過去の記録 ~12/04本日 12/05 | 今後の予定 12/06~


17:30-19:00   数理科学研究科棟(駒場) 002号室
Giovanni Felder 氏 (ETH Zurich)
Gaudin subalgebras and stable rational curves. (ENGLISH)
[ 講演概要 ]
We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.


Kavli IPMU Komaba Seminar

17:30-19:00   数理科学研究科棟(駒場) 002号室
Weiping Zhang 氏 (Chern Institute of Mathematics, Nankai University)
Geometric quantization on noncompact manifolds
[ 講演概要 ]
We will describe our analytic approach with Youlinag Tian to the Guillemin-Sternberg geometric quantization conjecture which can be summarized as "quantization commutes with reduction". We will aslo describe a recent extension to the case of noncompact symplectic manifolds. This is a joint work with Xiaonan Ma in which we solve a conjecture of Vergne mentioned in her ICM2006 plenary lecture.



16:30-18:00   数理科学研究科棟(駒場) 128号室
見村万佐人 氏 (東大数理)
Vanishing of quasi-homomorphisms and the stable commutator
lengths on special linear groups over euclidean rings



10:30-11:30   数理科学研究科棟(駒場) 056号室
Juergen Saal 氏 (University of Konstanz)
A hyperbolic fluid model based on Cattaneo's law
[ 講演概要 ]
In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).
One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.



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
Andrei Pajitnov 氏 (Univ. de Nantes)
Non-Abelian Novikov homology
[ 講演概要 ]
Classical construction of S.P. Novikov
associates to each circle-valued Morse map
a chain complex defined over a ring
of Laurent power series in one variable.

In this survey talk we shall explain several
results related to the construction and
properties of non-Abelian generalizations of the
Novikov complex.



10:30-12:00   数理科学研究科棟(駒場) 128号室
奥山裕介 氏 (京都工芸繊維大学)
Equidistribution and Nevanlinna theory

Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Junya Yagi 氏 (Rutgers University)
Chiral Algebras of (0,2) Models: Beyond Perturbation Theory
[ 講演概要 ]
The chiral algebras of two-dimensional sigma models with (0,2)
supersymmetry are infinite-dimensional generalizations of the chiral
rings of (2,2) models. Perturbatively, they enjoy rich mathematical
structures described by sheaves of chiral differential operators.
Nonperturbatively, however, they vanish completely for certain (0,2)
models with no left-moving fermions. In this talk, I will explain how
this vanishing phenomenon takes places. The vanishing of the chiral
algebra of a (0, 2) model implies that supersymmetry is spontaneously
broken in the model, which in turn suggests that no harmonic spinors
exist on the loop space of the target space. In particular, the
elliptic genus of the model vanishes, thereby providing a physics
proof of a special case of the Hoelhn-Stolz conjecture.



16:20-17:50   数理科学研究科棟(駒場) 117号室
池森俊文氏(高野 康 氏) 氏 (みずほ第一フィナンシャルテクノロジー(株))


13:40-14:50   数理科学研究科棟(駒場) 128号室
加藤 賢悟 氏 (広島大学大学院理学研究科数学専攻)
[ 講演概要 ]
In this talk, we consider the problem of estimating the innovation density in nonlinear autoregressive models. Specifically, we establish the convergence rate of the supremum distance between the residual-based kernel density estimator and the kernel density estimator using the unobservable actual innovation variables. The proof of the main theorem relies on empirical process theory instead of the conventional Taylor expansion approach. As applications, we obtain the exact rate of weak uniform consistency on the whole line, pointwise asymptotic normality of the residual-based kernel density estimator and the asymptotic distribution of a Bickel-Rosenblatt type global measure statistic related to it. We also examine the conditions of the main theorem for some specic time series model.
[ 参考URL ]



16:00-17:30   数理科学研究科棟(駒場) 002号室
小池 茂昭 氏 (埼玉大学・理学部数学科)
L^p 粘性解の弱ハルナック不等式の最近の進展
[ 講演概要 ]
Caffarelli による粘性解の regularity 研究 (1989 年) を基に, 1996 年に Caffarelli- Crandall-Kocan-Swiech によって L^p 粘性解の概念が導入された. L^p 粘性解とは, 通 常の粘性解理論では扱えなかった, 非有界非斉次項を持つ (非発散型) 偏微分方程 式にも適用可能な弱解である.
しかしながら, 係数に関しては有界係数しか研究されていなかった. その後, Swiech との共同研究により, 係数が非有界だが適当なべき乗可積分性を仮定して Aleksandrov-Bakelman-Pucci 型の最大値原理を導くことが可能になった.
本講演では, 非有界係数・非斉事項を持った, 完全非線形 2 階一様楕円型方程式 の L^p 粘性解の弱ハルナック不等式に関する最近のSwiech との共同研究の結果を紹 介する.



10:30-11:30   数理科学研究科棟(駒場) 056号室
Hermann Sohr 氏 (University Paderborn)
Recent results on weak and strong solutions of the Navier-Stokes equations
[ 講演概要 ]
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.

This condition is not only sufficient
- there are several well-known sufficient conditions in this context
- but also necessary, and yields therefore the largest possible class of such strong solutions.

As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.



