過去の記録

過去の記録 ~08/18本日 08/19 | 今後の予定 08/20~

2012年12月05日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 002号室
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
Jie Jiang 氏 (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences)
Convergence to Equilibrium of Bounded Solutions with Application of Lojasiewicz-Simon's inequality (ENGLISH)
[ 講演概要 ]
In this talk, we present the application of Lojasiewicz-Simon's inequality to the study on convergence of bounded global solutions to some evolution equations. We take a semi-linear parabolic initial-boundary problem as an example. With the help of Lojasiewicz-Simon's inequality we prove that the bounded global solution will converge to an equilibrium as time goes to infinity provided the nonlinear term is analytic in the unknown function. We also present the application of Lojasiewicz-Simon's inequality to the asymptotic behavior studies on phase-field models with Cattaneo law and chemotaxis models with volume-filling effect.

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
谷本溶 氏 (Univ. Goettingen)
Construction of two dimensional QFT through Longo-Witten endomorphisms (JAPANESE)

幾何コロキウム

10:30-12:00   数理科学研究科棟(駒場) 128号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
石田 裕昭 氏 (大阪市立大学数学研究所)
Maximal torus actions on complex manifolds (JAPANESE)
[ 講演概要 ]
We say that an effective action of a compact torus $T$ on a connected manifold $M$ is maximal if there is an orbit of dimension $2\\dim T-\\dim M$. In this talk, we give a one-to-one correspondence between the family of connected closed complex manifolds with maximal torus actions and the family of certain combinatorial objects, which is a generalization of the correspondence between complete nonsingular toric varieties and nonsingular complete fans. As an application, we construct a lot of concrete examples of non-K\\"{a}hler manifolds with maximal torus actions.

古典解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 270号室
Andrei Kapaev 氏 (SISSA, Trieste, Italy)
On the Riemann-Hilbert approach to the Malgrange divisor: $P_I^2$ case (ENGLISH)
[ 講演概要 ]
Equation $P_I^2$ is the second member in the hierarchy of ODEs associated with the classical Painlev\\’e first equation $P_I$ and can be solved via the Riemann-Hilbert (RH) problem approach. It is known also that solutions of equation $P_I^2$ as the functions of $x$ depending on the parameter $t$ can be used to construct a 4-parameter family of isomonodromic solutions to the KdV equation. Given the monodromy data, the set of points $(x,t)$, where the above mentioned RH problem is not solvable, is called the Malgrange divisor. The function $x=a(t)$, which parametrizes locally the Malgrange divisor, satisfies a nonlinear ODE which admits a Lax pair representation and can be also studied using an RH problem. We discuss the relations between these two kinds of the RH problems and the properties of their $t$-large genus 1 asymptotic solutions.

2012年12月04日(火)

数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
http://www.ms.u-tokyo.ac.jp/gcoe/index.html

金山寛 氏 (九州大学大学院工学研究院)
Tsunami simulation of Hakata Bay using the viscous shallow-water equations (JAPANESE)
[ 講演概要 ]
The tsunami caused by the great East Japan earthquake gave serious damage in the coastal areas of the Tohoku district. Numerical simulation is used for damage prediction as disaster measures to these tsunami hazards. Generally in the numerical simulation about the tsunami propagation to the coast from an open sea, shallow-water equations are used. This research focuses on viscous shallow-water equations and attempts to generate a computational method using finite element techniques based on the previous investigations of Kanayama and Ohtsuka (1978). First, the viscous shallow-water equation system is derived from the Navier-Stokes equations, based on the assumption of hydrostatic pressure in the direction of gravity. Next the numerical scheme is shown. Then, tsunami simulations of Hakata Bay and Tohoku-Oki are shown using the approach. Finally, a stability condition in L2 sense for the numerical scheme of a linearized viscous shallow-water problem is introduced from Kanayama and Ushijima (1988-1989) and its actual effectiveness is discussed from the view point of practical computation. This presentation will be done in Japanese.
[ 講演参考URL ]
http://www.infsup.jp/utnas/

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
橋本 義武 氏 (東京都市大学)
Conformal field theory for C2-cofinite vertex algebras (JAPANESE)
[ 講演概要 ]
This is a jount work with Akihiro Tsuchiya (Kavli IPMU).
We consider sheaves of covacua and conformal blocks over parameter spaces of n-pointed Riemann surfaces
for a vertex algebra of which the category of modules is not necessarily semi-simple.
We assume the C2-cofiniteness condition for vertex algebras.
We define "tensor product" of two modules over a C2-cofinite vertex algebra.

