過去の記録 ~09/22本日 09/23 | 今後の予定 09/24~

Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
J.Manuel Garcia-Islas 氏 (National Autonomous University of Mexico)
Quantum topological invariants and black hole entropy
[ 講演概要 ]
A type of topological invariants of three manifolds were
introduced by Turaev and Viro. We will define an invariant of graphs
embedded in a three dimensional manifold in a Turaev-Viro spirit.
The relation of these invariants to mathematical physics is
a really nice one. We will show how entropy of a three dimensional
black hole known as BTZ can be described using our formulation.



16:30-18:00   数理科学研究科棟(駒場) 056号室
酒匂宏樹 氏 (東大数理)
Solid groups and orbit equivalence rigidity


16:20-17:30   数理科学研究科棟(駒場) 126号室
日野 英逸 氏 (早稲田大学)
アイテムの選好度のモデルとパラメタ推定法 - Plackett-Luceモデルの一般化 -
[ 講演概要 ]
アイテムの比較やランキングデータが多数与えられたとき、一つ一つのアイテムが潜在的に持つ 価値を決定する問題は、心理学、経済学、政治学などの分野で古くから研究が行われているが、 近年機械学習の分野でも注目されている。 Plackett-Luceモデルはアイテムへのランキングの確率モデルであり、アイテム一つ一つに 多項分布のパラメタを割り当ててアイテム選択のプロセスを説明する。 本発表では、映画評の生成プロセスに注目し、Plackett-Luceの一般化として グループ化ランキングモデルを提案する。このモデルの尤度関数を直接評価することは 困難であるため、尤度関数の下界を与え、emアルゴリズムを用いて近似的に下界の 最大化を行うことでパラメタ推定を行う。 Toy exampleに対する実験結果と、映画評データに対する適用結果を紹介する。 時間が許せば、個人の嗜好に基づくパラメタの推定と、協調フィルタリングへの 応用についても言及する。
[ 参考URL ]



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
Kenneth Shackleton 氏 (東京工業大学, JSPS)
On computing distances in the pants complex
[ 講演概要 ]
The pants complex is an accurate combinatorial
model for the Weil-Petersson metric (WP) on Teichmueller space
(Brock). One hopes that many of the geometric properties
of WP are accurately replicated in the pants complex, and
this is the source of many open questions. We compare these
in general, and then focus on the 5-holed sphere and the
2-holed torus, the first non-trivial surfaces. We arrive at
an algorithm for computing distances in the (1-skeleton of the)
pants complex of either surface.
[ 参考URL ]



10:30-12:00   数理科学研究科棟(駒場) 128号室
橋本 健治 氏 (東大数理)



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)
村山斉 氏 (数物連携宇宙研究機構)
IPMU, Mathematics, Physics, and me
[ 講演概要 ]
Institute for the Physics and Mathematics of the Universe (IPMU) was founded to promote synergy between mathematics and physics, and to address deep mysteries about the universe. In this colloquium, I will discuss the mysteries IPMU will address, and why the interaction between mathematicians and physicists are crucial for this purpose. I will also talk about my personal journey about mathematics and physics.



16:30-18:00   数理科学研究科棟(駒場) 056号室
David Kerr 氏 (Texas A&M University)
Turbulence, representations, and trace-preserving actions


16:00-17:30   数理科学研究科棟(駒場) 002号室
谷口 雅治 氏 (東京工業大学大学院情報理工学研究科)
(The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations)

[ 講演概要 ]
We study the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity. For this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces. Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waves on the edges. This characterization also uniquely determines a pyramidal traveling front.


16:20-17:50   数理科学研究科棟(駒場) 052号室
伊藤 高一 氏 (IRI-DNL)
[ 講演概要 ]
[ 参考URL ]



16:30-18:45   数理科学研究科棟(駒場) 117号室
服部 新 氏 (北海道大学大学院理学研究院) 16:30-17:30
On a ramification bound of semi-stable torsion representations over a local field
朝倉 政典 氏 (北海道大学大学院理学研究院) 17:45-18:45
[ 講演概要 ]


17:30-19:00   数理科学研究科棟(駒場) 122号室
塩谷 匡介 氏 (日本銀行)
経済学と金融工学 ―Financial Economics入門―」(講義)
+M. Piazzesi and E. Swanson, "Futures Prices as Risk-Adjusted Forecasts
of Monetary Policy", Journal of Monetary Economics (2008)



