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過去の記録
過去の記録 ～01/24｜本日 01/25 | 今後の予定 01/26～
代数幾何学セミナー
13:00-14:30 数理科学研究科棟(駒場) 128号室
Yongnam Lee 氏 (Sogang U.)
Construction of surfaces of general type with pg=0 via
Q-Gorenstein smoothing
Yongnam Lee 氏 (Sogang U.)
Construction of surfaces of general type with pg=0 via
Q-Gorenstein smoothing
GCOEレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 118号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その4 Applications and open problems
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その4 Applications and open problems
[ 講演概要 ]
In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krötz-Stanton), random matrices (Huckleberry-Püttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
[ 参考URL ]In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krötz-Stanton), random matrices (Huckleberry-Püttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
2008年10月16日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Scott Morrison 氏 (UC Santa Barbara)
The $D_{2n}$ planar algebras
Scott Morrison 氏 (UC Santa Barbara)
The $D_{2n}$ planar algebras
講演会
15:00-16:00 数理科学研究科棟(駒場) 570号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その3 "Highest weight representations"
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その3 "Highest weight representations"
[ 講演概要 ]
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
[ 参考URL ]In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
Joseph F. Grotowski 氏 (University of Queensland)
Two-dimensional harmonic map heat flow versus four-dimensional Yang-Mills heat flow
Joseph F. Grotowski 氏 (University of Queensland)
Two-dimensional harmonic map heat flow versus four-dimensional Yang-Mills heat flow
[ 講演概要 ]
Harmonic map heat flow and Yang-Mills heat flow are the gradient flows associated to particular energy functionals. In the considered dimension, (i.e. dimension two for the harmonic map heat flow, dimension four for the Yang-Mills heat flow), the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. This leads to a number of interesting phenomena when considering both the functionals and the associated flows. In this talk we discuss qualitative similarities and differences between the flows.
Harmonic map heat flow and Yang-Mills heat flow are the gradient flows associated to particular energy functionals. In the considered dimension, (i.e. dimension two for the harmonic map heat flow, dimension four for the Yang-Mills heat flow), the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. This leads to a number of interesting phenomena when considering both the functionals and the associated flows. In this talk we discuss qualitative similarities and differences between the flows.
GCOEレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 123号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その3 Highest weight representations
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その3 Highest weight representations
[ 講演概要 ]
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
[ 参考URL ]In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
2008年10月15日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
八木厚志 氏 (大阪大学)
Asymptotic behavior of solutions for BCF model describing crystal surface growth
八木厚志 氏 (大阪大学)
Asymptotic behavior of solutions for BCF model describing crystal surface growth
[ 講演概要 ]
This talk is concerned with the initial-boundary value problem for a nonlinear parabolic equation which was presented Johnson et al. for describing the process of growth of a crystal surface on the
basis of the BCF theory. We will investigate asymptotic behavior of solutions by construct exponential attractors and a Lyapunov function and by examining a structure of the $\\omega$ limit set.
This talk is concerned with the initial-boundary value problem for a nonlinear parabolic equation which was presented Johnson et al. for describing the process of growth of a crystal surface on the
basis of the BCF theory. We will investigate asymptotic behavior of solutions by construct exponential attractors and a Lyapunov function and by examining a structure of the $\\omega$ limit set.
講演会
16:00-17:30 数理科学研究科棟(駒場) 002号室
George Sell 氏 (ミネソタ大学)
連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その2 The role of the 2D limit problem
George Sell 氏 (ミネソタ大学)
連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その2 The role of the 2D limit problem
[ 講演概要 ]
In both lectures we will examine a new topic of the thin
3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness
of strong solutions and the related theory of global
attractors.
In the second lecture, which will include a brief summary
of the first lecture, we will examine the role played by the
2D Limit Problem. These issues are a special challenge for
analysis because the 2D Limit Problem is NOT imbedded the
3D problem.
These lectures are based on joint work with Genevieve Raugel,Dragos Iftimie, and Luan Hoang.
In both lectures we will examine a new topic of the thin
3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness
of strong solutions and the related theory of global
attractors.
In the second lecture, which will include a brief summary
of the first lecture, we will examine the role played by the
2D Limit Problem. These issues are a special challenge for
analysis because the 2D Limit Problem is NOT imbedded the
3D problem.