解析学火曜セミナー

16:30-18:30   数理科学研究科棟(駒場) 128号室
Alexander Vasiliev 氏 (Department of Mathematics, University of Bergen, Norway) 16:30-17:30
Evolution of smooth shapes and the KP hierarchy (ENGLISH)
[ 講演概要 ]
We consider a homotopic evolution in the space of smooth
shapes starting from the unit circle. Based on the Loewner-Kufarev
equation we give a Hamiltonian formulation of this evolution and
provide conservation laws. The symmetries of the evolution are given
by the Virasoro algebra. The 'positive' Virasoro generators span the
holomorphic part of the complexified vector bundle over the space of
conformal embeddings of the unit disk into the complex plane and
smooth on the boundary. In the covariant formulation they are
conserved along the Hamiltonian flow. The 'negative' Virasoro
generators can be recovered by an iterative method making use of the
canonical Poisson structure. We study an embedding of the
Loewner-Kufarev trajectories into the Segal-Wilson Grassmannian,
construct the tau-function, the Baker-Akhiezer function, and finally,
give a class of solutions to the KP hierarchy, which are invariant on
Loewner-Kufarev trajectories.
Irina Markina 氏 (Department of Mathematics, University of Bergen, Norway) 17:30-18:30
Group of diffeomorphisms of the unit circle and sub-Riemannian geometry (ENGLISH)
[ 講演概要 ]
We consider the group of sense-preserving diffeomorphisms of the unit
circle and its central extension - the Virasoro-Bott group as
sub-Riemannian manifolds. Shortly, a sub-Riemannian manifold is a
smooth manifold M with a given sub-bundle D of the tangent bundle, and
with a metric defined on the sub-bundle D. The different sub-bundles
on considered groups are related to some spaces of normalized
univalent functions. We present formulas for geodesics for different
choices of metrics. The geodesic equations are generalizations of
Camassa-Holm, Huter-Saxton, KdV, and other known non-linear PDEs. We
show that any two points in these groups can be connected by a curve
tangent to the chosen sub-bundle. We also discuss the similarities and
peculiarities of the structure of sub-Riemannian geodesics on infinite
and finite dimensional manifolds.

2012年12月03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
川上 裕 氏 (山口大学)
ガウス写像の除外値数の上限の幾何学的意味について (JAPANESE)
[ 講演概要 ]
複素平面から閉リーマン面への正則写像の除外値数の最良の上限はその閉リーマン面のオイラー数と一致することが知られている. 本講演では,藤本坦孝氏により得られた,3次元ユークリッド空間内の完備極小曲面のガウス写像の除外値数の上限である“4”や講演者と中條大介氏との共同研究で得ることができた, 3次元アファイン空間内の弱完備な非固有アファイン波面のラグランジアンガウス写像の除外値数の最良の上限である“3”の幾何学的意味について解説する. また時間が許せば,ガウス写像の理論と正則曲線の理論との関係についても述べる予定である.

2012年12月01日(土)

東京無限可積分系セミナー

13:30-15:00   数理科学研究科棟(駒場) 117号室
アレクセイ シランティエフ 氏 (東大数理)
Manin matrices and quantum integrable systems (ENGLISH)
[ 講演概要 ]
Manin matrices (known also as right quantum matrices) is a class of
matrices with non-commutative entries. The natural generalization of the
usual determinant for these matrices is so-called column determinant.
Manin matrices, their determinants and minors have the most part of the
properties possessed by the usual number matrices. Manin matrices arise
from the RLL-relations and help to find quantum analogues of Poisson
commuting traces of powers of Lax operators and to establish relations
between different types of quantum commuting families. The RLL-relations
also give us q-analogues of Manin matrices in the case of trigonometric
R-matrix (which define commutation relations for the quantum affine
algebra).

2012年11月30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) 123号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)。

Siegfried BOECHERER 氏 (University of Tokyo)
What do Siegel Eisenstein series know about all modular forms? (ENGLISH)
[ 講演概要 ]
Eisenstein series came up in C.L.Siegel's famous work on quadratic forms. The main properties of such Eisensetin series such as analytic continuation and explict form of Fourier expansion are well understood. Nowadays, we use Eisenstein series of higher rank symplectic groups and their restrictions to study properties of all modular forms. I will try to survey the use of “pullbacks of Eisenstein series”: Basis problem, L-functions, p-adic properties, rationality and integrality questions.

