講演会

過去の記録 ~03/28次回の予定今後の予定 03/29~


過去の記録

2013年01月30日(水)

17:15-18:15   数理科学研究科棟(駒場) 118号室
浅野裕樹 氏 (東大数理)
Group actions with Rohlin property (ENGLISH)

2013年01月16日(水)

10:00-11:00   数理科学研究科棟(駒場) 123号室
R\'emi Boutonnet 氏 (ENS Lyon)
$W^*$-superrigidity of mixing Gaussian actions of rigid groups (ENGLISH)

2013年01月16日(水)

11:30-12:30   数理科学研究科棟(駒場) 123号室
Tim de Laat 氏 (University of Copenhagen)
The Approximation Property for Lie groups (ENGLISH)

2013年01月16日(水)

14:40-15:40   数理科学研究科棟(駒場) 118号室
Arnaud Brothier 氏 (KU Leuven)
Unique Cartan decomposition for II$_1$ factors arising from cross section equivalence relations (ENGLISH)

2013年01月16日(水)

15:55-16:55   数理科学研究科棟(駒場) 118号室
Michael Hartglass 氏 (UC Berkeley)
Rigid $C^*$ tensor categories of bimodules over interpolated
free group factors (ENGLISH)

2013年01月16日(水)

17:10-18:10   数理科学研究科棟(駒場) 118号室
James Tener 氏 (UC Berkeley)
Manifestly unitary conformal field theory (ENGLISH)

2013年01月11日(金)

10:00-11:00   数理科学研究科棟(駒場) 123号室
Sven Raum 氏 (KU Leuven)
A duality between easy quantum groups and reflection groups (ENGLISH)

2013年01月11日(金)

11:15-12:15   数理科学研究科棟(駒場) 123号室
An Speelman 氏 (KU Leuven)
Some non-uniqueness results for Cartan subalgebras in II$_1$ factors (ENGLISH)

2013年01月11日(金)

14:00-15:00   数理科学研究科棟(駒場) 123号室
Ionut Chifan 氏 (University of Iowa)
Structural results for II$_1$ factors of negatively curved groups (ENGLISH)

2013年01月11日(金)

15:15-16:15   数理科学研究科棟(駒場) 123号室
Karen Strung 氏 (Universit\"at M\"unster)
UHF slicing and classification of nuclear $C^*$-algebras (ENGLISH)

2013年01月11日(金)

16:30-17:30   数理科学研究科棟(駒場) 123号室
Hannes Thiel 氏 (University of Copenhagen)
The generator problem for $C^*$-algebras (ENGLISH)

2012年11月28日(水)

10:45-11:45   数理科学研究科棟(駒場) 002号室
本講演会はGCOEの活動の一環として行われます.
Pascal Chossat 氏 (CNRS / University of Nice)
Pattern formation in the hyperbolic plane (ENGLISH)
[ 講演概要 ]
Initially motivated by a model for the visual perception of textures by the cortex, the problem of pattern formation in the hyperbolic plane, or equivalently the Poincaré disc D, shows some similar but mostly quite different features from the same problem posed on the Euclidean plane. The hyperbolic structure induces a large variety of possible periodic patterns and even the bifurcation of "hyperbolic" traveling waves. We call these patterns "H-planforms". I shall show how H-planforms are determined by the means of equivariant bifurcation theory and Helgason-Fourier analysis in D. However the question of their observability is still open. The talk will be illustrated with pictures of H-planforms that have been computed using non trivial algorithms based on harmonic analysis in D.

2012年11月22日(木)

13:30-14:15   数理科学研究科棟(駒場) 002号室
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Danielle Hilhorst 氏 (CNRS / Univ. Paris-Sud)
A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type (ENGLISH)
[ 講演概要 ]
A family of singular limits of reaction-diffusion systems of activator-inhibitor type in which stable stationary sharp-interface patterns may form is investigated. For concreteness, the analysis is performed for the FitzHugh-Nagumo model on a suitably rescaled bounded domain in $\\R^N$, with $N \\geq 2$. It is proved that when the system is sufficiently close to the limit the dynamics starting from the appropriate smooth initial data breaks down into five distinct stages on well-separated time scales, each of which can be approximated by a suitable reduced problem. The analysis allows to follow fully the progressive refinement of spatiotemporal patterns forming in the systems under consideration and provides a framework for understanding the pattern formation scenarios in a large class of physical, chemical, and biological systems modeled by the class of reaction-diffusion equations, which we consider. This is joint work with Marie Henry and Cyrill Muratov.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html

