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Seminar information archive
Seminar information archive ～05/08｜Today's seminar 05/09 | Future seminars 05/10～
2007/12/11
Tuesday Seminar on Topology
16:30-18:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Xavier G\'omez-Mont (CIMAT, Mexico) 16:30-17:30
A Singular Version of The Poincar\\'e-Hopf Theorem
Chen Ruan cohomology of cotangent orbifolds and Chas-Sullivan string topology
Xavier G\'omez-Mont (CIMAT, Mexico) 16:30-17:30
A Singular Version of The Poincar\\'e-Hopf Theorem
[ Abstract ]
The Poincar\\'e-Hopf Theorem asserts that the Euler Characteristic of a compact manifold is the sum of the indices of any vector field on it with isolated singularities.
A hypersurface in real or complex number space may be considered as the limit of the smooth hypersurfaces obtained from nearby regular values. The singularity contains “hidden” topology, which is unfolded by a smooth regeneration. At the singularity one has an algebraic invariant, the Jacobi Algebra, which is obtained by considering analytic functions modulo the partial derivatives. It contains topological information of the singularity.
One may consider vector fields tangent to a hypersurface with isolated singularities, and define topologically an index, which coincides with the sum of the Poincar\\'e-Hopf indices of a regeneration of it tangent to a nearby smooth hypersurface.
I will explain how to compute the index of a vector field X tangent to an isolated hypersurface singularity V using Homological Algebra, as the Euler Characteristic of the homology of the complex obtained by contracting differential forms on V with the vector field X. The formula contains several terms, but the higher order terms may be translated from the invariants of the singular point to invariants in the Jacobi Algebra, making this translation a local version of the Poincar\\'e-Hopf Theorem.
I will also explain how some of these ideas can be extended to complete intersections.
Miguel A. Xicotencatl (CINVESTAV, Mexico) 17:40-18:40The Poincar\\'e-Hopf Theorem asserts that the Euler Characteristic of a compact manifold is the sum of the indices of any vector field on it with isolated singularities.
A hypersurface in real or complex number space may be considered as the limit of the smooth hypersurfaces obtained from nearby regular values. The singularity contains “hidden” topology, which is unfolded by a smooth regeneration. At the singularity one has an algebraic invariant, the Jacobi Algebra, which is obtained by considering analytic functions modulo the partial derivatives. It contains topological information of the singularity.
One may consider vector fields tangent to a hypersurface with isolated singularities, and define topologically an index, which coincides with the sum of the Poincar\\'e-Hopf indices of a regeneration of it tangent to a nearby smooth hypersurface.
I will explain how to compute the index of a vector field X tangent to an isolated hypersurface singularity V using Homological Algebra, as the Euler Characteristic of the homology of the complex obtained by contracting differential forms on V with the vector field X. The formula contains several terms, but the higher order terms may be translated from the invariants of the singular point to invariants in the Jacobi Algebra, making this translation a local version of the Poincar\\'e-Hopf Theorem.
I will also explain how some of these ideas can be extended to complete intersections.
Chen Ruan cohomology of cotangent orbifolds and Chas-Sullivan string topology
[ Abstract ]
(Joint with: A. Gonzalez, E. Lupercio, C. Segovia, and B. Uribe)
At the end of 90's, two theories of topology were invented roughly at the same time and attracted considerable interest in the mathematical community. One is the Chas-Sullivan's loop product on the homology of loop space and the second one is Chen-Ruan's stringy cohomology of orbifold. It was an observation of Chen that inertia orbifold (which carries Chen-Ruan cohomology) is the space of constant loops of an orbifold. Therefore, two theories should interact. In this work we show that for an interesting family of orbifolds, the virtual orbifold cohomology, turns out to be a subalgebra of the homology of the loop orbifold, and is isomorphic, as algebras, to the Chen-Ruan orbifold cohomology of its cotangent orbifold.
(Joint with: A. Gonzalez, E. Lupercio, C. Segovia, and B. Uribe)
At the end of 90's, two theories of topology were invented roughly at the same time and attracted considerable interest in the mathematical community. One is the Chas-Sullivan's loop product on the homology of loop space and the second one is Chen-Ruan's stringy cohomology of orbifold. It was an observation of Chen that inertia orbifold (which carries Chen-Ruan cohomology) is the space of constant loops of an orbifold. Therefore, two theories should interact. In this work we show that for an interesting family of orbifolds, the virtual orbifold cohomology, turns out to be a subalgebra of the homology of the loop orbifold, and is isomorphic, as algebras, to the Chen-Ruan orbifold cohomology of its cotangent orbifold.