数理人口学・数理生物学セミナー

14:30-15:30   数理科学研究科棟(駒場) 056号室
Michael Tildesley 氏 ( Infectious Disease Epidemiology (Modelling) at the University of Warwick)
Targeting control in the presence of uncertainty (ENGLISH)
[ 講演概要 ]
The availability of epidemiological data in the early stages of an outbreak of an infectious disease is vital to enable modellers to make accurate predictions regarding the likely spread of disease and preferred intervention strategies. However, in some countries, epidemic data are not available whilst necessary demographic data are only available at an aggregate scale. Here we investigate the ability of models of livestock infectious diseases to predict epidemic spread and optimal control policies in the event of uncertainty. We focus on investigating predictions in the presence of uncertainty regarding contact networks, demographic data and epidemiological parameters. Our results indicate that mathematical models could be utilized in regions where individual farm-level data are not available, to allow predictive analyses to be carried out regarding the likely spread of disease. This method can also be used for contingency planning in collaboration with policy makers to determine preferred control strategies in the event of a future outbreak of infectious disease in livestock.

統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
矢田 和善 氏 (筑波大学 数理物質科学研究科)
Effective PCA for high-dimensional, non-Gaussian data under power spiked model (JAPANESE)
[ 講演概要 ]
In this talk, we introduce a general spiked model called the power spiked model in high-dimensional settings. We first consider asymptotic properties of the conventional estimator of eigenvalues under the power spiked model. We give several conditions on the dimension $p$, the sample size $n$ and the high-dimensional noise structure in order to hold several consistency properties of the estimator. We show that the estimator is affected by the noise structure, directly, so that the estimator becomes inconsistent for such cases. In order to overcome such difficulties in a high-dimensional situation, we develop new PCAs called the noise-reduction methodology and the cross-data-matrix methodology under the power spiked model. This is a joint work with Prof. Aoshima (University of Tsukuba).
[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/11.html

2012年11月29日(木)

Lie群論・表現論セミナー

16:30-17:30   数理科学研究科棟(駒場) 122号室
いつもと部屋が違います
渡部正樹 氏 (東京大学大学院数理科学研究科)
On a relation between certain character values of symmetric groups (JAPANESE)
[ 講演概要 ]
We present a relation of new kind between character values of
symmetric groups which explains a curious phenomenon in character
tables of symmetric groups. Similar relations for characters of
Brauer and walled Brauer algebras and projective characters of
symmetric groups are also presented.

GCOEレクチャーズ

10:00-12:10   数理科学研究科棟(駒場) 123号室
Haim Brezis 氏 (Rutgers University / Technion)
Sobolev maps with values into the circle (ENGLISH)
[ 講演概要 ]
Sobolev functions with values into R are very well understood and play an immense role in many branches of Mathematics. By contrast, the theory of Sobolev maps with values into the unit circle is still under construction. Such maps occur e.g. in the asymptotic analysis of the Ginzburg-Landau model. The reason one is interested in Sobolev maps, rather than smooth maps is to allow singularities such as x/|x| in 2D or line singularities 3D which appear in physical problems. Our focus in these lectures is not the Ginzburg-Landau equation per se, but rather the intrinsic study of the function space W^{1,p} of maps from a smooth domain in R^N taking their values into the unit circle. Such classes of maps have an amazingly rich structure. Geometrical and Topological effects are already noticeable in this simple framework, since S^1 has nontrivial topology. Moreover the fact that the target space is the circle (as opposed to higher-dimensional manifolds) offers the option to introduce a lifting. We'll see that "optimal liftings" are in one-to-one correspondence with minimal connections (resp. minimal surfaces) spanned by the topological singularities of u.
I will also discuss the question of uniqueness of lifting . A key ingredient in some of the proofs is a formula (due to myself, Bourgain and Mironescu) which provides an original way of approximating Sobolev norms (or the total variation) by nonlocal functionals. Nonconvex versions of these functionals raise very challenging questions recently tackled together with H.-M. Nguyen. Comparable functionals also occur in Image Processing and suggest exciting interactions with this field.