2012年11月22日(木)

14:25-15:10   数理科学研究科棟(駒場) 002号室
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Thanh Nam Ngyuen 氏 (University of Paris-Sud)
Formal asymptotic limit of a diffuse interface tumor-growth model (ENGLISH)
[ 講演概要 ]
We consider a diffuse interface tumor-growth model, which has the form of a phase-field system. We discuss the singular limit of this problem. More precisely, we formally prove that as the reaction coefficient tends to zero, the solution converges to the solution of a free boundary problem.

This is a joint work with Danielle Hilhorst, Johannes Kampmann and Kristoffer G. van der Zee.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html

2012年11月22日(木)

15:30-16:15   数理科学研究科棟(駒場) 002号室
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Peter Gordon 氏 (Akron University)
Gelfand type problem for two phase porous media (ENGLISH)
[ 講演概要 ]
In this talk I will introduce a generalization of well known Gelfand problem arising in a Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two phase materials, where, in contrast to classical Gelfand problem which utilizes single temperature approach, the state of the system is described by two different temperatures. As a result the problem is modeled by a system of two coupled nonlinear heat equations. The new ingredient in such a generalized Gelfand problem is a presence of inter-phase heat exchange which can be viewed as a strength of coupling for the system.

I will show that similar to classical Gelfand problem the thermal explosion (blow up of solution) for generalized Gelfand problem occurs exclusively due to the absence of stationary temperature distribution, that is non-existence of solution of corresponding elliptic problem. I also will show that the presence of inter-phase heat exchange delays a thermal explosion. Moreover, in the limit of infinite heat exchange between phases the problem of thermal explosion in two phase porous media reduces to classical Gelfand problem with re-normalized constants. The latter result partially justifies a single temperature approach to two phase systems often used in a physical literature.

This is a joint work with Vitaly Moroz (Swansea University).
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html

2012年11月22日(木)

16:25-17:10   数理科学研究科棟(駒場) 002号室
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Cyrill Muratov 氏 (New Jersey Institute of Technology)
On the shape of charged drops: an isoperimetric problem with a competing non-local term (ENGLISH)
[ 講演概要 ]
In this talk I will give an overview of my recent work with H. Knuepfer on the analysis of a class of geometric problems in the calculus of variations. I will discuss the basic questions of existence and non-existence of energy minimizers for the isoperimetric problem with a competing non-local term. A complete answer will be given for the case of slowly decaying kernels in two space dimensions, and qualitative properties of the minimizers will be established for general Riesz kernels.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html

2012年11月19日(月)

16:45-17:45   数理科学研究科棟(駒場) 126号室
Hendrik Weber 氏 (University of Warwick)
Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size (ENGLISH)
[ 講演概要 ]
We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one transition from -1 to 1. We are interested in the competition between the ``energy'' that should be minimized due to the small noise strength and the ``entropy'' that is induced by the large system size.
Our methods handle system sizes that are exponential with respect to the inverse noise strength, up to the ``critical'' exponential size predicted by the heuristics. We capture the competition between energy and entropy through upper and lower bounds on the probability of extra transitions between $\\pm 1$. These bounds are sharp on the exponential scale and imply in particular that the probability of having one and only one transition from -1 to +1 is exponentially close to one. In addition, we show that the position of the transition layer is uniformly distributed over the system on scales larger than the logarithm of the inverse noise strength.
Our arguments rely on local large deviation bounds, the strong Markov property, the symmetry of the potential, and measure-preserving reflections.
This is a joint work with Felix Otto and Maria Westdickenberg.

2012年10月30日(火)

17:00-18:00   数理科学研究科棟(駒場) 470号室
Frank Lutz 氏 (ベルリン工科大学)
Discrete Topologgy of Cellular Microstructures
and Complicatedness Measurements for Cell Complexes (JAPANESE)
[ 講演概要 ]
Our first aim is to use methods from discrete and geometric topology
to recover structural information from the composition of
monocrystalline materials that have a periodic foam structure
(such as gas hydrates and transition metal alloys) and also of
polycrystalline materials (such as metals and certain ceramics).

