過去の記録 ~03/27本日 03/28 | 今後の予定 03/29~


16:30-18:00   数理科学研究科棟(駒場) 118号室
N. Christopher Phillips 氏 (Univ. Oregon)
Large subalgebras of crossed product C*-algebras (ENGLISH)
[ 講演概要 ]
This is work in progress; not everything has been checked.
We define a "large subalgebra" and a "centrally large subalgebra" of a C*-algebra. The motivating example is what we now call the "orbit breaking subalgebra" of the crossed product by a minimal homeomorphism h of a compact metric space X. Let v be the standard unitary in the crossed product C* (Z, X, h). For a closed subset Y of X, we form the subalgebra of C* (Z, X, h) generated by C (X) and all elements f v for f in C (X) such that f vanishes on Y. When each orbit meets Y at most once, this subalgebra is centrally large in the crossed product. Crossed products by smooth free minimal actions of Zd also contain centrally large subalgebras which are simple direct limits, with no dimension growth, of recursive subhomogeneous algebras.
If B is a large subalgebra of A, then the Cuntz semigroups of A and B are the almost the same: if one deletes the classes of nonzero projections, then the inclusion is a bijection on what is left. Also (joint work with Dawn Archey), if B is a centrally large subalgebra of A, and B has stable rank one, then so does A. Moreover, if B is a centrally large subalgebra of A, if B is Z-stable, and if A is nuclear, then A is Z-stable.



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
Ismar Volic 氏 (Wellesley College)
Homotopy-theoretic methods in the study of spaces of knots and links (ENGLISH)
[ 講演概要 ]
I will survey the ways in which some homotopy-theoretic
methods, manifold calculus of functors main among them, have in recent
years been used for extracting information about the topology of
spaces of knots and links. Cosimplicial spaces and operads will also
be featured. I will end with some recent results about spaces of
homotopy string links and in particular about how one can use functor
calculus in combination with configuration space integrals to extract
information about Milnor invariants.


16:30-18:00   数理科学研究科棟(駒場) 128号室
Rafe Mazzeo 氏 (Stanford University)
This talk was cancelled! (JAPANESE)


10:30-11:30   数理科学研究科棟(駒場) 056号室
Jie Jiang 氏 (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences)
On convergence to equilibrium with applications of Lojasiewicz-Simon
inequality (I) (ENGLISH)


16:30-18:00   数理科学研究科棟(駒場) 126号室
疋田辰之 氏 (京都大学大学院理学研究科)
Affine Springer fibers of type A and combinatorics of diagonal
Affine Springer fibers of type A and combinatorics of diagonal
coinvariants (JAPANESE)
[ 講演概要 ]
We introduce certain filtrations on the homology of
affine Springer fibers of type A and give combinatorial formulas for the bigraded Frobenius series of the associated graded modules.
The results are essentially given by generalizations of the symmetric function introduced by Haglund, Haiman, Loehr, Remmel, and Ulyanov which is conjectured to coincide with the bigraded Frobenius series of the ring of diagonal coinvariants.



15:30-17:00   数理科学研究科棟(駒場) 122号室
川谷 康太郎 氏 (名古屋大学多元数理科学研究科)
A hyperbolic metric and stability conditions on K3 surfaces with $¥rho=1$ (JAPANESE)
[ 講演概要 ]
We introduce a hyperbolic metric on the (normalized) space of stability conditions on projective K3 surfaces $X$ with Picard rank 1. Furthermore we demonstrate how this hyperbolic metric is helpful for us by discussing two or three topics.


10:30-12:00   数理科学研究科棟(駒場) 126号室
金子 宏 氏 (東京理科大)
A Dirichlet space on ends of tree and Dirichlet forms with a nodewise orthogonal property (JAPANESE)



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.
田中 研太郎 氏 (東京工業大学)
条件付き独立性と線形代数 (JAPANESE)
[ 講演概要 ]
確率モデルにおける条件付き独立性の構造を表す手法として, グラフを用いた表現手法(グラフィカルモデリング)がよく使われる. しかし, グラフでは表すことのできない条件付き独立性の構造を持つ確率モデルが多数存在することが知られている. この欠点を克服するために, imset と呼ばれるものを用いた線形代数的な表現手法が Studeny(2005) によって提案されている. 今回の発表では, まず, imset について分かりやすく説明した後, 条件付き独立性の間に成り立つ関係式を自動的に導出する最近の手法について報告する. また, ベイジアンネットワークのデータからの構造推定に対する応用についても簡単に解説する.
[ 参考URL ]



10:30-11:30   数理科学研究科棟(駒場) 002号室
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.


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)


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.


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.



16:30-18:00   数理科学研究科棟(駒場) 002号室

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.
[ 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
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.


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.



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.



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



16:30-17:30   数理科学研究科棟(駒場) 123号室
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.


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.


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).
[ 参考URL ]



16:30-17:30   数理科学研究科棟(駒場) 122号室
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.


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.



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.


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)


10:45-11:45   数理科学研究科棟(駒場) 002号室
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.

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