2012年11月28日(水)

幾何コロキウム

10:30-12:00   数理科学研究科棟(駒場) 128号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
本多正平 氏 (九州大学)
リッチ曲率と角度 (JAPANESE)
[ 講演概要 ]
リッチ曲率が下に有界なリーマン多様体の極限空間(これは距離空間)を考える.この極限空間を調べること,特にその regularity を調べることは様々な幾何と接点を持ち,多くの応用を持つ.この講演ではそのような regularity に関する一結果を紹介する.具体的には,そのような空間の上で角度が定義できること,そしてその応用として,極限空間は必ず弱い意味で二階微分可能構造を持つことを紹介する.また,時間が許せばその後の進展についても述べたい.

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
縄田紀夫 氏 (千葉大数学)
Fundamental group of simple $C^*$-algebras with unique trace (JAPANESE)

講演会

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.

GCOEレクチャーズ

13:30-14:30   数理科学研究科棟(駒場) 123号室
Haim Brezis 氏 (Rutgers University / Technion)
How Poincare became my hero (ENGLISH)
[ 講演概要 ]
I recently discovered little-known texts of Poincare which include fundamental results on PDEs together with prophetic insights into their future impact on various branches of modern mathematics.

GCOEレクチャーズ

14:50-17:30   数理科学研究科棟(駒場) 123号室
Haim Brezis 氏 (Rutgers University / Technion)
Can you hear the degree of a map from the circle into itself? An intriguing story which is not yet finished (ENGLISH)
[ 講演概要 ]
A few years ago - following a suggestion by I. M. Gelfand - I discovered an intriguing connection between the topological degree of a map from the circle into itself and its Fourier coefficients. This relation is easily justified when the map is smooth. However, the situation turns out to be much more delicate if one assumes only continuity, or even Holder continuity. I will present recent developments and open problems. The initial motivation for this direction of research came from the analysis of the Ginzburg-Landau model.

2012年11月27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
野澤 啓 氏 (JSPS-IHES フェロー)
葉層構造の特性類の有限的側面について (JAPANESE)
[ 講演概要 ]
Thurstonの例により、葉層構造の二次特性類は有界でないことが知られている。本講演では、横断的な共形平坦構造などを持つ葉層構造に対しては(例外的な場合を除き)二次特性類が有限性を持つことを、非有界性や葉層構造の剛性との関連と共に説明する。
(本講演はSantiago de Compostela大学のJesús Antonio Álvarez
López氏との共同研究 arXiv:1205.3375に基づく。)

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
今野宏 氏 (東京大学大学院数理科学研究科)
旗多様体のケーラー偏極の実偏極への収束 (JAPANESE)
[ 講演概要 ]
In this talk we will discuss geometric quantization of a flag manifold. In particular, we construct a family of complex structures on a flag manifold that converge 'at the quantum level' to the real polarization coming from the Gelfand-Cetlin integrable system.
Our construction is based on a toric degeneration of flag varieties and a deformation of K¥"ahler structure on toric varieties by symplectic potentials.
This is a joint work with Mark Hamilton.

2012年11月26日(月)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
桂 利行 氏 (法政大学理工学部)
超特殊K3曲面上の有理曲線の配置について (JAPANESE)
[ 講演概要 ]
正標数の代数的閉体$k$上の超特異K3曲面のArtin不変量が1のとき超特殊K3曲面という。標数が3以上であれば、このようなK3曲面は、2つの超特異楕円曲線の直積であるアーべル曲面からつくられるKummer曲面になることが知られている。この講演では$S$上の有理曲線の配置をアーベル曲面の因子の構造を用いて考察し、標数が2ならば$(21)_5$-symmetric configurationが存在すること、また標数3ならば$(16)_{10}$-symmetric configurationと$(280_{4}, 112_{10})$-configurationが存在することを示す。また、後者は、$p^{a} + 1$次のFermat hypersurfaceのline configurationや、N\\'eron-S\\'everi群${\\rm NS}(S)$がLeech latticeを用いて捉えられることと関係することを述べる。

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
納谷 信 氏 (名古屋大学大学院多元数理科学研究科)
四元数CR幾何 (JAPANESE)
[ 講演概要 ]
四元数CR構造は、四元数多様体の実超曲面をモデルとする幾何構造である。本講演では、この構造の定義や基本事項を説明した後に、O.Biquardの四元数接触構造との比較、ならびにツイスターCR多様体の構成について述べる。

2012年11月22日(木)

講演会

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.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/gcoe/index_007.html

講演会

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.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/gcoe/index_007.html

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