過去の記録 ~05/23本日 05/24 | 今後の予定 05/25~



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
Jeff Viaclovsky 氏 (University of Wisconsin)
Critical metrics on connected sums of Einstein four-manifolds (ENGLISH)
[ 講演概要 ]
I will discuss a gluing procedure designed to obtain critical metrics of quadratic Riemannian functionals on connected sums of certain Einstein four-manifolds. Start with two Einstein four-manifolds of positive scalar curvature which are "rigid". Using the Green's function for the conformal Laplacian, convert one of these into an asymptotically flat (AF) scalar-flat metric. A "naive" approximate critical metric is obtained by identifying the boundary of a large ball in the AF metric with the boundary of a small ball in the other compact Einstein metric, using cutoff functions to glue together the AF metric with a suitably scaled compact metric in order to obtain a smooth metric on the connected sum. It turns out that this naive approximate metric is too rough, and must be refined in order to compute the leading term of the Kuranishi map. The main application is an existence result using two well-known Einstein manifolds as building blocks: the Fubini-Study metric on $¥mathbb{CP}^2$ and the product metric on $S^2 ¥times S^2$. Using these factors in various gluing configurations, a zero of the Kuranishi map is then found for a specific quadratic Riemannian functional on certain connected sums. The exact functional depends on the geometry of the factors, and also on the mass of the AF metric. Using certain quotients of $S^2 ¥times S^2$ as one of the gluing factors, several non-simply connected examples are also obtained. This is joint work with Matt Gursky.



16:30-18:00   数理科学研究科棟(駒場) 118号室
武石拓也 氏 (東大数理)
On nuclearity of $C^*$-algebras associated with Fell bundles over \\'etale groupoids (ENGLISH)


17:30-18:30   数理科学研究科棟(駒場) 056号室
Deepam Patel 氏 (University of Amsterdam)
Motivic structure on higher homotopy of non-nilpotent spaces (ENGLISH)
[ 講演概要 ]
In his fundamental paper on the projective line minus three points, Deligne constructed certain extensions of mixed Tate motives arising from the fundamental group of the projective line minus three points. Since then, motivic structures on homotopy groups have been studied by many authors. In this talk, we will construct a motivic structure on the (nilpotent completion of) n-th homotopy group of P^{n} minus n+2 hyperplanes in general position.

(本講演は「東京北京パリ数論幾何セミナー」として、インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)



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
藤 博之 氏 (東京大学大学院数理科学研究科)
色付きHOMFLYホモロジーと超A-多項式 (JAPANESE)
[ 講演概要 ]
本講演では,結び目に対する色付きHOMFLYホモロジーとその漸近的振る舞いに関する研究を紹介する.近年,色付きHOMFLY多項式の圏化がスペクトル系列に基づく公理系による定義と位相的弦理論に基づく物理的定義の双方が提唱され,それらの興味深い一致が様々な形で確かめられている.我々の研究では,完全対称表現に対する色付きHOMFLYホモロジーの漸近的振る舞いに関して,体積予想と類似の解析を行い,その結果,A-多項式の一般化となる“超 A-多項式”を通じて,色付きHOMFLYホモロジーのある量子構造が見出された.本講演では,こうした圏化の側面について,物理的解釈を交えながら紹介したい.尚,本講演はS. Gukov, M. Stosic, P. Sulkowski の3氏との共同研究に基づく.


16:30-18:00   数理科学研究科棟(駒場) 126号室
笹木集夢 氏 (東海大学)
A characterization of non-tube type Hermitian symmetric spaces by visible actions
[ 講演概要 ]
We consider a non-symmetric complex Stein manifold D
which is realized as a line bundle over the complexification of a non-compact irreducible Hermitian symmetric space G/K.

In this talk, we will explain that the compact group action on D is strongly visible in the sense of Toshiyuki Kobayashi if and only if G/K is of non-tube type.
In particular, we focus on our construction of slice which meets every orbit in D from the viewpoint of group theory, namely,
we find an A-part of a generalized Cartan decomposition for homogeneous space D.