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
佐野 友二 氏 (東京大学IPMU)
Multiplier ideal sheaves and Futaki invariant on toric Fano manifolds.
[ 講演概要 ]
I would like to discuss the subvarieties cut off by the multiplier
ideal sheaves (MIS) and Futaki invariant on toric Fano manifolds.
Futaki invariant is one of the necessary conditions for the existence
of Kahler-Einstein metrics on Fano manifolds,
on the other hand MIS is one of the sufficient conditions introduced by Nadel.
Especially I would like to focus on the MIS related to the Monge-Ampere equation
for Kahler-Einstein metrics on non-KE toric Fano manifolds.
The motivation of this work comes from the investigation of the
relationship with slope stability
of polarized manifolds introduced by Ross and Thomas.
This talk will be based on a part of the joint work with Akito Futaki



10:30-12:00   数理科学研究科棟(駒場) 128号室
山ノ井 克俊 氏 (熊本大自然)



13:30-16:00   数理科学研究科棟(駒場) 117号室
孫 娟娟 氏 (東大数理) 13:30-14:30
Confluent KZ equations for $sl_2$ and quantization of monodromy preserving deformation
[ 講演概要 ]
We obtain a system of confluent Knizhnik-Zamolodchikov (KZ) equations which generalizes that of KZ equations for $sl_2$,
and give integral solutions of the system. We also study the relation between the system and monodromy preserving deformation theory,
and recover quantizations of Painlev\\'e equations P_I-P_V with affine Weyl group symmetry which are introduced by H.Nagoya.
Paul A. Pearce 氏 (Univ. of Melbourne) 15:00-16:00
Exact Solution and Physical Combinatorics of Critical Dense
[ 講演概要 ]
A Yang-Baxter integrable model of critical dense polymers on the
square lattice
is introduced corresponding to the first member ${\\cal LM}(1,2)$ of a
family of logarithmic
minimal models. The model has no local degrees of freedom, only non-
local degrees
of freedom in the form of extended polymers. The model is built
diagrammatically using the
planar Temperley-Lieb algebra and solved exactly on finite width
strips using transfer matrix
techniques. The bulk and boundary free energies and finite-size
corrections are
obtained from the Euler-Maclaurin formula. The spectra are classified
by selection rules and
the physical combinatorics of the eigenvalue patterns of zeros in the
spectral-parameter plane. This yields explicit finitized conformal
In particular, in the scaling limit, we confirm the central charge
$c=-2$ and conformal weights
$\\Delta_{1,s}=\\frac{(2-s)^2-1}{8}$ for $s=1,2,3,\\ldots$ where $s-1$ is
the number
of defects.



16:30-18:00   数理科学研究科棟(駒場) 156号室
見村万佐人 氏 (東大数理)
On Lubotzky's property $(\\tau)$ and expander graphs


16:20-17:30   数理科学研究科棟(駒場) 126号室
福水 健次 氏 (統計数理研究所)
[ 講演概要 ]
再生核ヒルベルト空間を用いて、ヒルベルト多様体として指数分布族を 構成する方法について述べる。無限次元指数分布族に関しては、Orlicz 空間を用いたPistone & Sempi (1995) の構成法が知られているが、 有限サンプルによる推定を考える場合、尤度関数が多様体上の連続汎関 数にならない点が問題となる。本講演の構成では、再生核ヒルベルト空 間を用いることにより尤度関数は連続となり、統計的推定の議論が容易 となる。再生核ヒルベルト空間が有限次元の場合は通常の有限次元指数 分布族の推定理論と一致し、無限次元の場合はその自然な拡張を与える。 本講演では、統計的推定への応用として、正則化最尤推定法と、特異点 を持つモデルの漸近理論に関して述べる。
[ 参考URL ]



16:30-17:30   数理科学研究科棟(駒場) 126号室
中岡 慎治 氏 (東京大学大学院数理科学研究科)
[ 講演概要 ]
凝集して群生することは必ずしもメリットとはならず、Allee 効果による突然の


16:30-18:00   数理科学研究科棟(駒場) 470号室
W. Rundell 氏 (Texas A&M Univ.)
Some Unsolved Inverse Spectral Problems
[ 講演概要 ]
Perhaps the first well-studied inverse problem
was the determination of the potential $q(x)$ in
$-u'' + q(x) u = \\lambda_n u$ given the eigenvalues
$\\{\\lambda_n\\}$. Despite its venerable age and
the fact that a considerable literature is still being published,
there are several major outstanding problems;
some are quite simple to state.
This seminar will outline some of these.
We will try to show why the problems are hard,
but leave it to the audience to attempt solutions.


