## 過去の記録

### 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

[ 講演概要 ]

#### 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

[ 講演概要 ]

### 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

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

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

#### 講演会

15:30-16:15   数理科学研究科棟(駒場) 002号室

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

#### 講演会

16:25-17:10   数理科学研究科棟(駒場) 002号室

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

### 2012年11月21日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Giovanni Pisante 氏 (Seconda Università degli Studi di Napoli)
Shape Optimization And Asymptotic For The Twisted Dirichlet Eigenvalue (ENGLISH)
[ 講演概要 ]
Aim of the talk is to discuss some recent results obtained with G. Croce and A. Henrot on a generalization of the functional defining the first twisted eigenvalue.
We look at the set functional defined by minimizing a Rayleigh quotient involving Lebesgue norms with different exponents p and q among functions satisfying a zero boundary condition as well as a zero mean condition of order q.
First under suitable conditions on p and q, that ensure the existence of a minimizing function, we investigate the validity of an isoperimetric type inequality of the Reyleigh-Faber-Krahn type.
Then we study the limit of the functional for p and q tending to 1 and to infinity and discuss the relation with the limits of the second eigenvalues of the p-laplacian operator.

#### 古典解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
Philip Boalch 氏 (ENS-DMA & CNRS Paris)
Beyond the fundamental group (ENGLISH)
[ 講演概要 ]
Moduli spaces of representations of the fundamental group of a Riemann surface have been studied from numerous points of view and appear in many parts of mathematics and theoretical physics. They form an interesting class of symplectic manifolds, they often have Kahler or hyperkahler metrics (in which case they are diffeomorphic to spaces of Higgs bundles, i.e. Hitchin integrable systems), and they admit nonlinear actions of braid groups and mapping class groups with fascinating dynamical properties. The aim of this talk is to describe some aspects of this story and sketch their extension to the context of the "wild fundamental group", which naturally appears when one considers {\\em meromorphic} connections on Riemann surfaces. In particular some new examples of hyperkahler manifolds appear in this way, some of which are familiar from classical work on the Painleve equations.

### 2012年11月20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

3次元双曲幾何と団代数 (JAPANESE)
[ 講演概要 ]
クラスター代数は2000年にFomin-Zelevinskyによって発見された代数系である.