16:30-18:00   数理科学研究科棟(駒場) 128号室
吉野 邦生 氏 (東京都市大学)
Analytic Properties of Eigen Values of Daubechies Localization Operator
[ 講演概要 ]


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
Adam Clay 氏 (University of British Columbia)
A topological approach to left orderable groups
[ 講演概要 ]
A group G is said to be left orderable if there is a strict
total ordering of its elements such that gin G. Left orderable groups have been useful in solving many problems in topology, and now we find that topology is returning the favour: the set of all left orderings of a group is denoted by LO(G), and it admits a natural topology, under which LO(G) becomes a compact topological
space. In general, the structure of the space LO(G) is not well understood, although there are surprising results in a few special cases.
For example, the space of left orderings of the braid group B_n for n>2
contains isolated points (yet it is uncountable), while the space of left
orderings of the fundamental group of the Klein bottle is finite.

Twice in recent years, the space of left orderings has been used very
successfully to solve difficult open problems from the field of left
orderable groups, even though the connection between the topology of LO(G) and the algebraic properties of G was still unclear. I will explain the
newest understanding of this connection, and highlight some potential
applications of further advances.



16:20-17:50   数理科学研究科棟(駒場) 117号室
池森俊文 氏 (みずほ第一フィナンシャルテクノロジー(株)取締役社長)


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)
Louis Nirenberg
(New York University)
On solving fully nonlinear elliptic Partial Differential Equations

[ 講演概要 ]
The talk will present some results in recent work by R.Harvey and B. Lawson: Dirichlet duality and the nonlinear Dirichlet problem, Comm. Pure Appl. Math. 62 (2009), 396-443. It concerns solving boundary value problems for elliptic equations of the form F(D'2u) = 0. They find generalized solutions which are merely continuous . The talk will be expository. No knowledge of Partial Differential Equations will be necessary.



15:00-16:00   数理科学研究科棟(駒場) 123号室
阿部知行 氏 (東京大学大学院数理科学研究科)



15:30-17:00   数理科学研究科棟(駒場) 128号室
Herbert Spohn 氏 (ミュンヘン工科大学・九州大学)
The stochastic Burgers equation and its discretization


16:30-18:45   数理科学研究科棟(駒場) 056号室
津嶋 貴弘 氏 (東京大学大学院数理科学研究科) 16:30-17:30
Elementary computation of ramified component of the Jacobi sum
[ 講演概要 ]
R. Coleman and W. McCallum calculated the Jacobi sum Hecke characters using their computation of the stable reduction of the Fermat curve in 1988. In my talk, we give an elementary proof of the main result of them without using rigid geometry or the stable model of the Fermat curve.
Christopher Deninger 氏 (Universität Münster) 17:45-18:45
P-divisible groups and the p-adic Corona problem



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
高田 敏恵 氏 (新潟大学)
On the $SO(N)$ and $Sp(N)$ free energy of a closed oriented 3-manifold
[ 講演概要 ]
We give an explicit formula of the $SO(N)$ and $Sp(N)$ free energy
of a lens space and show that the genus $g$ terms of it are analytic
in a neighborhood at zero, where we can choose the neighborhood
independently of $g$.
Moreover, it is proved that for any closed oriented 3-manifold $M$
and any $g$, the genus $g$ terms of $SO(N)$ and $Sp(N)$ free energy
of $M$ coincide up to sign.



10:30-12:00   数理科学研究科棟(駒場) 128号室
上野康平 氏 (京都大学大学院理学研究科)
Weighted Green functions of polynomial skew products on C^2


16:40-18:10   数理科学研究科棟(駒場) 126号室
Colin Ingalls 氏 (University of New Brunswick and RIMS)
Rationality of the Brauer-Severi Varieties of Skylanin algebras
[ 講演概要 ]
Iskovskih's conjecture states that a conic bundle over
a surface is rational if and only if the surface has a pencil of
rational curves which meet the discriminant in 3 or fewer points,
(with one exceptional case). We generalize Iskovskih's proof that
such conic bundles are rational, to the case of projective space
bundles of higher dimension. The proof involves maximal orders
and toric geometry. As a corollary we show that the Brauer-Severi
variety of a Sklyanin algebra is rational.



13:30-16:00   数理科学研究科棟(駒場) 117号室
岡崎武生 氏 (京都大学) 13:30-14:30
On weak endoscopic lift (117号室)
[ 講演概要 ]
rank 2のsymplectic 群の保型表現$\\pi$の spinor L-関数(4次)が殆どの素点で楕円保型形式のL-関数の積になっているものをweak ndoscopic liftと呼びます. $\\pi$がtemperedならば, 全てのweak endoscopic liftはrank 4のtheta関数(theta lift)でかける事がBrooks Roberts氏により知られています.
本公演では, このtheta liftの明示的な構成法やその周辺に関する話題(Siegel 三次多様体など)についてお話したいと思います.
井原健太郎 氏 (POSTEC) 15:00-16:00
Derivations and Automorphisms on the noncommutative algebra of power series.

[ 講演概要 ]
We discuss a relationship between a class of derivations and a class of automorphisms on the noncommutative algebra of formal power series in two variables. Each class relates bijectively by exponential and logarithm maps. In this talk we define a specific class of derivations, which generates a noncommutaive Lie algebra whose defining relations are related to a classical Witt algebra. The main claim is the explicit description of the
automorphisms which are corresponding to the derivations via exponential map.



10:40-12:10   数理科学研究科棟(駒場) 128号室
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (6)


16:30-18:00   数理科学研究科棟(駒場) 128号室
酒匂宏樹 氏 (東大数理)
Recent results for amalgamated free products of type II$_1$ factors



14:40-16:10   数理科学研究科棟(駒場) 128号室
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (5)

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