Algebraic Geometry Seminar
10:00-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Dmitry KALEDIN (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 7
Dmitry KALEDIN (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 7
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
井上順子 (鳥取大学)
Characterization of some smooth vectors for irreducible representations of exponential solvable Lie groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
井上順子 (鳥取大学)
Characterization of some smooth vectors for irreducible representations of exponential solvable Lie groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/12/10
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
杉山健一 (千葉大学)
岩澤予想の幾何学的類似の量子化(予想される結果)
杉山健一 (千葉大学)
岩澤予想の幾何学的類似の量子化(予想される結果)
Kavli IPMU Komaba Seminar
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Dmitry Kaledin (Steklov Institute and The University of Tokyo)
Deligne conjecture and the Drinfeld double.
Dmitry Kaledin (Steklov Institute and The University of Tokyo)
Deligne conjecture and the Drinfeld double.
[ Abstract ]
Deligne conjecture describes the structure which exists on
the Hochschild cohomology $HH(A)$ of an associative algebra
$A$. Several proofs exists, but they all combinatorial to a certain
extent. I will present another proof which is more categorical in
nature (in particular, the input data are not the algebra $A$, but
rather, the tensor category of $A$-bimodules). Combinatorics is
still there, but now it looks more natural -- in particular, the
action of the Gerstenhaber operad, which is know to consist of
homology of pure braid groups, is induced by the action of the braid
groups themselves on the so-called "Drinfeld double" of the category
$A$-bimod.
If time permits, I will also discuss what additional structures
appear in the Calabi-Yau case, and what one needs to impose to
insure Hodge-to-de Rham degeneration.
Deligne conjecture describes the structure which exists on
the Hochschild cohomology $HH(A)$ of an associative algebra
$A$. Several proofs exists, but they all combinatorial to a certain
extent. I will present another proof which is more categorical in
nature (in particular, the input data are not the algebra $A$, but
rather, the tensor category of $A$-bimodules). Combinatorics is
still there, but now it looks more natural -- in particular, the
action of the Gerstenhaber operad, which is know to consist of
homology of pure braid groups, is induced by the action of the braid
groups themselves on the so-called "Drinfeld double" of the category
$A$-bimod.
If time permits, I will also discuss what additional structures
appear in the Calabi-Yau case, and what one needs to impose to
insure Hodge-to-de Rham degeneration.
2007/12/06
Lectures
10:40-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
Mikael Pichot (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
Applied Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
柳田 英二 (東北大学大学院理学研究科)
藤田型方程式における時間大域解の挙動について
柳田 英二 (東北大学大学院理学研究科)
藤田型方程式における時間大域解の挙動について
[ Abstract ]
この講演では,藤田型の半線形放物型偏微分方程式に関する M. Fila, J. King, P. Polacik, M. Winkler らとの共同研究による成果についてその概要を紹介する.全空間上の藤田型方程式については,これまで様々な挙動を示す時間大域解の存在が示されている.そこで大域解の時間的挙動と初期値の空間的挙動の関係を詳細に調べることにより,大域解をいくつかに分類し,その挙動がそれぞれ異なるメカニズムに支配されていることを明らかにする.時間が許せば,最近の進展や関連する話題についても触れる予定である.
この講演では,藤田型の半線形放物型偏微分方程式に関する M. Fila, J. King, P. Polacik, M. Winkler らとの共同研究による成果についてその概要を紹介する.全空間上の藤田型方程式については,これまで様々な挙動を示す時間大域解の存在が示されている.そこで大域解の時間的挙動と初期値の空間的挙動の関係を詳細に調べることにより,大域解をいくつかに分類し,その挙動がそれぞれ異なるメカニズムに支配されていることを明らかにする.時間が許せば,最近の進展や関連する話題についても触れる予定である.
2007/12/05
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
中村健太郎 (東京大学大学院数理科学研究科)
Classification of two dimensional trianguline representations of p-adic fields
中村健太郎 (東京大学大学院数理科学研究科)
Classification of two dimensional trianguline representations of p-adic fields
[ Abstract ]
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
Seminar on Probability and Statistics
16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
今野 良彦 (日本女子大学理学部)
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html
今野 良彦 (日本女子大学理学部)
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
[ Abstract ]
James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
[ Reference URL ]James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html
2007/12/04
Seminar on Mathematics for various disciplines
15:00-17:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Pavel Krejci (Weierstrass Institute for Applied Analysis and Stochastics) 15:00-16:00
Quasilinear hyperbolic equations with hysteresis
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Victor Isakov (Wichita State University) 16:15-17:15
Carleman estimates for second order operators with two large parameters
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Pavel Krejci (Weierstrass Institute for Applied Analysis and Stochastics) 15:00-16:00
Quasilinear hyperbolic equations with hysteresis
[ Abstract ]
We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.