These lectures are based on joint work with Genevieve Raugel,Dragos Iftimie, and Luan Hoang.
講演会
15:00-16:00 数理科学研究科棟(駒場) 570号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その2 "Geometric Background"
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その2 "Geometric Background"
[ 講演概要 ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ 参考URL ]In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
GCOEレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 122号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その2 Geometric background
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その2 Geometric background
[ 講演概要 ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ 参考URL ]In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert
2008年10月14日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Jeffrey Herschel Giansiracusa 氏 (Oxford University)
Pontrjagin-Thom maps and the Deligne-Mumford compactification
Tea: 16:00 - 16:30 コモンルーム
Jeffrey Herschel Giansiracusa 氏 (Oxford University)
Pontrjagin-Thom maps and the Deligne-Mumford compactification
[ 講演概要 ]
An embedding f: M -> N produces, via a construction of Pontrjagin-Thom, a map from N to the Thom space of the normal bundle over M. If f is an arbitrary map then one instead gets a map from N to the infinite loop space of the Thom spectrum of the normal bundle of f. We extend this Pontrjagin-Thom construction of wrong-way maps to differentiable stacks and use it to produce interesting maps from the Deligne-Mumford compactification of the moduli space of curves to certain infinite loop spaces. We show that these maps are surjective on mod p homology in a range of degrees. We thus produce large new families of torsion cohomology classes on the Deligne-Mumford compactification.
An embedding f: M -> N produces, via a construction of Pontrjagin-Thom, a map from N to the Thom space of the normal bundle over M. If f is an arbitrary map then one instead gets a map from N to the infinite loop space of the Thom spectrum of the normal bundle of f. We extend this Pontrjagin-Thom construction of wrong-way maps to differentiable stacks and use it to produce interesting maps from the Deligne-Mumford compactification of the moduli space of curves to certain infinite loop spaces. We show that these maps are surjective on mod p homology in a range of degrees. We thus produce large new families of torsion cohomology classes on the Deligne-Mumford compactification.
講演会
16:00-17:30 数理科学研究科棟(駒場) 002号室
George Sell 氏 (ミネソタ大学)
連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その1
Ultimate boundedness of solutions with large data and global attractors
George Sell 氏 (ミネソタ大学)
連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その1
Ultimate boundedness of solutions with large data and global attractors
[ 講演概要 ]
In both lectures we will examine a new topic of the thin 3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness of strong solutions and the related theory of global attractors.
In the second lecture, which will include a brief summary of the first lecture, we will examine the role played by the 2D Limit Problem. These issues are a special challenge for analysis because the 2D Limit Problem is NOT imbedded the 3D problem.
These lectures are based on joint work with Genevieve Raugel, Dragos Iftimie, and Luan Hoang.
In both lectures we will examine a new topic of the thin 3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness of strong solutions and the related theory of global attractors.
In the second lecture, which will include a brief summary of the first lecture, we will examine the role played by the 2D Limit Problem. These issues are a special challenge for analysis because the 2D Limit Problem is NOT imbedded the 3D problem.
These lectures are based on joint work with Genevieve Raugel, Dragos Iftimie, and Luan Hoang.
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
GCOE講演会と共催です.部屋と時間が通常と異なりますのでご注意ください
George Sell 氏 (ミネソタ大学)
Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors
GCOE講演会と共催です.部屋と時間が通常と異なりますのでご注意ください
George Sell 氏 (ミネソタ大学)
Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors
[ 講演概要 ]
グローバルCOE連続講演会と共催です.詳細はそちらをご覧ください.
グローバルCOE連続講演会と共催です.詳細はそちらをご覧ください.