For more general complexes, even with a billion of faces, homological
information can be obtained with computational homology packages
such as CHomP or RedHom. These packages extensively use discrete Morse
theory as a preprocessing step. Although it is NP-hard to find optimal
discrete Morse functions, most data appears to be easy and it is
in fact hard to construct ``complicated'' examples. As we will see,
random discrete Morse theory will allow us to measure the
``complicatedness'' of complexes.

2012年10月18日(木)

16:00-17:00   数理科学研究科棟(駒場) 470号室
Anatoly Yagola 氏 (Lomonosov Moscow State University)
Multidimensional ill-posed problems (ENGLISH)
[ 講演概要 ]
It is very important now to develop methods of solving multidimensional ill-posed problems using regularization procedures and parallel computers. The main purpose of the talk is to show how 2D and 3D Fredholm integral equations of the 1st kind can be effectively solved.
We will consider ill-posed problems on compact sets of convex functions [1] and functions convex along lines parallel to coordinate axes [2].
Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the permanent magnetization due to the complications of magnetization distributions over the ship body, and errors and noises of measurement data degrade the accuracy and quality of the parameter identification. In this paper, we use a two step sequential solutions to solve the inversion problem. In the first step, a numerical model is built and used to determine the induced magnetization of the ship. In the second step, we solve a type of continuous magnetization inversion problem by solving 2D and 3D Fredholm integral
equations of the 1st kind. We use parallel computing which allows solve the inverse problem with high accuracy. Tikhonov regularization has been applied in solving the inversion problems. The proposed methods have been validated using simulation data with added noises [4, 6].
2D and 3D inverse problems also could be found in tomography [3] and electron microscopy [5]. We will demonstrate examples of applied problems and discuss methods of numerical solving.
This paper was supported by the Visby program and RFBR grants 11-01-00040–а and 12-01-91153-NSFC-a.

2012年10月17日(水)

15:00-16:00   数理科学研究科棟(駒場) 370号室
Vjacheslav Yurko 氏 (Saratov University)
Inverse problems for differential operators on spatial networks (ENGLISH)

2012年07月23日(月)

16:30-17:30   数理科学研究科棟(駒場) 126号室
Thomas W. Roby 氏 (University of Connecticut)
Combinatorial Ergodicity (ENGLISH)
[ 講演概要 ]
Many cyclic actions $\\tau$ on a finite set $S$ of
combinatorial objects, along with many natural
statistics $\\phi$ on $S$, exhibit``combinatorial ergodicity'':
the average of $\\phi$ over each $\\tau$-orbit in $S$ is
the same as the average of $\\phi$ over the whole set $S$.
One example is the case where $S$ is the set of
length $n$ binary strings $a_{1}\\dots a_{n}$
with exactly $k$ 1's,
$\\tau$ is the map that cyclically rotates them,
and $\\phi$ is the number of \\textit{inversions}
(i.e, pairs $(a_{i},a_{j})=(1,0)$ for $iJ$ less than $j$).

This phenomenon was first noticed by Panyushev
in 2007 in the context of antichains in root posets;
Armstrong, Stump, and Thomas proved his
conjecture in 2011.
We describe a theoretical framework for results of this kind,
and discuss old and new results for products of two chains.

This is joint work with Jim Propp.

2012年07月12日(木)

16:30-17:30   数理科学研究科棟(駒場) 370号室
M. Lavrentiev 氏 (Sobolev Institute of Mathematics)
Real time tsunami parameters evaluation (ENGLISH)
[ 講演概要 ]
We would like to propose several improvements to the existing software tools for tsunami modeling. Combination of optimaly located system of sensors with advantages of modern hardware architectures will make it possible to deliver calculated parameters of tsunami wave in 12-15 minutes after seismic event.