#### Lie群論・表現論セミナー

16:30-17:30   数理科学研究科棟(駒場) 126号室
Ali Baklouti 氏 (Sfax University)
On the geometry of discontinuous subgroups acting on some homogeneous spaces (ENGLISH)
[ 講演概要 ]
Let $G$ be a Lie group, $H$ a closed subgroup of $G$ and \\Gamma$a discontinuous subgroup for the homogeneous space$G/H$. I first introduce the deformation space${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$of the action of$\\Gamma$on$G/H$in the sense of Kobayashi and some of its refined versions, namely the Clifford--Klein space of deformations of the form${\\mathcal{X}}=\\Gamma \\backslash G/H$. The deformation space${\\mathcal{T}}^{G_o}(\\Gamma, G,H)$of marked$(G,H)$-structures on${\\mathcal{X}}$in the sense of Goldman is also introduced. As an important motivation, I will explain the connection between the spaces${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$and${\\mathcal{T}}^{G_o}(\\Gamma, G, H)$and study some of their topological features, namely the rigidity in the sense of Selberg--Weil--Kobayashi and the stability in the sense of Kobayashi--Nasrin. The latter appears to be of major interest to write down the connection explicitly. ### 2012年11月19日(月) #### 講演会 16:45-17:45 数理科学研究科棟(駒場) 126号室 Hendrik Weber 氏 (University of Warwick) Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size (ENGLISH) [ 講演概要 ] We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one transition from -1 to 1. We are interested in the competition between the energy'' that should be minimized due to the small noise strength and the entropy'' that is induced by the large system size. Our methods handle system sizes that are exponential with respect to the inverse noise strength, up to the critical'' exponential size predicted by the heuristics. We capture the competition between energy and entropy through upper and lower bounds on the probability of extra transitions between$\\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. #### 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 戸田 幸伸 氏 (IPMU) Stability conditions and birational geometry (JAPANESE) [ 講演概要 ] I propose a conjecture which claims that MMP for a smooth projective variety is realized as a variation of Bridgeland moduli spaces of semistable objects in the derived category of coherent sheaves. I will discuss the surface case and extremal contractions for 3-folds. In the former case, the conjecture is completely solved. In the latter case, I will construct the perverse t-structure associated to the extremal contraction, and construct a candidate of the desired stability condition as a double tilting of the perverse heart. #### GCOEセミナー 15:30-17:00 数理科学研究科棟(駒場) 056号室 Alfred Ramani 氏 (Ecole Polytechnique) Linearisable mappings (ENGLISH) [ 講演概要 ] We present a series of results on linearisable second-order mappings. Three distinct families of such mappings do exist: projective, mappings of Gambier type and mappings which we have dubbed "of third kind". Our starting point are the linearisable mappings belonging to the QRT family. We show how they can be linearised and how in some cases their explicit solution can be constructed. We discuss also the growth property of these mappings, a property intimately related to linearisability. In the second part of the talk we address the question of the extension of these mappings to a non-autonomous form. We show that the QRT invariant can also be extended (to a quantity which depends explicitly on the independent variable). Using this non-autonomous form we show that it is possible to construct the explicit solution of all third-kind mappings. We discuss also the relation of mappings of the third kind to Gambier-type mappings. We show that a large subclass of third-kind mappings can be considered as the discrete derivative of Gambier-type ones. #### 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 小森 洋平 氏 (早稲田大学) トーラス上の種数２のリーマン面の退化族について (JAPANESE) [ 講演概要 ] ある固定したトーラスの2重分岐被覆として得られる種数2のリーマン面を一般ファイバーに持つ、リーマン面の退化族を構成し、その特異ファイバーと正則切断を決定する。 ### 2012年11月16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 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)。 二木昭人 氏 (東京大学) 複素微分幾何に現れる積分不変量について (JAPANESE) [ 講演概要 ] コンパクト複素多様体のもっともなじみ深い不変量は Chern 類であろう.この講演ではその secondary classes にあたる正則ベクトル場を含んだ積分不変量の族で,次のような3つを含むものについて紹介する. (1) 各 k に対し,k 次 Chern 形式が調和形式であるようなケーラー計量が存在するための障害となる不変量. (2) 非ケーラー多様体でも定義される不変量で,横断的正則葉層構造の特性類やLefchetz 数などから自然に得られる不変量. (3) 代数多様体に対し,漸近的 Chow 半安定性の障害となる不変量. これらの3つの族の共通部分にケーラー・アインシュタイン計量が存在するための障害がある. #### GCOEセミナー 16:30-18:00 数理科学研究科棟(駒場) 122号室 Dietmar Bisch 氏 (Vanderbilt University) Subfactors with small Jones index (ENGLISH) ### 2012年11月14日(水) #### 代数学コロキウム 18:00-19:00 数理科学研究科棟(駒場) 002号室 いつもと時間・場所が異なりますのでご注意ください. Pierre Berthelot 氏 (Université de Rennes 1) De Rham-Witt complexes with coefficients and rigid cohomology (ENGLISH) [ 講演概要 ] For a smooth scheme over a perfect field of characteristic p, we will explain a generalization of the classical comparison theorem between crystalline cohomology and de Rham-Witt cohomology to the case of cohomologies with coefficients in a p-torsion free crystal. This provides in particular a description of the rigid cohomology of a proper singular scheme in terms of a de Rham-Witt complex built from a closed immersion into a smooth scheme. (本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います.) #### 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. 河井公大朗 氏 (東北大学) Construction of coassociative submanifolds (JAPANESE) [ 講演概要 ] The notion of coassociative submanifolds is defined as the special class of the minimal submanifolds in G_2 manifolds. In this talk, we introduce the method to construct coassociative submanifolds by using the symmetry of the Lie group action. As an application, we give explicit examples in the 7-dimensional Euclidean space and in the anti-self-dual bundle over the 4-sphere. ### 2012年11月13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 北山 貴裕 氏 (京都大学数理解析研究所，日本学術振興会PD) The virtual fibering theorem and sutured manifold hierarchies (JAPANESE) [ 講演概要 ] In 2007 Agol showed that every irreducible 3-manifold whose fundamental group is nontrivial and virtually residually finite rationally solvable (RFRS) is virtually fibered. In the proof he used the theory of least-weight taut normal surfaces introduced and developed by Oertel and Tollefson-Wang. We give another proof using complexities of sutured manifolds. This is a joint work with Stefan Friedl (University of Cologne). #### 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 Oskar Hamlet 氏 (Chalmers University) Tight maps, a classification (ENGLISH) [ 講演概要 ] Tight maps/homomorphisms were introduced during the study of rigidity properties of surface groups in Hermitian Lie groups. In this talk I'll discuss the properties of tight maps, their connection to rigidity theory and my work classifying them. ### 2012年11月12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 安武 和範 氏 (九州大学大学院数理学研究院) On Fano fourfolds with nef vector bundles$Λ^2T_X\$ (JAPANESE)
[ 講演概要 ]
By using results about extremal contractions on smooth fourfolds, we give a classification of fano fourfolds whose the second exterior power of tangent bundles are numerically effective.

