[English]

Tea: 16:00 -- 16:30 コモンルーム

世話係

河野俊丈

河澄響矢

10月1日 -- 056号室, 16:30 -- 18:00

門田 直之 (東京理科大学)

Abstract: To consider holomorphic fibrations complex surfaces over complex curves and Lefschetz fibrations over surfaces is one method for the study of complex surfaces of general type and symplectic 4-manifods, respectively. In this talk, by comparing the geography problem of relatively minimal holomorphic fibrations with that of relatively minimal Lefschetz fibrations (i.e., the characterization of pairs (x,y) of certain invariants x and ycorresponding to relatively minimal holomorphic fibrations and relatively minimal Lefschetz fibrations), we observe the difference between complex surfaces of general type and symplectic 4-manifolds. In particular, we construct Lefschetz fibrations violating the "slope inequality" which holds for any relatively minimal holomorphic fibrations.

10月8日 -- 056号室, 16:30 -- 18:00

清水 達郎 (東京大学大学院数理科学研究科)

Abstract: In this talk, we define an invariant of rational homology 3-spheres with values in a space $\mathcal A(\emptyset)$ of Jacobi diagrams by using vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston invariant $z^{KKT}$ and that of Fukaya and Watanabe's Morse homotopy invariant $z^{FW}$. As an application of our invariant, we prove that $z^{KKT}=z^{FW}$ for integral homology 3-spheres.

10月15日 -- 056号室, 16:30 -- 18:00

高瀬 将道 (成蹊大学)

Abstract: This is a joint work with Osamu Saeki (IMI, Kyushu University). A special generic map is a generic map which has only definite fold as its singularities. We study the condition for a special generic map from a closed n-manifold to the p-space (n+1>p), to factor through a codimension one immersion (or an embedding). In particular, for the cases where p = 1 and 2 we obtain complete results. Our techniques are related to Smale-Hirsch theory, topology of the space of immersions, relation between the space of topological immersions and that of smooth immersions, sphere eversions, differentiable structures of homotopy spheres, diffeomorphism group of spheres, free group actions on the sphere, etc.

10月22日 -- 056号室, 16:30 -- 18:00

井上 玲 (千葉大学)

Abstract: The cluster algebra was introduced by Fomin and Zelevinsky around 2000. The characteristic operation in the algebra called 'mutation' is related to various notions in mathematics and mathematical physics. In this talk I review a basics of the cluster algebra, and introduce its application to study the complex volume of knot complements in S

10月29日 -- 056号室, 16:30 -- 18:00

Daniel Matei (IMAR, Bucharest)

Abstract: We discuss restrictions imposed by the complex structure on fundamental groups of quasi-projective algebraic varieties with mild singularities. We investigate quasi-projectivity of various geometric classes of finitely presented groups.

11月5日 -- 123号室, 16:30 -- 18:00

Carlos Moraga Ferrándiz (東京大学大学院数理科学研究科, 日本学術振興会)

Abstract: Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class. A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.

The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.

11月12日 -- 056号室, 16:30 -- 18:00

Alexander Voronov (University of Minnesota)

Abstract: We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.

11月19日 -- 056号室, 16:30 -- 18:00

児玉 大樹 (東京大学大学院数理科学研究科)

Abstract: 任意の無理数αに対して、ルベーグ測度について基本領域を持つ 円周上の極小微分同相写像で回転数がαとなるものを構成した。

これは松元重則氏（日本大学）との共同研究である。

11月26日 -- 056号室, 16:30 -- 18:00

徳永 浩雄 (首都大学東京)

Abstract: Sは有理楕円曲面とする．Sの生成ファイバーは 1変数有理函数体上の楕円曲線であり，楕円曲線の 群構造を利用してSの切断C_1からS上の曲線 C_2を構成することできる．本講演では，このアイ デアに基づいて得られるある7次のline-conic arrangementsについて解説する．

12月3日 -- 056号室, 17:00 -- 18:00

Bruno Martelli (Università di Pisa)

Abstract: (joint work with A. Kolpakov)

We introduce a simple algorithm which transforms every four-dimensional cubulation into a cusped finite-volume hyperbolic four-manifold. Combinatorially distinct cubulations give rise to topologically distinct manifolds. Using this algorithm we construct the first examples of finite-volume hyperbolic four-manifolds with one cusp. More generally, we show that the number of k-cusped hyperbolic four-manifolds with volume smaller than V grows like C^{V log V} for any fixed k. As a corollary, we deduce that the 3-torus bounds geometrically a hyperbolic manifold.

Martelli氏の講演はキャンセルになりました。

12月10日 -- 056号室, 16:30 -- 18:00

丹下 基生 (筑波大学)

Abstract: Akbulut and Yasui defined cork, and plug to produce many exotic pairs. In this talk, we introduce a plug with respect to Fintushel-Stern's knot surgery or more 4-dimensional local moves and and argue by using Heegaard Fleor theory.

12月17日 -- 056号室, 16:30 -- 18:00

中村 伊南沙 (東京大学大学院数理科学研究科)

Abstract: For an oriented surface link F in R

12月24日 -- 056号室, 16:30 -- 18:00

Tirasan Khandhawit (Kavli IPMU)

Abstract: In this talk, I will try to give an overview of the construction of stable homotopy type for monopole Floer homology. The construction associates a stable homotopy object to 3-manifolds, which will recover the Floer groups by appropriate homology theory. The main ingredients are finite dimensional approximation technique and Conley index theory. In addition, I will demonstrate construction for certain 3-manifolds such as the 3-torus.

1月14日 -- 056号室, 17:00 -- 18:00

Rinat Kashaev (University of Geneva)

Abstract: Quantum Teichmüller theory can be promoted to a generalized TQFT within the combinatorial framework of shaped triangulations with the tetrahedral weight functions given in terms of the Weil-Gelfand-Zak transformation of Faddeev.FN"s quantum dilogarithm. By using simple examples, I will illustrate the connection of this theory with the hyperbolic geometry in three dimensions.

1月21日 -- 056号室

16:30 -- 17:30

粕谷 直彦 (東京大学大学院数理科学研究科)

Abstract: We prove that the Chern class of a closed contact manifold is an obstruction for codimension two contact embeddings in the odd dimensional Euclidean space. By Gromov's h-principle, for any closed contact 3-manifold with trivial first Chern class, there is a contact structure on

17:30 -- 18:30

李 暁龍 (東京大学大学院数理科学研究科)

Abstract: For 3-dimensional homoclinic classes of saddles with index 2, a new sufficient condition for creating weak contracting eigenvalues is provided. Our perturbation makes use of small angles between stable and unstable subspaces of saddles. In particular, by recovering the unstable eigenvector, we can designate that the newly created weak eigenvalue is contracting. As applications, we obtain C

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