2012年06月18日(月)

09:45-12:30   数理科学研究科棟(駒場) 002号室
本講演は,サマースクール『ゆらぎと微分方程式』の第三日目のプログラムです.
James Nolen 氏 (Duke University) 09:45-10:45
Fluctuation of solutions to PDEs with random coefficients (Part 2) (ENGLISH)
[ 講演概要 ]
This is continuation of the previous day's lecture.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/
Leonid Ryzhik 氏 (Stanford University) 11:00-12:30
Weak coupling limits for particles and PDEs (Part 2) (ENGLISH)
[ 講演概要 ]
This is continuation of the previous day's lecture.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

2012年06月17日(日)

09:45-17:30   数理科学研究科棟(駒場) 002号室
本講演は,サマースクール『ゆらぎと微分方程式』の第二日目のプログラムです.
James Nolen 氏 (Duke University) 09:45-17:30
Fluctuation of solutions to PDEs with random coefficients (Part 1) (JAPANESE)
[ 講演概要 ]
For PDEs with random coefficients, it is interesting to understand whether the solutions exhibit some universal statistical behavior that is independent of the details of the coefficients. In particular, how do solutions fluctuate around the mean behavior? We will discuss this issue in the context of three examples:

(1) Traveling fronts in random media in one dimension.
(2) Elliptic homogenization problems.
(3) Random Hamilton-Jacobi equations.

The relation between PDE tools and probabilistic ideas will be
explained.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

Leonid Ryzhik 氏 (Stanford Univeristy) 13:00-14:45
Weak coupling limits for particles and PDEs (Part 1) (JAPANESE)
[ 講演概要 ]
Weak random fluctuations in medium parameters may lead to a non-trivial effect after large times and propagation over long distances. We will consider several examples when the large time limit can be treated:

(1) a particle in a weakly random velocity field.
(2) weak random fluctuations of Hamilton equations, and
(3) the linear Scrhoedinger equation with a weak random potential.

The role of long range correlation of the random fluctuations will also be discussed.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/
Gregoire Nadin 氏 (CNRS / Paris 6) 15:15-17:15
Asymptotic spreading for heterogeneous Fisher-KPP reaction-diffusion equations (JAPANESE)
[ 講演概要 ]
The solutions of the heterogeneous Fisher-KPP equation associated with compactly supported initial data are known to take off from the unstable steady state 0 and to converge to the steady state 1 for large times. The aim of this lecture is to estimate the speed at which the interface between 0 and 1 spreads.

Using the new notion of generalized principal eigenvalues for non-compact elliptic operators, we will derive such estimates which will be proved to be optimal for several classes of heterogeneity such as periodic, almost periodic or random stationary ergodic ones.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

2012年06月16日(土)

13:15-17:00   数理科学研究科棟(駒場) 002号室
本講演は,サマースクール『ゆらぎと微分方程式』の第一日目のプログラムです.
舟木 直久 氏 (東京大学大学院数理科学研究科) 13:15-14:45
微分方程式における確率解析の視点 (JAPANESE)
[ 講演概要 ]
本講演は,サマースクール『ゆらぎと微分方程式』のプログラムの一部として行われます.

この講演では,確率論の基礎的な概念や用語を簡単にまとめた上で,ランダムな項を持つ偏微分方程式の研究において重要な役割を果たす確率場の定常性とエルゴード性について解説する.その後ブラウン運動を導入し,いくつかの例を与える.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/
乙部 厳己 氏 (信州大学) 15:00-17:00
関数解析的視点による確率(偏)微分方程式 (JAPANESE)
[ 講演概要 ]
本講演は,サマースクール『ゆらぎと微分方程式』のプログラムの一部として行われます.

通常,確率論の基礎理論は,抽象的な確率空間の上で述べられるが,むしろ,それらを連続関数の空間上に測度を構成する問題,あるいは(非線形)汎関数の構成という解析学上の問題としてとらえた方が,直観的・具体的でわかりやすいことも多い.この講演では,確率論に関する何らの予備知識も仮定せずに,上の立場から確率微分方程式を特徴付ける.とくに以下のテーマに重点を置く.

(1) 線形の2階放物型方程式との関係
(2) これを常微分方程式に雑音を加えたモデルという立場でとらえると,例えば非線形項がヘルダー連続でしかない常微分方程式に一意性が回復するなど,粘性消去の考え方が自然に表れることへの注意
(3) (主に放物型の)方程式に雑音項を加える,いわゆる確率偏微分方程式の定式化について簡単に紹介し,雑音効果による一意性の回復の問題や解の爆発の消滅などについても触れる.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

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