#### 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
A.G. Aleksandrov 氏 (Institute of Control Sciences, Russian Acad. of Sci.)
Residues of meromorphic differential forms (ENGLISH)
[ 講演概要 ]
The purpose of the talk is to discuss several interesting aspects
of the classical residue theory originated by H. Poincar\\'e, J. de Rham and J. Leray and their followers. Focus topics of our studies are some of the less known applications, developed by the author in the past few years in complex analysis, topology and geometry of singular varieties and in the theory of differential equations. Almost all considerations are based essentially on properties of a special class of meromorphic differential forms called logarithmic or multi-logarithmic forms.

### 2012年11月10日(土)

#### 調和解析駒場セミナー

13:00-18:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.

Perturbed Besov spaces by short-range type potential
in exterior domains (JAPANESE)
[ 講演概要 ]
In this talk we will define perturbed Besov spaces by a short-range potential over exterior domains. These spaces will be available for obtaining the Strichartz estimates of wave equation with a potential in exterior domains.
We will pay attention to observe the equivalence relation between the perturbed Besov spaces and the free ones.

Optimal constants and extremisers for some smoothing estimates (JAPANESE)
[ 講演概要 ]
Our purpose is to study the optimal constant and extremising initial data for a broad class of smoothing estimates for slutions of linear dispersive equations.
Firstly, we discuss the existence/nonexistence of extremisers and then we provide an explicit formula and new observations for the optimal constant.
The talk is based on joint work with Neal Bez (University of Birmingham).
Victor I. Burenkov 氏 (Russia/United Kingdom) 16:30-17:50
Spectral stability of the p-Laplacian (JAPANESE)
[ 講演概要 ]
Dependence of the eigenvalues of the p-Laplacian upon domain perturbation will be under discussion. Namely Lipschitz-type estimates for deviation of the eigenvalues following a domain perturbation will be presented. Such estimates are obtained for the class of open sets admitting open sets with arbitrarily strong degeneration and are expressed in terms of suitable measures of vicinity of two open sets, such as the \\lq\\lq atlas distance" between these sets or the \\lq\\lq lower Hausdor-Pompeiu
deviation" of their boundaries. In the case of open sets with Holder continuous boundaries, our results essentially improve a result known for the rst eigenvalue [2].
Joint work with P. D. Lamberti. The results were recently published in [1].
Supported by the grant of RFBR (project 08-01-00443).

References:
[1] V.I. Burenkov, P.D. Lamberti, Spectral stability of the p-Laplacian, Nonlinear Analysis, 71, 2009, 2227-2235.
[2] J. Fleckinger, E.M. Harrell and F. de Thelin, Boundary behaviour and estimates for solutions for equations containing the p-Laplacian, Electronic Journal of Dierential Equations, 38, 1999, 1-19.

### 2012年11月09日(金)

#### 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

Tuning parameter selection in sparse regression modeling (JAPANESE)
[ 講演概要 ]
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html

### 2012年11月07日(水)

#### 古典解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

パンルヴェ函数のWKB解析とパラメトリックStokes現象 (JAPANESE)
[ 講演概要 ]
パンルヴェ函数の漸近挙動の研究、および接続問題は、他分野への応用という観点からも非常に重要なテーマである。今回は(2階の古典的な)パンルヴェ方程式を完全WKB解析の立場から考察する。特に、方程式に含まれる「独立変数以外のパラメータ」の値を変化させた際にもある種のStokes現象(パラメトリックStokes現象)が起こることを紹介し、漸近挙動の不連続な変化を記述する接続公式を導く。