[ Reference URL ]We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Victor Isakov (Wichita State University) 16:15-17:15
Carleman estimates for second order operators with two large parameters
[ Abstract ]
We obtain new Carleman type estimates for general second order linear partial differential operators. These estimates hold for the weight functions under pseudoconvexity conditions relating the operator and weight function. We discuss these conditions. We give applications to uniqueness and stability of the continuation and inverse problems for elasticity system with residual stress without smallness assumptions on residual stress. This is a joint work with Nanhee Kim.
[ Reference URL ]We obtain new Carleman type estimates for general second order linear partial differential operators. These estimates hold for the weight functions under pseudoconvexity conditions relating the operator and weight function. We discuss these conditions. We give applications to uniqueness and stability of the continuation and inverse problems for elasticity system with residual stress without smallness assumptions on residual stress. This is a joint work with Nanhee Kim.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
今野 宏 (東京大学大学院数理科学研究科)
Morse theory for abelian hyperkahler quotients
今野 宏 (東京大学大学院数理科学研究科)
Morse theory for abelian hyperkahler quotients
[ Abstract ]
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.
2007/12/03
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
甲斐千舟 (九州大学)
等質有界領域の対称性条件、性質の良い有界領域実現について
甲斐千舟 (九州大学)
等質有界領域の対称性条件、性質の良い有界領域実現について
2007/11/29
Lectures
10:40-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
Mikael Pichot (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
2007/11/27
Algebraic Geometry Seminar
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Alexander Kuznetsov (Steklov Inst)
Categorical resolutions of singularities
Alexander Kuznetsov (Steklov Inst)
Categorical resolutions of singularities
[ Abstract ]
I will give a definition of a categorical resolution of singularities and explain how such resolutions can be constructed.
I will give a definition of a categorical resolution of singularities and explain how such resolutions can be constructed.
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
小松 彦三郎 (東大数理(名誉教授))
Heaviside's theory of signal transmission on submarine cables
小松 彦三郎 (東大数理(名誉教授))
Heaviside's theory of signal transmission on submarine cables
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
石井 敦 (京都大学数理解析研究所)
A quandle cocycle invariant for handlebody-links
石井 敦 (京都大学数理解析研究所)
A quandle cocycle invariant for handlebody-links
[ Abstract ]
[joint work with Masahide Iwakiri (Osaka City University)]
A handlebody-link is a disjoint union of circles and a
finite trivalent graph embedded in a closed 3-manifold.
We consider it up to isotopies and IH-moves.
Then it represents an ambient isotopy class of
handlebodies embedded in the closed 3-manifold.
In this talk, I explain how a quandle cocycle invariant
is defined for handlebody-links.
[joint work with Masahide Iwakiri (Osaka City University)]
A handlebody-link is a disjoint union of circles and a
finite trivalent graph embedded in a closed 3-manifold.
We consider it up to isotopies and IH-moves.
Then it represents an ambient isotopy class of
handlebodies embedded in the closed 3-manifold.
In this talk, I explain how a quandle cocycle invariant
is defined for handlebody-links.
2007/11/26
Kavli IPMU Komaba Seminar
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Mich\"ael Pevzner (Universit\'e de Reims and the University of Tokyo)
Kontsevich quantization of Poisson manifolds and Duflo isomorphism.
Mich\"ael Pevzner (Universit\'e de Reims and the University of Tokyo)
Kontsevich quantization of Poisson manifolds and Duflo isomorphism.
[ Abstract ]
Abstract: Since the fundamental results by Chevalley, Harish-Chandra and Dixmier one knows that the set of invariant polynomials on the dual of a Lie algebra of a particular type (solvable, simple or nilpotent) is isomorphic, as an algebra, to the center of the enveloping algebra. This fact was generalized to an arbitrary finite-dimensional real Lie algebra by M. Duflo in late 1970's. His proof was based on the Kirillov's orbits method that parametrizes infinitesimal characters of unitary irreducible representations of the corresponding Lie group in terms of co-adjoint orbits.
