,講演者の提案した保存的上流差分法および有限要素法を紹介したい.これらスキームは,KS系の解の基本性質である正値性保存と質量保存を厳密に再現し,解が凝集による集中化を起こしても安定な計算が遂行可能である.さらに,離散$L^p$空間における離散的解析半群の理論を応用して,陽的な誤差評価が導出される.なお当日の講演では,誤差解析等の理論よりは,離散スキームの構成方法や条件の説明に焦点をおきたい.
細胞性粘菌の凝集現象を記述するモデルとして広く知られるKeller-Segel(KS)系に対して,講演者の提案した保存的上流差分法および有限要素法を紹介したい.これらスキームは,KS系の解の基本性質である正値性保存と質量保存を厳密に再現し,解が凝集による集中化を起こしても安定な計算が遂行可能である.さらに,離散$L^p$空間における離散的解析半群の理論を応用して,陽的な誤差評価が導出される.なお当日の講演では,誤差解析等の理論よりは,離散スキームの構成方法や条件の説明に焦点をおきたい.
2008/06/04
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
坂内 健一 (慶應義塾大学理工学部 )
$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure
(joint work with G. Kings)
坂内 健一 (慶應義塾大学理工学部 )
$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure
(joint work with G. Kings)
[ Abstract ]
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and
p-adic Eisenstein series.
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and
p-adic Eisenstein series.
PDE Real Analysis Seminar
16:00-18:15 Room #056 (Graduate School of Math. Sci. Bldg.)
William Rundell (Department of Mathematics, Texas A&M University) 16:00-17:00
Inverse Obstacle Recovery when the boundary condition is also unknown
The Inverse Scattering Problem for an Isotropic Medium
William Rundell (Department of Mathematics, Texas A&M University) 16:00-17:00
Inverse Obstacle Recovery when the boundary condition is also unknown
[ Abstract ]
We consider the inverse problem of recovering the shape, location
and surface properties of an object where the surrounding medium
is both conductive and homogeneous. It is assumed that the physical situation is modeled by either harmonic functions or solutions of the Helmholtz equation and that the boundary condition on the obstacle is one of impedance type. We measure either Cauchy data, on an accessible part of the exterior boundary or the far field pattern resulting from a plane wave. Given sets of Cauchy data pairs we wish to recover both the shape and location of the unknown obstacle together with its impedance.
It turns out this adds considerable complexity to the analysis. We give a local injectivity result and use two different algorithms
to investigate numerical reconstructions. The setting is in two space dimensions, but indications of possible extensions (and difficulties) to three dimensions are provided. We also look at the case of a nonlinear impedance function.
David Colton (Department of Mathematical Sciences, University of Delaware) 17:15-18:15We consider the inverse problem of recovering the shape, location
and surface properties of an object where the surrounding medium
is both conductive and homogeneous. It is assumed that the physical situation is modeled by either harmonic functions or solutions of the Helmholtz equation and that the boundary condition on the obstacle is one of impedance type. We measure either Cauchy data, on an accessible part of the exterior boundary or the far field pattern resulting from a plane wave. Given sets of Cauchy data pairs we wish to recover both the shape and location of the unknown obstacle together with its impedance.
It turns out this adds considerable complexity to the analysis. We give a local injectivity result and use two different algorithms
to investigate numerical reconstructions. The setting is in two space dimensions, but indications of possible extensions (and difficulties) to three dimensions are provided. We also look at the case of a nonlinear impedance function.
The Inverse Scattering Problem for an Isotropic Medium
[ Abstract ]
This talk is concerned with the inverse electromagnetic scattering problem for an isotropic inhomogeneous infinite cylinder. After formulating the direct scattering problem we proceed to the inverse scattering problem which is the main theme of this lecture. After discussing what is known about uniqueness for the inverse problem,we will proceed to the definition and properties of the far field operator. This leads to the study of a rather unusual spectral problem for partial differential equations called the interior transmission problem. We will state what is known about this problem including its role in determining lower bounds for the index of refraction from a knowledge of the far field pattern of the scattered wave, The talk is concluded by briefly considering the case of limited aperture data,in particular the use of the gap reciprocity method to determine the shape and location of buried objects. Numerical examples will be given as well as a number of open problems.