We note that our choice of A-part is an abelian.



10:30-12:00   数理科学研究科棟(駒場) 126号室
二木 昭人 氏 (東大数理)
ケーラー・アインシュタイン計量と K 安定性 (JAPANESE)
[ 講演概要 ]
ケーラー・アインシュタイン計量の存在と K 安定性の同値性に関する Chen-Donaldson-Sun, Tian の証明の概略を解説する.



16:30-18:00   数理科学研究科棟(駒場) 126号室
大島芳樹 氏 (Kavli IPMU, the University of Tokyo)
Zuckerman導来関手加群の離散的分岐則 (JAPANESE)
[ 講演概要 ]
We consider the restriction of Zuckerman's derived functor modules with respect to symmetric pairs of real reductive groups. When they are discretely decomposable, explicit formulas for the branching laws are obtained by using a realization as D-module on the flag variety and the generalized BGG resolution. In this talk we would like to illustrate how to derive the formulas with a few examples.



13:30-15:30   数理科学研究科棟(駒場) 002号室
Simon Wood 氏 (Kavli IPMU)
On the extended algebra of type sl_2 at positive rational level (ENGLISH)
[ 講演概要 ]
I will be presenting my recent work with Akihiro Tsuchiya
I will explain how to construct a certain VOA called the "extended
algebra of type sl_2 at positive rational level"
as a subVOA of a lattice VOA, by means of screening operators. I will
then show that this VOA carries a kind of exterior sl_2 action and then
show how one can compute the structure Zhu's algebra and the Poisson
algebra as well as classify all simple modules by using the screening
operators and the sl_2 action. Important concepts such as screening
operators or Zhu's algebra and the Poisson algebra of a VOA will be
reviewed in the talk.



16:30-18:00   数理科学研究科棟(駒場) 002号室
Tea: 16:00 - 16:30 コモンルーム
川室 圭子 氏 (University of Iowa)
Open book foliation and application to contact topology (ENGLISH)
[ 講演概要 ]
Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).



16:00-17:30   数理科学研究科棟(駒場) 118号室
安藤浩志 氏 (IHES)
Ultraproducts of von Neumann algebras (JAPANESE)


15:00-17:30   数理科学研究科棟(駒場) 050号室
お茶&Coffee&お菓子: 16:00~16:30 (大講義室ロビー)。

野口潤次郎 氏 (東京大学大学院数理科学研究科) 15:00-16:00
値分布と多変数関数論 (JAPANESE)
[ 講演概要 ]
一方、ピカールの定理はネヴァンリンナにより定量的な値分布論へと発展した。高次元値分布を展開しようとすると多変数関数論の基礎が必要になってくる。その基礎的な部分はW. Stollがやった。私が研究に参加し始めたのは1972年頃で、GriffithsーKingのActa論文や小林双曲的多様体の理論が広まり始めた時期であった。その頃に考え始めた問題がどのように進展し、解決したもの、未解決問題、出てきた問題について考えてみたい。
大島 利雄 氏 (東京大学大学院数理科学研究科) 16:30-17:30
微分方程式をめぐって (JAPANESE)
[ 講演概要 ]



15:45-18:00   数理科学研究科棟(駒場) 118号室
Lucio Cirio 氏 (Univ. M\"unster) 15:45-16:45
Infinitesimal 2-Yang-Baxter operators from a categorification
of the Knizhnik-Zamolodchikov connection (ENGLISH)
Sutanu Roy 氏 (Univ. G\"ottingen) 17:00-18:00
Twisted tensor product of $C^*$-algebras (ENGLISH)


10:00-12:15   数理科学研究科棟(駒場) 056号室

Irene Vignon-Clementel 氏 (INRIA Paris Rocquencourt )
Complex flow at the boundaries of branched models: numerical aspects (ENGLISH)
[ 講演参考URL ]


