過去の記録

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

Two positive solutions for an inhomogeneous scalar field equation
[ 講演概要 ]
We consider the following nonlinear elliptic equation:
$$-\\Delta u+u=g(u)+f(x), x \\in R^N,$$
where $N\\ge 3$. When $f(x)\\equiv 0$, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though $f(x) \\not\\equiv 0$, we can expect the existence of a nontrivial solution if $f(x)$ is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when $\\| f\\|_{L^2}$ is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.

統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 126号室

Bayesian learning of biological pathways on genomic data assimilation
[ 講演概要 ]
States of living cells are controlled by networks of biochemical reactions, referred to as biological pathways, which comprise of, for instance, phosphorylation and binding of protein molecules, gene expressions mediated by transcription factor activities. In systems biology, mathematical modeling and simulation, based on biochemical rate equations, have proved to be a popular approach for unraveling complex machinery of cellular mechanisms. To proceed to simulations, however, it is vital to find the effective values of kinetic rate constants that are difficult to measure directly from in vivo and in vitro experiments. Furthermore, once a set of hypothetical models is given, a proper statistical criterion is needed to test the reliability of the constructed models in terms of predictability and biological robustness. The aim of this research is to present a new statistical technology, called Genomic Data Assimilation, for handling data-driven model construction of biological pathways. The method starts with a knowledge-based pathway modeling with hybrid functional Petri net. It then proceeds to the Bayesian learning of model parameters for which experimental data are available. This process uses time course measurements of biochemical reactants, e.g. gene expression profiles. Another important issue that we consider is statistical evaluation and comparison of the constructed hypothetical models. For this purpose, we developed a new Bayesian information-theoretic measure that assesses the predictability and the biological robustness of models. In this talk, I will detail mathematical aspects of the proposed method, and then, show some statistical issues to be addressed.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/06.html

2008年07月08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
Otto van Koert 氏 (北海道大学大学院理学研究科, JSPS)
Contact homology of left-handed stabilizations and connected sums
[ 講演概要 ]
In this talk, we will give a brief introduction to contact homology, an invariant of contact manifolds defined by counting holomorphic curves in the symplectization of a contact manifold. We shall show that certain left-handed stabilizations of contact open books have vanishing contact homology.
This is done by finding restrictions on the behavior of holomorphic curves in connected sums. An additional application of this behavior of holomorphic curves is a long exact sequence for linearized contact homology.

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

construction of extended affine Lie algebras from multiloop Lie algebras
[ 講演概要 ]
affine Lie algebra の Kac-Moody Lie algebra とは異なる一般化として、extended affine Lie algebra と呼ばれる Lie algebra の class を考える。
ほとんどの extended affine Lie algebra は、有限次元 simple Lie algebra と、有限個の互いに可換な有限位数自己同型を用いて構成できることがすでに知られている。
この講演では、上の構成によって得られる extended affine Lie algebra がどのような場合に(適当な意味で)同型となるか、という問題に関する結果をお話ししたい。
[ 参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

2008年07月07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

Henon 写像の複素力学系

2008年07月03日(木)

統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

http://www.ism.ac.jp/~nisiyama/pism080626.pdf
にまとめてある。
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/05.html

2008年07月02日(水)

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

(安田正大氏との共同研究)

2008年07月01日(火)

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

[ 講演概要 ]
MacWilliams変換と呼ばれる変換で不変な複素2変数斉次多項式に対して、zeta多項式と呼ばれる複素1変数多項式を定義する。
TypeIV extremal と呼ばれる不変式の無限列に対し、deg = 0 (mod 6) の場合には、対応する全ての zeta多項式の零点が同一円周上に乗るという事が証明されているが、deg = 2,4 (mod 6) の場合は未解決であった。
この講演では、不変式に対する微分作用素を用いて、deg = 4 (mod6) の場合にも全てのzeta多項式の零点が同一円周上に乗るということを示したい。

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

On the Johnson homomorphisms of the automorphism group of
a free metabelian group
[ 講演概要 ]
The main object of our research is the automorphism group of a
free group. To be brief, the Johnson homomorphisms are studied in order to
describe one by one approximations of the automorphism group of a free group
. They play important roles on the study of the homology groups of the autom
orphism group of a free group. In general, to determine their images are ver
y difficult problem. In this talk, we define the Johnson homomorphisms of th
e automorphism group of a free metabelian group, and determine their images.
Using these results, we can give a lower bound on the image of the Johnson
homomorphisms of the automorphism group of a free group.

2008年06月30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

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.

2008年06月26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

Solid groups and orbit equivalence rigidity

統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 126号室

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 ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/04.html

2008年06月24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
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 ]
http://www.is.titech.ac.jp/~kjshack5/FYEO.pdf

2008年06月23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

5次対称群が作用するK3曲面のある1次元族の周期写像と逆写像

2008年06月20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)

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.

2008年06月19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
David Kerr 氏 (Texas A&M University)
Turbulence, representations, and trace-preserving actions

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

Allen-Cahn方程式における角錐型進行波の一意性と安定性
(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.

講演会

16:20-17:50   数理科学研究科棟(駒場) 052号室

インターネットにおける数理科学的手法と実際「DNSとWebアクセス」
[ 講演概要 ]
テーマごとに個別の企業活動を紹介し、第一線で活躍する企業研究者を招聘し、現場レポートを聴き、議論を行うことで、インターネット数理科学の原理とその応用の実際を紹介する。
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/lecture/2008/inet/index.html

2008年06月18日(水)

代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 117号室

On a ramification bound of semi-stable torsion representations over a local field

Beilinson-Tate予想と楕円曲面のK_1の不分解元
[ 講演概要 ]
(佐藤周友氏との共同研究)

これは、p進レギュレーターの非消滅と関係しており、

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

+M. Piazzesi and E. Swanson, "Futures Prices as Risk-Adjusted Forecasts
of Monetary Policy", Journal of Monetary Economics (2008)

2008年06月17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

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
(arXiv:0711.0614).

2008年06月16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

2008年06月14日(土)

東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室

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
Polymers
[ 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
complex
spectral-parameter plane. This yields explicit finitized conformal
characters.
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.

2008年06月12日(木)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 156号室

On Lubotzky's property $(\\tau)$ and expander graphs