[English]

Tea: 16:00 -- 16:30 コモンルーム

世話係

河野俊丈

河澄響矢

4月12日 -- 056号室, 16:30 -- 18:00

廣瀬 進 (東京理科大学理工学部数学科)

Abstract: ４次元球面内に標準的に埋め込まれた向き付け可能曲面上の 向きを保つ可微分同相写像が向きを保つ４次元球面上の可微分同相写像に 拡張できるための必要十分条件は，その曲面に対する Rokhlin の２次形式を 保つことであることが知られている． 本講演では，向き付け不可能な閉曲面に対する同様の問題についての 現在進行中の試みについて話す．

4月26日 -- 056号室, 16:30 -- 18:00,

吉野 太郎 (東京大学大学院数理科学研究科)

Abstract: Suppose that a Lie group $G$ acts on a manifold $M$. The quotient space $X:=G\backslash M$ is locally compact, but not Hausdorff in general. Our aim is to understand such a non-Hausdorff space $X$. The space $X$ has the crack $S$. Roughly speaking, $S$ is the causal subset of non-Hausdorffness of $X$, and especially $X\setminus S$ is Hausdorff.

We introduce the concept of `topological blow-up' as a `repair' of the crack. The `repaired' space $\tilde{X}$ is locally compact and Hausdorff space containing $X\setminus S$ as its open subset. Moreover, the original space $X$ can be recovered from the pair of $(\tilde{X}, S)$.

5月10日 -- 056号室, 16:30 -- 18:00

伊藤 哲也（東京大学大学院数理科学研究科）

Abstract: The set of all left orderings of a group G admits a natural topology. In general the space of left orderings is homeomorphic to the union of Cantor set and finitely many isolated points. In this talk I will give a new method to construct left orderings corresponding to isolated points, and will explain how such isolated orderings reflect the structures of groups.

5月17日 -- 056号室, 16:30 -- 18:00

石井 敦（筑波大学 大学院数理物質科学研究科）

Abstract: This is a joint work with Masahide Iwakiri, Yeonhee Jang and Kanako Oshiro. We introduce quandle coloring invariants and quandle cocycle invariants with non-commutative flows for knots, spatial graphs, handlebody-knots, where a handlebody-knot is a handlebody embedded in the $3$-sphere. Two handlebody-knots are equivalent if one can be transformed into the other by an isotopy of $S^3$. The quandle coloring (resp. cocycle) invariant is a ``twisted'' quandle coloring (resp. cocycle) invariant.

5月24日 -- 056号室, 16:30 -- 18:00

吉永 正彦 (京都大学大学院理学研究科)

Abstract: The homotopy type of complements of complex hyperplane arrangements have a special property, so called minimality (Dimca-Papadima and Randell, around 2000). Since then several approaches based on (continuous, discrete) Morse theory have appeared. In this talk, we introduce the "dual" object, which we call minimal stratification for real two dimensional cases. A merit is that the minimal stratification can be explicitly described in terms of semi-algebraic sets. We also see associated presentation of the fundamental group. This talk is based on arXiv:1105.1857

5月31日 -- 056号室, 17:00 -- 18:00

盛田 健彦 (大阪大学大学院理学研究科)

Abstract: This is a joint work with Yusuke Tokunaga. Let M be an N dimensional compact connected smooth Riemannian manifold without boundary and let E

(1) T has a unique measure with maximum total exponent.

(2) Any measure with maximum total exponent for T has zero entropy.

(3) Any measure with maximum total exponent for T is fully supported.

On the contrary, we show that for r greater than or equal to 2, a generic element in E

6月7日 -- 056号室, 16:30 -- 18:00,

金井 雅彦 (東京大学大学院数理科学研究科)

Abstract: It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.

6月14日 -- 056号室, 17:00 -- 18:00

満渕 俊樹 (大阪大学大学院理学研究科)

Abstract: For polarized algebraic manifolds, the concept of K-stability introduced by Tian and Donaldson is conjecturally strongly correlated to the existence of constant scalar curvature metrics (or more generally extremal Kähler metrics) in the polarization class. This is known as Donaldson-Tian-Yau's conjecture. Recently, a remarkable progress has been made by many authors toward its solution. In this talk, I'll discuss the topic mainly with emphasis on the existence part of the conjecture.

6月28日 -- 056号室, 16:30 -- 18:00

二木 昌宏（東京大学大学院数理科学研究科）

Abstract: The directed Fukaya category defined by Seidel is a " categorification" of the Milnor lattice of hypersurface singularities. Sebastiani-Thom showed that the Milnor lattice and its monodromy behave as tensor product for the sum of singularities. A directed Fukaya category version of this theorem was conjectured by Auroux-Katzarkov- Orlov (and checked for the Landau-Ginzburg mirror of P^1 \times P^1). In this talk I introduce the directed Fukaya category and show that a Sebastiani-Thom type splitting holds in the case that one of the potential is of complex dimension 1.

7月5日 -- 056号室, 16:30 -- 18:00

Catherine Oikonomides（東京大学大学院数理科学研究科, JSPS）

Abstract: Foliation C*-algebras have been defined abstractly by Alain Connes, in the 1980s, as part of the theory of Noncommutative Geometry. However, very few concrete examples of foliation C*-algebras have been studied until now. In this talk, we want to explain how to compute the K-theory of the C*-algebra of codimension one foliations which are "almost without holonomy", meaning that the holonomy of all the noncompact leaves of the foliation is trivial. Such foliations have a fairly simple geometrical structure, which is well known thanks to theorems by Imanishi, Hector and others. We will give some concrete examples on 3-manifolds, in particular the 3-sphere with the Reeb foliation, and also some slighty more complicated examples.

7月12日 -- 056号室, 16:30 -- 18:00

川室 圭子 (University of Iowa)

Abstract: I will show a self linking number formula, in language of braids, for transverse knots in contact manifolds that admit planar open book decompositions. Our formula extends the Bennequin's for the standar contact 3-sphere.

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