The Kontsevich' Formality theorem implies not only the existence of the Duflo map but shows that it is canonical. We shall describe this construction and indicate how does this construction extend to the whole Poisson cohomology of an arbitrary finite-dimensional real Lie algebra.
Abstract: Since the fundamental results by Chevalley, Harish-Chandra and Dixmier one knows that the set of invariant polynomials on the dual of a Lie algebra of a particular type (solvable, simple or nilpotent) is isomorphic, as an algebra, to the center of the enveloping algebra. This fact was generalized to an arbitrary finite-dimensional real Lie algebra by M. Duflo in late 1970's. His proof was based on the Kirillov's orbits method that parametrizes infinitesimal characters of unitary irreducible representations of the corresponding Lie group in terms of co-adjoint orbits.
The Kontsevich' Formality theorem implies not only the existence of the Duflo map but shows that it is canonical. We shall describe this construction and indicate how does this construction extend to the whole Poisson cohomology of an arbitrary finite-dimensional real Lie algebra.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
金子宏 (東京理科大学)
Analysis related to probability theory based on p-adic hierarchical structure
金子宏 (東京理科大学)
Analysis related to probability theory based on p-adic hierarchical structure
2007/11/22
Applied Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
佐藤 洋平 (早稲田大学・基幹理工学部・数学科)
Critical frequencyをもつ非線形シュレディンガー方程式のマルチピーク解
佐藤 洋平 (早稲田大学・基幹理工学部・数学科)
Critical frequencyをもつ非線形シュレディンガー方程式のマルチピーク解
[ Abstract ]
非線形シュレディンガー方程式
$$ -\\epsilon2 \\Delta u +V(x)u= u^p, u>0 \\ \\hbox{in} \\R^N,
u\\in H1(\\R^N)$$
において、$\\epsilon \\to 0$ としたときに V(x) の k個の極小点にピークが集中していくマルチピーク解 $u_\\epsilon$ について考える。
ここで、p はsuperlinear, subcriticalの条件を満たし, ポテンシャル関数 V(x) は非負の有界な関数で $\\liminf_{|x|\\to \\infty}V(x)>0$ を満たすとする。
もし V(x) の各極小点に集中するピークがあるとしたら、そのピークの形状や大きさはその極小値が正であるか、0であるかによって大きく異なることが知られている。
この講演では V(x) の各極小値が正であるか 0 であるかにかかわらず、各 k個の極小点にピークが集中するマルチピーク解 $u_\\epsilon$ を構成する。
非線形シュレディンガー方程式
$$ -\\epsilon2 \\Delta u +V(x)u= u^p, u>0 \\ \\hbox{in} \\R^N,
u\\in H1(\\R^N)$$
において、$\\epsilon \\to 0$ としたときに V(x) の k個の極小点にピークが集中していくマルチピーク解 $u_\\epsilon$ について考える。
ここで、p はsuperlinear, subcriticalの条件を満たし, ポテンシャル関数 V(x) は非負の有界な関数で $\\liminf_{|x|\\to \\infty}V(x)>0$ を満たすとする。
もし V(x) の各極小点に集中するピークがあるとしたら、そのピークの形状や大きさはその極小値が正であるか、0であるかによって大きく異なることが知られている。
この講演では V(x) の各極小値が正であるか 0 であるかにかかわらず、各 k個の極小点にピークが集中するマルチピーク解 $u_\\epsilon$ を構成する。
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
張欽 (東大数理)
Spatial property of the canonical map associated to von Neumann algebras
張欽 (東大数理)
Spatial property of the canonical map associated to von Neumann algebras
Lectures
10:40-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
Mikael Pichot (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
2007/11/21
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Christopher Rasmussen (京都大学数理解析研究所)
Abelian varieties with constrained torsion
Christopher Rasmussen (京都大学数理解析研究所)
Abelian varieties with constrained torsion
[ Abstract ]
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\\Q$.
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\\Q$.
Seminar on Probability and Statistics
16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
宮尾 祐介 (東京大学理学部情報科学科)
自然言語処理における構造的・統計的モデル
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/10.html
宮尾 祐介 (東京大学理学部情報科学科)
自然言語処理における構造的・統計的モデル
[ Abstract ]
本発表では,自然言語処理において代表的な問題である機械翻訳と構文解析に ついて,言語の構造的性質と統計的性質をどのようなモデルで表現するかにつ いて概説する.これらの問題に対しては,古くは構造的規則性に着目し,翻訳 規則や文法などの規則体系を明らかにすることが主な研究目標であった.しか し,統計モデルの自然言語処理への応用が90年代に提案され,大きな成功をお さめたことから,現在では主流となっている.最近では,統計モデルを構造化 することによって言語の複雑な構造をとらえるアプローチがさかんに研究され ており,本発表では,これらの構造的・統計的モデルが言語の構造をどのよう にモデル化しているかを述べる.