10:30-12:00   数理科学研究科棟(駒場) 128号室
相原 義弘 氏 (沼津高専)
Deficiencies of holomorphic curves in algebraic manifolds



16:30-18:00   数理科学研究科棟(駒場) 056号室
谷本溶 氏 (東大数理)
Another analogue of the Borel-Weil theory on loop groups


16:00-17:30   数理科学研究科棟(駒場) 002号室
齊藤 宣一 氏 (東京大学大学院数理科学研究科)
[ 講演概要 ]



16:30-17:30   数理科学研究科棟(駒場) 117号室
坂内 健一 氏 (慶應義塾大学理工学部 )
$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure
(joint work with G. Kings)

[ 講演概要 ]
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and
p-adic Eisenstein series.


16:00-18:15   数理科学研究科棟(駒場) 056号室
William Rundell 氏 (Department of Mathematics, Texas A&M University) 16:00-17:00
Inverse Obstacle Recovery when the boundary condition is also unknown
[ 講演概要 ]
We consider the inverse problem of recovering the shape, location
and surface properties of an object where the surrounding medium
is both conductive and homogeneous. It is assumed that the physical situation is modeled by either harmonic functions or solutions of the Helmholtz equation and that the boundary condition on the obstacle is one of impedance type. We measure either Cauchy data, on an accessible part of the exterior boundary or the far field pattern resulting from a plane wave. Given sets of Cauchy data pairs we wish to recover both the shape and location of the unknown obstacle together with its impedance.
It turns out this adds considerable complexity to the analysis. We give a local injectivity result and use two different algorithms
to investigate numerical reconstructions. The setting is in two space dimensions, but indications of possible extensions (and difficulties) to three dimensions are provided. We also look at the case of a nonlinear impedance function.
David Colton 氏 (Department of Mathematical Sciences, University of Delaware) 17:15-18:15
The Inverse Scattering Problem for an Isotropic Medium
[ 講演概要 ]
This talk is concerned with the inverse electromagnetic scattering problem for an isotropic inhomogeneous infinite cylinder. After formulating the direct scattering problem we proceed to the inverse scattering problem which is the main theme of this lecture. After discussing what is known about uniqueness for the inverse problem,we will proceed to the definition and properties of the far field operator. This leads to the study of a rather unusual spectral problem for partial differential equations called the interior transmission problem. We will state what is known about this problem including its role in determining lower bounds for the index of refraction from a knowledge of the far field pattern of the scattered wave, The talk is concluded by briefly considering the case of limited aperture data,in particular the use of the gap reciprocity method to determine the shape and location of buried objects. Numerical examples will be given as well as a number of open problems.



16:30-18:00   数理科学研究科棟(駒場) 126号室
示野 信一 氏 (岡山理科大)
Matrix valued commuting differential operators with B2 symmetry
[ 講演概要 ]
B2 型のWeyl群の作用による対称性を持つ2次正方行列値の2階の可換な微分作用素を構成した。
作用素は Iida (Publ. Res. Inst. Math. Sci. Kyoto Univ. 32 (1996)) により計算された Sp(2,R)/U(2) の等質ベクトル束上の不変微分作用素の動径成分を特別な場合として含み、係数は楕円関数を用いて表される。
講演では、群の場合、可換な作用素の構成、spin Calogero-Sutherland 模型との関係について述べる。
[ 参考URL ]


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
山口 祥司 氏 (東京大学大学院数理科学研究科)
On the geometry of certain slices of the character variety of a knot group
[ 講演概要 ]
joint work with Fumikazu Nagasato (Meijo University)
This talk is concerned with certain subsets in the character variety of a knot group.
These subsets are called '"slices", which are defined as a level set of a regular function associated to a meridian of a knot.
They are related to character varieties for branched covers along the knot.
Some investigations indicate that an equivariant theory for a knot is connected to a theory for branched covers via slices, for example, the equivariant signature of a knot and the equivariant Casson invariant.
In this talk, we will construct a map from slices into the character varieties for branched covers and investigate the properties.
In particular, we focus on slices called "trace-free", which are used to define the Casson-Lin invariant, and the relation to the character variety for two--fold branched cover.

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