## 過去の記録

#### 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。

### 2012年11月06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

[ 講演概要 ]

その後、有理数体の絶対ガロア群が'結び目全体が張る空間'に

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Thierry Ramond 氏 (Univ. Paris, Orsay)
Resonance free domains for homoclinic orbits (ENGLISH)

#### 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

An explicit construction of spherical designs on S^3 (JAPANESE)
[ 講演概要 ]
The existence of spherical t-designs on S^d for any t and d are proved by Seymour--Zaslavsky in 1984.
However, explicit constructions of spherical designs were not known for d > 2 and large t.
In this talk, for a given spherical t-design Y on S^2, we give an
algorithm to make a spherical 2t-design X on S^3 which maps Y by a Hopf map. In particular, by combining with the results of Kuperberg in 2005, we have an explicit construction of spherical t-designs on S^3 for any t.

### 2012年11月05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

トリゴナル曲線のモジュライの有理性 (JAPANESE)
[ 講演概要 ]

### 2012年10月31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

Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits (JAPANESE)
[ 講演概要 ]
Hofer-Zehnder (HZ) capacity is an invariant of symplectic manifolds, which is important in symplectic topology and Hamiltonian dynamics. The energy-capacity inequality (due to Hofer and many others) claims that HZ capacity of a domain is bounded from above by its dispalcement energy.
In this talk, we prove a variant of this inequality, which is applicable to nondisplaceable domains. We also give some applications, including case of disc cotangent bundles.

### 2012年10月30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

http://www.ms.u-tokyo.ac.jp/gcoe/index.html

[ 講演概要 ]

[ 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) 126号室
Tea: 16:00 - 16:30 コモンルーム

Applications of knot theory to molecular biology (JAPANESE)
[ 講演概要 ]
In this talk we discuss applications of knot theory to studies of DNA
and proteins.
Especially we will consider (1)topological characterization of
mechanisms of site-specific recombination systems,
(2)modeling knotted DNA and proteins in confined regions using lattice
knots, and
(3)mechanism of topoisomerases and signed crossing changes.

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Francis Nier 氏 (Univ. Rennes 1)
About the method of characteristics (ENGLISH)
[ 講演概要 ]
While studying the mean field dynamics of a systems of bosons, one is led to solve a transport equation for a probability measure in an infinite dimensional phase-space. Since those probability measures are characterized after testing with cylindrical or polynomial observables, which make classes which are not invariant after composing with a nonlinear flow. Thus the standard method of characteristics for transport equations cannot be extended at once to the infinite dimensional case. A solution comes from techniques developed for optimal transport and a probabilistic interpretation of trajectories.

#### 講演会

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.