過去の記録

2009年06月02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
Alexander Voronov 氏 (University of Minnesota)
Graph homology: Koszul duality = Verdier duality
[ 講演概要 ]
Graph cohomology appears in computation of the cohomology of the moduli space of Riemann surfaces and the outer automorphism group of a free group. In the former case, it is graph cohomology of the commutative and Lie types, in the latter it is ribbon graph cohomology, that is to say, graph cohomology of the associative type. The presence of these three basic types of algebraic structures hints at a relation between Koszul duality for operads and Poincare-Lefschetz duality for manifolds. I will show how the more general Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This is a joint work with Andrey Lazarev.

解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

2009年05月28日(木)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

The Rohlin property for automorphisms of the Jiang-Su algebra

2009年05月27日(水)

代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室
Gombodorj Bayarmagnai 氏 (東京大学大学院数理科学研究科)
The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)

2009年05月26日(火)

解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Myriam Ounaies 氏 (Strasbourg大学数学科)
Intrepolation problems in H￥"ormander algebras
[ 講演概要 ]
We call Hörmander algebras the spaces $A_p(\\mathbb C)$ of entire functions $f$ such that, for all $z$ in $\\mathbb C$, \$|f(z)|\\le Ae^{Bp(z)},\$ where $A$ and $B$ are some positive constants (depending on $f$) and $p$ is a subharmonic weight. We consider the following interpolation problem : Given a discrete sequence $\\{a_j\\}$ of complex numbers and a sequence of complex values $\\{b_j\\}$, under what conditions does there exist a function $f\\in A_p(\\mathbb C)$ such that $f(a_j)=b_j$ for all $j$ ? In other words, what is the trace of $A_p(\\mathbb C)$ on $\\{a_j\\}$ ?
We say that $\\{a_j\\}$ is an interpolating sequence if the trace is defined by the space of all $\\{b_j\\}$ satisfying $|b_j|\\le A'e^{B'p(a_j)}$, for some constants $A',B'>0$.
We use Hörmander's $L^2$-estimates for the $\\bar\\partial$-equation to describe the trace when the weight $p$ is radial and doubling and to characterize the interpolating sequences for more general weights.

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

Configuration space integrals and the cohomology of the space of long embeddings

[ 講演概要 ]
It is known that some non-trivial cohomology classes, such as finite type invariants for (long) 1-knots (Bott-Taubes, Kohno, ...) and invariants for codimension two, odd dimensional long embeddings (Bott, Cattaneo-Rossi, Watanabe) are given as configuration space integrals associated with trivalent graphs.
In this talk, I will describe more cohomology classes by means of configuration space integral, in particular those arising from non-trivalent graphs and a new formulation of the Haefliger invariant for long 3-embeddings in 6-space, in relation to Budney's little balls operad action and Roseman-Takase's deform-spinning.
This is in part a joint work with Tadayuki Watanabe.

2009年05月25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) 126号室

Brody曲線の空間の幾何と平均次元

2009年05月22日(金)

談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)

[ 講演概要 ]

代数幾何学セミナー

15:00-16:30   数理科学研究科棟(駒場) 128号室
Prof. Steven Zucker 氏 (Johns Hopkins University)
The RBS compactification: a real stratified space in
algebraic geometry

2009年05月20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

Stability of the Burgers vortex
[ 講演概要 ]
The Burgers vortex is an exact vortex solution to the three dimensional stationary Navier-Stokes equations for viscous incompressible fluids in the presence of an axisymmetric background straining flow. In this talk we discuss the stability of the Burgers vortex with respect to two or three dimensional perturbation flows.

数理ファイナンスセミナー

17:30-19:00   数理科学研究科棟(駒場) 122号室

Financial inverse problem and reconstruction of infinitely divisible distributions with Gaussian component (小谷真一氏(関西学院大)との共同研究)

代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室

Generalized Whittaker functions for degenerate principal series of GL(4,R)

2009年05月19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
Mark Hamilton 氏 (東京大学大学院数理科学研究科, JSPS)
Geometric quantization of integrable systems
[ 講演概要 ]
The theory of geometric quantization is one way of producing a "quantum system" from a "classical system," and has been studied a great deal over the past several decades. It also has surprising ties to representation theory. However, despite this, there still does not exist a satisfactory theory of quantization for systems with singularities.

Geometric quantization requires the choice of a polarization; when using a real polarization to quantize a regular enough manifold, a result of Sniatycki says that the quantization can be found by counting certain objects, called Bohr-Sommerfeld fibres. However, there are many types of systems to which this result does not apply. One such type is the class of completely integrable systems, which are examples coming from mechanics that have many nice properties, but which are nontheless too singular for Sniatycki's theorem to apply.

In this talk we will explore one approach to the quantization of integrable systems, and show a Sniatycki-type relationship to Bohr-Sommerfeld fibres. However, some surprising features appear, including infinite-dimensional contributions and strong dependence on the polarization.

This is joint work with Eva Miranda.

2009年05月18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) 126号室

Conformal symmetries of self-dual hyperbolic monopole metrics (joint work with Jeff Viaclovsky)

2009年05月16日(土)

保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

3次元上半空間のスペクトル理論とエルミート保型形式
[ 講演概要 ]
3次元上半空間のスペクトル理論のエルミート保型形式への応用につい
て述べます。内容はジーゲル保型形式に対して2次元上半空間のスペクトル理論を応用す
るという今井氏による発見、及びその実際的応用のエルミート版への類似です。具体的に
は小嶋氏により発見されたエルミート版斉藤・黒川リフトに逆定理による解析的証明を与
えること、レベル付エルミート・アイゼンシュタイン級数のフーリエ係数の決定、それを

による記述、についてです。これらにおいて必要となる「3次元上半空間のマース形式の

ク・サルナック型の結果についても述べます。(p進エルミート・アイゼンシュタイン級

The Eisenstein series for $GL(3,Z)$ induced from cusp forms
[ 講演概要 ]

2009年04月30日(木)

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

ギーラー・マインハルト方程式に対するシャドウ系おける多重スポットの不安定性
[ 講演概要 ]

この系にはスポットパターンと呼ばれる定常解が存在することが知られており、この解は、その値が非常に大きい点(スポット)を持つこととその近傍の外側では急激に値が減少することにより特徴付けされる。

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Measure Equivalence Rigidity and Bi-exactness of Groups