This talk is concerned with the inverse electromagnetic scattering problem for an isotropic inhomogeneous infinite cylinder. After formulating the direct scattering problem we proceed to the inverse scattering problem which is the main theme of this lecture. After discussing what is known about uniqueness for the inverse problem,we will proceed to the definition and properties of the far field operator. This leads to the study of a rather unusual spectral problem for partial differential equations called the interior transmission problem. We will state what is known about this problem including its role in determining lower bounds for the index of refraction from a knowledge of the far field pattern of the scattered wave, The talk is concluded by briefly considering the case of limited aperture data,in particular the use of the gap reciprocity method to determine the shape and location of buried objects. Numerical examples will be given as well as a number of open problems.
2008/06/03
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
示野 信一 (岡山理科大)
Matrix valued commuting differential operators with B2 symmetry
http://akagi.ms.u-tokyo.ac.jp/seminar.html
示野 信一 (岡山理科大)
Matrix valued commuting differential operators with B2 symmetry
[ Abstract ]
B2 型のWeyl群の作用による対称性を持つ2次正方行列値の2階の可換な微分作用素を構成した。
作用素は Iida (Publ. Res. Inst. Math. Sci. Kyoto Univ. 32 (1996)) により計算された Sp(2,R)/U(2) の等質ベクトル束上の不変微分作用素の動径成分を特別な場合として含み、係数は楕円関数を用いて表される。
講演では、群の場合、可換な作用素の構成、spin Calogero-Sutherland 模型との関係について述べる。
[ Reference URL ]B2 型のWeyl群の作用による対称性を持つ2次正方行列値の2階の可換な微分作用素を構成した。
作用素は Iida (Publ. Res. Inst. Math. Sci. Kyoto Univ. 32 (1996)) により計算された Sp(2,R)/U(2) の等質ベクトル束上の不変微分作用素の動径成分を特別な場合として含み、係数は楕円関数を用いて表される。
講演では、群の場合、可換な作用素の構成、spin Calogero-Sutherland 模型との関係について述べる。
http://akagi.ms.u-tokyo.ac.jp/seminar.html
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
山口 祥司 (東京大学大学院数理科学研究科)
On the geometry of certain slices of the character variety of a knot group
山口 祥司 (東京大学大学院数理科学研究科)
On the geometry of certain slices of the character variety of a knot group
[ Abstract ]
joint work with Fumikazu Nagasato (Meijo University)
This talk is concerned with certain subsets in the character variety of a knot group.
These subsets are called '"slices", which are defined as a level set of a regular function associated to a meridian of a knot.
They are related to character varieties for branched covers along the knot.
Some investigations indicate that an equivariant theory for a knot is connected to a theory for branched covers via slices, for example, the equivariant signature of a knot and the equivariant Casson invariant.
In this talk, we will construct a map from slices into the character varieties for branched covers and investigate the properties.
In particular, we focus on slices called "trace-free", which are used to define the Casson-Lin invariant, and the relation to the character variety for two--fold branched cover.
joint work with Fumikazu Nagasato (Meijo University)
This talk is concerned with certain subsets in the character variety of a knot group.
These subsets are called '"slices", which are defined as a level set of a regular function associated to a meridian of a knot.
They are related to character varieties for branched covers along the knot.
Some investigations indicate that an equivariant theory for a knot is connected to a theory for branched covers via slices, for example, the equivariant signature of a knot and the equivariant Casson invariant.
In this talk, we will construct a map from slices into the character varieties for branched covers and investigate the properties.
In particular, we focus on slices called "trace-free", which are used to define the Casson-Lin invariant, and the relation to the character variety for two--fold branched cover.
2008/06/02
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
本多 宣博 (東工大理工)
A new series of compact minitwistor spaces and Moishezon twistor spaces over them
本多 宣博 (東工大理工)
A new series of compact minitwistor spaces and Moishezon twistor spaces over them
Kavli IPMU Komaba Seminar
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Shinobu Hikami (The University of Tokyo)
Intersection theory from duality and replica
Shinobu Hikami (The University of Tokyo)
Intersection theory from duality and replica
[ Abstract ]
Kontsevich's work on Airy matrix integrals has led to explicit results for the
intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on N by N matrices and N-point functions of k by k matrices, plus the replica method, familiar in the theory of disordered systems, allows one to recover Kontsevich's results on the intersection numbers, and to generalize them to other models. This provides an alternative and simple way to compute intersection numbers with one marked point, and leads also to some new results. This is a joint work with E. Brezin (Comm.Math. Phys. in press, arXiv:0708.2210).