講演会
15:00-16:00 数理科学研究科棟(駒場) 570号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その1 "Overview and Examples"
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
GCOEレクチャー"Holomorphic extensions of unitary representations" その1 "Overview and Examples"
[ 講演概要 ]
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
[ 参考URL ]In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Jan Moellers 氏 (Paderborn University)
The Dirichlet-to-Neumann map as a pseudodifferential
operator
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Jan Moellers 氏 (Paderborn University)
The Dirichlet-to-Neumann map as a pseudodifferential
operator
[ 講演概要 ]
Both Dirichlet and Neumann boundary conditions for the Laplace equation are of fundamental importance in Mathematics and Physics. Given a compact connected Riemannian manifold $M$ with boundary $\\partial M$ the Dirichlet-to-Neumann operator $\\Lambda_g$ maps Dirichlet boundary data $f$ to the corresponding Neumann boundary data $\\Lambda_g f =(\\partial_\\nu u)|_{\\partial M}$ where $u$ denotes the unique solution to the Dirichlet problem $\\laplace_g u=0$ in $M$, $u|_{\\partial M} = f$.
The main statement is that this operator is a first order elliptic pseudodifferential operator on the boundary $\\partial M$.
We will first give a brief overview of how to define the Dirichlet-to-Neumann operator as a map $\\Lambda_g:H^{1/2}(\\partial M)\\longrightarrow H^{-1/2}(\\partial M)$ between Sobolev spaces. In order to show that it is actually a pseudodifferential operator we introduce tangential pseudodifferential operators. This allows us to derive a
microlocal factorization of the Laplacian near boundary points. Together with a regularity statement for the heat equation this will finally give the main result.
[ 参考URL ]Both Dirichlet and Neumann boundary conditions for the Laplace equation are of fundamental importance in Mathematics and Physics. Given a compact connected Riemannian manifold $M$ with boundary $\\partial M$ the Dirichlet-to-Neumann operator $\\Lambda_g$ maps Dirichlet boundary data $f$ to the corresponding Neumann boundary data $\\Lambda_g f =(\\partial_\\nu u)|_{\\partial M}$ where $u$ denotes the unique solution to the Dirichlet problem $\\laplace_g u=0$ in $M$, $u|_{\\partial M} = f$.
The main statement is that this operator is a first order elliptic pseudodifferential operator on the boundary $\\partial M$.
We will first give a brief overview of how to define the Dirichlet-to-Neumann operator as a map $\\Lambda_g:H^{1/2}(\\partial M)\\longrightarrow H^{-1/2}(\\partial M)$ between Sobolev spaces. In order to show that it is actually a pseudodifferential operator we introduce tangential pseudodifferential operators. This allows us to derive a
microlocal factorization of the Laplacian near boundary points. Together with a regularity statement for the heat equation this will finally give the main result.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
GCOEレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 118号室
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations" その1 "Overview and Examples"
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations" その1 "Overview and Examples"
[ 講演概要 ]
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
[ 参考URL ]In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert
2008年10月10日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 128号室
岩根 和郎 氏 (岩根研究所)
岩根研究所における画像処理技術の紹介Ⅰ; 画像の数学的解析によるCV技術開発と3次元GIS
岩根 和郎 氏 (岩根研究所)
岩根研究所における画像処理技術の紹介Ⅰ; 画像の数学的解析によるCV技術開発と3次元GIS
2008年10月06日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
杉山 健一 氏 (千葉大理)
Lichtenbaum予想の幾何学的類似
杉山 健一 氏 (千葉大理)
Lichtenbaum予想の幾何学的類似
2008年10月03日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 128号室
岡本 龍明 氏 (NTT研究所)
暗号の基礎編
岡本 龍明 氏 (NTT研究所)
暗号の基礎編
2008年09月29日(月)
代数学コロキウム
16:30-17:30 数理科学研究科棟(駒場) 117号室
いつもと曜日が異なりますのでご注意下さい.
Christopher Deninger 氏 (Munster大学)
A determinant for p-adic group algebras
いつもと曜日が異なりますのでご注意下さい.
Christopher Deninger 氏 (Munster大学)
A determinant for p-adic group algebras
[ 講演概要 ]
For a discrete countable group G there is a classical determinant on the units of the L^1-convolution algebra of G. It is defined using functional analysis and can be used for example to calculate the entropy of certain G-actions. We will discuss a p-adic analogue of this theory. Instead of functional analysis the definition of the p-adic determinant uses algebraic K-theory. It has an application to the study of the p-adic distribution of periodic G-orbits in certain G-action.