14:30-15:30   数理科学研究科棟(駒場) 118号室
Stefano Rossi 氏 (Univ. Roma II)
The connected component of a compact quantum group (ENGLISH)


13:15-14:15   数理科学研究科棟(駒場) 118号室
Jean Roydor 氏 (Univ. Bordeaux)
Two Amir-Cambern type theorems for $C^*$-algebras (ENGLISH)


10:30-11:30   数理科学研究科棟(駒場) 128号室
Caterina Zeppieri 氏 (Universität Münster)
Geometric rigidity for incompatible fields and an application to strain-gradient plasticity (ENGLISH)
[ 講演概要 ]
Motivated by the study of nonlinear plane elasticity in presence of edge dislocations, in this talk we show that in dimension two the Friesecke, James, and Müller Rigidity Estimate holds true also for matrix-fields with nonzero curl, modulo an error depending on the total mass of the curl.
The above generalised rigidity is then used to derive a strain-gradient model for plasticity from semi-discrete nonlinear dislocation energies by Gamma-convergence.
The above results are obtained in collaboration with S. Müller (University of Bonn, Germany) and L. Scardia (University of Glasgow, UK).



09:45-12:00   数理科学研究科棟(駒場) 123号室
Tristan Bice 氏 (York Univ.) 09:45-10:45
Traces and Ultrapowers (ENGLISH)
David Penneys 氏 (Univ. Toronto) 11:00-12:00
Constructing subfactors with jellyfish (ENGLISH)


13:30-18:15   数理科学研究科棟(駒場) 123号室
Danny Hey 氏 (Univ. Toronto) 13:30-14:30
Classification and the Toms-Winter Conjecture (ENGLISH)
Stephen Curran 氏 (UCLA) 14:45-15:45
Free probability and planar algebras (ENGLISH)
Rasmus Bentmann 氏 (Univ. Copenhagen) 16:00-17:00
Kirchberg $X$-algebras with real rank zero and intermediate cancellation (ENGLISH)
Luis Santiago-Moreno 氏 (Univ. Oregon) 17:15-18:15
Classifying $C^*$-algebras up to W-stability (ENGLISH)


14:45-15:45   数理科学研究科棟(駒場) 123号室
このセミナーはMiniworkshop on Operator Algebras IVの一環として行われます
Stephen Curran 氏 (UCLA)
Free probability and planar algebras (ENGLISH)
[ 講演参考URL ]



10:30-12:00   数理科学研究科棟(駒場) 056号室
Benjamin Burton 氏 (The University of Queensland, Australia)
Knots, algorithms and linear programming: the quest to solve unknot recognition in polynomial time (ENGLISH)
[ 講演概要 ]
In this talk we explore new approaches to the old and difficult computational problem of unknot recognition. Although the best known algorithms for this problem run in exponential time, there is increasing evidence that a polynomial time solution might be possible. We outline several promising approaches, in which computational geometry, linear programming and greedy algorithms all play starring roles. We finish with a new algorithm that combines techniques from topology and combinatorial optimisation, which is the first to exhibit "real world" polynomial time behaviour: although it is still exponential time in theory, exhaustive experimentation shows that this algorithm can solve unknot recognition for "practical" inputs by running just a linear number of linear programs.

This is joint work with Melih Ozlen.