Kontsevich's work on Airy matrix integrals has led to explicit results for the
intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on N by N matrices and N-point functions of k by k matrices, plus the replica method, familiar in the theory of disordered systems, allows one to recover Kontsevich's results on the intersection numbers, and to generalize them to other models. This provides an alternative and simple way to compute intersection numbers with one marked point, and leads also to some new results. This is a joint work with E. Brezin (Comm.Math. Phys. in press, arXiv:0708.2210).
2008/05/29
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Rolf Dyre Svegstrup (東大数理)
2D models in AQFT from wedge algebras
Rolf Dyre Svegstrup (東大数理)
2D models in AQFT from wedge algebras
2008/05/27
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
笹木集夢 (早稲田大学)
Visible actions on multiplicity-free spaces
http://akagi.ms.u-tokyo.ac.jp/seminar.html
笹木集夢 (早稲田大学)
Visible actions on multiplicity-free spaces
[ Abstract ]
The holomorphic action of a Lie group G on a complex manifold D is called strongly visible if there exist a real submanifold S such that D':=G・S is open in D and an anti-holomorphic diffeomorphism σ which is an identity map on S and preserves each G-orbit in D'.
In this talk, we treat the case where D is a multiplicity-free space V of a connected complex reductive Lie group G(C), and show that the action of a compact real form of G(C) on V is strongly visible.
[ Reference URL ]The holomorphic action of a Lie group G on a complex manifold D is called strongly visible if there exist a real submanifold S such that D':=G・S is open in D and an anti-holomorphic diffeomorphism σ which is an identity map on S and preserves each G-orbit in D'.
In this talk, we treat the case where D is a multiplicity-free space V of a connected complex reductive Lie group G(C), and show that the action of a compact real form of G(C) on V is strongly visible.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/05/26
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
下村 俊 (慶大理工)
角領域における値分布論とその応用
下村 俊 (慶大理工)
角領域における値分布論とその応用
2008/05/24
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Raimandus Vidunas
(神戸大学理学部
) 13:30-14:30
Identities between Appell's and univariate hyeprgeometric functions
Whittaker functions with one-dimensional $K$-type on a semisimple Lie group of Hermitian type
Raimandus Vidunas
(神戸大学理学部
) 13:30-14:30
Identities between Appell's and univariate hyeprgeometric functions
[ Abstract ]
We look for univariate specializations of Appell'd bivariante hypergeometric functions that can be expressed in terms of univaraite ${}_{i+1} F_{i} ~(i=1,2,3)$ HGF's. The method is identifying cases when the partial differential equations for Appell's functions imply hypegeometric ordinary differential equations for their univariate specializations. In general, ordinary differential equations for univariate specializations of Apell's functions have order at moast 4.
示野 信一 (岡山理科大学理学部) 14:45-15:45We look for univariate specializations of Appell'd bivariante hypergeometric functions that can be expressed in terms of univaraite ${}_{i+1} F_{i} ~(i=1,2,3)$ HGF's. The method is identifying cases when the partial differential equations for Appell's functions imply hypegeometric ordinary differential equations for their univariate specializations. In general, ordinary differential equations for univariate specializations of Apell's functions have order at moast 4.
Whittaker functions with one-dimensional $K$-type on a semisimple Lie group of Hermitian type
[ Abstract ]
橋爪(Hiroshima J. Math. 12(1982))が与えたクラス1 Whittaker関数の表示式のHermitian対称空間上の1次元$K$-typeに付随したWhittaker関数への拡張を与える。またHeckeman-Opdamの超幾何関数の極限として、クラス1または1次元$K$-type を持つWhittaker関数が得られることを調べる。後者は石井-織田-平野(Math. Proc. Cambridge Philos. Soc. 41 (2006))の類似であり、一部は大島利雄氏との共同研究である。
橋爪(Hiroshima J. Math. 12(1982))が与えたクラス1 Whittaker関数の表示式のHermitian対称空間上の1次元$K$-typeに付随したWhittaker関数への拡張を与える。またHeckeman-Opdamの超幾何関数の極限として、クラス1または1次元$K$-type を持つWhittaker関数が得られることを調べる。後者は石井-織田-平野(Math. Proc. Cambridge Philos. Soc. 41 (2006))の類似であり、一部は大島利雄氏との共同研究である。
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