For a discrete countable group G there is a classical determinant on the units of the L^1-convolution algebra of G. It is defined using functional analysis and can be used for example to calculate the entropy of certain G-actions. We will discuss a p-adic analogue of this theory. Instead of functional analysis the definition of the p-adic determinant uses algebraic K-theory. It has an application to the study of the p-adic distribution of periodic G-orbits in certain G-action.
2008年09月22日(月)
講演会
14:45-15:45 数理科学研究科棟(駒場) 122号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Invariance principle for the random conductance model
with unbounded conductances (a joint work with Martin Barlow)
Jean-Dominique Deuschel 氏 (TU Berlin)
Invariance principle for the random conductance model
with unbounded conductances (a joint work with Martin Barlow)
講演会
16:00-17:00 数理科学研究科棟(駒場) 122号室
Sergio Albeverio 氏 (Bonn 大学)
Asymptotic expansions of infinite dimensional integrals with applications (quantum mechanics, mathematical finance, biology)
Sergio Albeverio 氏 (Bonn 大学)
Asymptotic expansions of infinite dimensional integrals with applications (quantum mechanics, mathematical finance, biology)
2008年09月17日(水)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
ティータイム@コモンルーム 16:00~
Cyril Houdayer 氏 (UCLA)
Free Araki-Woods Factors and Connes's Bicentralizer Problem
ティータイム@コモンルーム 16:00~
Cyril Houdayer 氏 (UCLA)
Free Araki-Woods Factors and Connes's Bicentralizer Problem
2008年09月09日(火)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Yves de Cornulier 氏 (CNRS, Rennes)
The space of subgroups of an abelian group
Yves de Cornulier 氏 (CNRS, Rennes)
The space of subgroups of an abelian group
2008年09月08日(月)
Lie群論・表現論セミナー
11:00-12:00 数理科学研究科棟(駒場) 126号室
Federico Incitti 氏 (ローマ第 1 大学)
Dyck partitions, quasi-minuscule quotients and Kazhdan-Lusztig polynomials
http://akagi.ms.u-tokyo.ac.jp/seminar.html
Federico Incitti 氏 (ローマ第 1 大学)
Dyck partitions, quasi-minuscule quotients and Kazhdan-Lusztig polynomials
[ 講演概要 ]
Kazhdan-Lusztig polynomials were first defined by Kazhdan and Lusztig in [Invent. Math., 53 (1979), 165-184]. Since then, numerous applications have been found, especially to representation theory and to the geometry of Schubert varieties. In 1987 Deodhar introduced parabolic analogues of these polynomials. These are related to their ordinary counterparts in several ways, and also play a direct role in other areas, including geometry of partial flag manifolds and the theory of Macdonald polynomials.
In this talk I study the parabolic Kazhdan-Lusztig polynomials of the quasi-minuscule quotients of the symmetric group. More precisely, I will first show how these quotients are closely related to ``rooted partitions'' and then I will give explicit, closed combinatorial formulas for the polynomials. These are based on a special class of rooted partitions the ``rooted-Dyck'' partitions, and imply that they are always (either zero or) a power of $q$.
I will conclude with some enumerative results on Dyck and rooted-Dyck partitions, showing a connection with random walks on regular trees.
This is partly based on a joint work with Francesco Brenti and Mario Marietti.
[ 参考URL ]Kazhdan-Lusztig polynomials were first defined by Kazhdan and Lusztig in [Invent. Math., 53 (1979), 165-184]. Since then, numerous applications have been found, especially to representation theory and to the geometry of Schubert varieties. In 1987 Deodhar introduced parabolic analogues of these polynomials. These are related to their ordinary counterparts in several ways, and also play a direct role in other areas, including geometry of partial flag manifolds and the theory of Macdonald polynomials.
In this talk I study the parabolic Kazhdan-Lusztig polynomials of the quasi-minuscule quotients of the symmetric group. More precisely, I will first show how these quotients are closely related to ``rooted partitions'' and then I will give explicit, closed combinatorial formulas for the polynomials. These are based on a special class of rooted partitions the ``rooted-Dyck'' partitions, and imply that they are always (either zero or) a power of $q$.
I will conclude with some enumerative results on Dyck and rooted-Dyck partitions, showing a connection with random walks on regular trees.
This is partly based on a joint work with Francesco Brenti and Mario Marietti.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
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