14:50-16:00   数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
前園 宣彦 氏 (九州大学)
符号検定の連続化と有意確率の近似について (JAPANESE)
[ 講演概要 ]
本講演では符号検定の連続化とその分布の近似を議論する.カーネル型分布関数の推 定量を利用して検定統計量を構成し,そのPitmanの漸近相対効率は符号検定と同じで あることを示す.また新しい検定統計量はdistribution-freeではないが,漸近分布 は母集団分布に依存しないことを議論し,近似分布の改良であるエッジワース展開を 求める.カーネルの取り方により,エッジワース展開が分布に依存しないように構成 することが可能であることも示す.本研究は九州大学大学院数理学府・魯夢欣さんと の共同研究である.
[ 講演参考URL ]



16:00-17:30   数理科学研究科棟(駒場) 117号室
Frederic Le Roux 氏 (Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie)
The rotation set around a fixed point for surface homeomorphisms. (ENGLISH)
[ 講演概要 ]
We propose two definitions of a local rotation set. As applications, one
gets some criteria for the existence of periodic orbits, and a clear
explanation of Gambaudo-Le Calvez-Pecou's version of the Naishul theorem:
for surface diffeomorphisms, the rotation number of the derivative at a
fixed point which is not a sink nor a source is a topological invariant.
Tha local rotation set also provide an unexpected topological
characterization for the parabolic fixed points of holomorphic maps.



14:50-16:00   数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
田中 冬彦 氏 (東京大学)
ベイズ予測に基いた波動関数の推定と純粋状態モデルの無情報事前分布 (JAPANESE)
[ 講演概要 ]
近年、量子状態トモグラフィにみられるように、量子物理実験において、統計的手法を用いた推定精度の向上が注目されている。本発表では、波動関数のパラメータ族が与えられた下で、少数の実験データから波動関数を推定する問題を考える。物理分野では、一般に、点推定に基いた推定しか議論されていないが、データが少ない場合にはパラメータの推定量の統計誤差が無視できない。本発表ではベイズ予測の考え方に基いた推定量を提案する。例として位置パラメータをもつガウス型の波動関数の推定を取り上げ、フィデリティ損失の下で、最尤推定(点推定)に基く推定より、ジェフリーズ事前分布を用いたベイズ予測に基く推定が一様に推定誤差を小さくすることを示す。後者は最良共変推定量にもなっている。 一方、このようなモデル(純粋状態モデル)における無情報事前分布の問題も、物理分野ではほとんど研究されてこなかった。本講演ではBernardoの考え方に注目し、パラメータ空間のコンパクト性を仮定した下で、純粋に量子論的な事前分布を提案する。導出の際に最小エントロピーが出てくるため、統計的モデリングなどへの応用も期待される。
[ 講演参考URL ]


17:00-18:00   数理科学研究科棟(駒場) 270号室
Oleg Emanouilov 氏 (Colorado State University)
Uniqueness for inverse boundary value problems by Dirichlet-to
-Neumann map on subboundaries (ENGLISH)
[ 講演概要 ]
We consider inverse boundary value problems for elliptic equations of second order and survey recent results on the uniqueness mainly by partial boundary data. In particular, in two dimensions, we show uniqueness results by means of Dirichlet data supported on an arbitrary subboundary $\\widetilde\\Gamma$ and Neumann data measured on $\\widetilde\\Gamma$. We describe the key idea for the proof: complex geometric optics solutions which are constructed by a Carleman estimate. Also we show the uniqueness by Dirichlet-to-Neumann map on subboundaries in three dimensions.



17:00-18:00   数理科学研究科棟(駒場) 270号室
M.I. Tribelsky 氏 (Landau Institute)
Resonant Light Scattering by Small Particles (ENGLISH)
[ 講演概要 ]
The problem of light scattering by a small spherical particle is studied within the framework of the exact solution of the Maxwell equations. It is shown that if imaginary part of the dielectric permittivity of the particle is small enough, the problem exhibits sharp giant resonances with very unusual properties. Specifically, the characteristic values of the electric and magnetic fields inside the particle and in its immediate vicinity are singular in the particle size. In non-dissipative case these quantities do not have definite limits when the radius of the particle tends to zero. The field of the Poynting vector in the immediate vicinity of the particle includes singular points, whose number, types and positions are very sensitive to the changes in the incident light frequency. As an example a bifurcation diagram, describing the behavior of the singular points in the vicinity of the dipole resonance for a particle with a certain fixed size is discussed.

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