[ Reference URL ]本発表では,自然言語処理において代表的な問題である機械翻訳と構文解析に ついて,言語の構造的性質と統計的性質をどのようなモデルで表現するかにつ いて概説する.これらの問題に対しては,古くは構造的規則性に着目し,翻訳 規則や文法などの規則体系を明らかにすることが主な研究目標であった.しか し,統計モデルの自然言語処理への応用が90年代に提案され,大きな成功をお さめたことから,現在では主流となっている.最近では,統計モデルを構造化 することによって言語の複雑な構造をとらえるアプローチがさかんに研究され ており,本発表では,これらの構造的・統計的モデルが言語の構造をどのよう にモデル化しているかを述べる.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/10.html
2007/11/20
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
長郷 文和 (東京工業大学大学院理工学研究科)
A certain slice of the character variety of a knot group
and the knot contact homology
長郷 文和 (東京工業大学大学院理工学研究科)
A certain slice of the character variety of a knot group
and the knot contact homology
[ Abstract ]
For a knot $K$ in 3-sphere, we can consider representations of
the knot group $G_K$ into $SL(2,\\mathbb{C})$.
Their characters construct an algebraic set.
This is so-called the $SL(2,\\mathbb{C})$-character variety of
$G_K$ and denoted by $X(G_K)$.
In this talk, we introduce a slice (a subset) $S_0(K)$ of $X(G_K)$.
In fact, this slice is closely related to the A-polynomial
and the abelian knot contact homology.
For example, the A-polynomial $A_K(m,l)$ of a knot $K$ is
a two-variable polynomial knot invariant defined by using
the character variety $X(G_K)$.
Then we can show that for any {\\it small knot} $K$, the number of
irreducible components of $S_0(K)$ gives an upper bound of
the maximal degree of the A-polynomial $A_K(m,l)$ in terms of
the variable $l$.
Moreover, for any 2-bridge knot $K$, we can show that
the coordinate ring of $S_0(K)$ is exactly the degree 0
abelian knot contact homology $HC_0^{ab}(K)$.
We will mainly explain these facts.
For a knot $K$ in 3-sphere, we can consider representations of
the knot group $G_K$ into $SL(2,\\mathbb{C})$.
Their characters construct an algebraic set.
This is so-called the $SL(2,\\mathbb{C})$-character variety of
$G_K$ and denoted by $X(G_K)$.
In this talk, we introduce a slice (a subset) $S_0(K)$ of $X(G_K)$.
In fact, this slice is closely related to the A-polynomial
and the abelian knot contact homology.
For example, the A-polynomial $A_K(m,l)$ of a knot $K$ is
a two-variable polynomial knot invariant defined by using
the character variety $X(G_K)$.
Then we can show that for any {\\it small knot} $K$, the number of
irreducible components of $S_0(K)$ gives an upper bound of
the maximal degree of the A-polynomial $A_K(m,l)$ in terms of
the variable $l$.
Moreover, for any 2-bridge knot $K$, we can show that
the coordinate ring of $S_0(K)$ is exactly the degree 0
abelian knot contact homology $HC_0^{ab}(K)$.
We will mainly explain these facts.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
西山 享 (京都大学)
Asymptotic cone for semisimple elements and the associated variety of degenerate principal series
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
西山 享 (京都大学)
Asymptotic cone for semisimple elements and the associated variety of degenerate principal series
[ Abstract ]
Let $ a $ be a hyperbolic element in a semisimple Lie algebra over the real number field. Let $ K $ be the complexification of a maximal compact subgroup of the corresponding real adjoint group. We study the asymptotic cone of the semisimple orbit through $ a $ under the adjoint action by $ K $. The resulting asymptotic cone is the associated variety of a degenerate principal series representation induced from the parabolic associated to $ a $.
[ Reference URL ]Let $ a $ be a hyperbolic element in a semisimple Lie algebra over the real number field. Let $ K $ be the complexification of a maximal compact subgroup of the corresponding real adjoint group. We study the asymptotic cone of the semisimple orbit through $ a $ under the adjoint action by $ K $. The resulting asymptotic cone is the associated variety of a degenerate principal series representation induced from the parabolic associated to $ a $.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
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