17:00 -- 18:30 数理科学研究科棟(東京大学駒場キャンパス)
Tea: 16:30 -- 17:00 コモンルーム

Last updated November 22, 2017
河野 俊丈
河澄 響矢
北山 貴裕
逆井 卓也

9月26日 [Lie群論・表現論セミナーと合同] -- 056号室, 17:00 -- 18:30

関口 英子 (東京大学大学院数理科学研究科)

Representations of Semisimple Lie Groups and Penrose Transform

Abstract: The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.
I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.
To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.
Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive $k$-planes and that of negative $k$-planes.

10月3日 -- 056号室, 17:00 -- 18:00

Athanase Papadopoulos (IRMA, Université de Strasbourg)

Transitional geometry

Abstract: I will describe transitions, that is, paths between hyperbolic and spherical geometry, passing through the Euclidean. This is based on joint work with Norbert A’Campo and recent joint work with A’Campo and Yi Huang.

10月10日 -- 056号室, 17:30 -- 18:30

與倉 昭治 (鹿児島大学)

Poset-stratified spaces and some applications

Abstract: A poset-stratified space is a continuous map from a topological space to a poset with the Alexandroff topology. In this talk I will discuss some thoughts about poset-stratified spaces from a naive general-topological viewpoint, some applications such as hyperplane arrangements and poset-stratified space structures of hom-sets, and related topics such as characteristic classes of vector bundles, dependence of maps (by Borsuk) and dependence of cohomology classes (by Thom).

10月17日 -- 056号室, 17:00 -- 18:30

石井 敦 (筑波大学)

Generalizations of twisted Alexander invariants and quandle cocycle invariants

Abstract: We introduce augmented Alexander matrices, and construct link invariants. An augmented Alexander matrix is defined with an augmented Alexander pair, which gives an extension of a quandle. This framework gives the twisted Alexander invariant and the quandle cocycle invariant. This is a joint work with Kanako Oshiro.

10月24日 [Lie群論・表現論セミナーと合同] -- 056号室, 17:30 -- 18:30

宮岡 礼子 (東北大学)


Abstract: 球面の等径超曲面のガウス写像による像は,複素2次超曲面Q_n(C)の極小ラグランジュ部分多様体の豊富な例を与える. 簡単な場合,これはQ_n(C)の実形となり,そのフレアホモロジーは既知である. ここでは相異なる主曲率の個数が3,4,6の場合に得られた結果を報告する. 当研究は,入江博(茨城大),Hui Ma(清華大学),大仁田義裕(大阪市大)との共同研究である.

10月31日 -- 056号室, 17:00 -- 18:30

Yash Lodha (École Polytechnique Fédérale de Lausanne)

Nonamenable groups of piecewise projective homeomorphisms

Abstract: Groups of piecewise projective homeomorphisms provide elegant examples of groups that are non amenable, yet do not contain non abelian free subgroups. In this talk I will present a survey of these groups and discuss their striking properties. I will discuss properties such as (non)amenability, finiteness properties, normal subgroup structure, actions by various degrees of regularity and Tarski numbers.

11月7日 -- 056号室, 17:00 -- 18:30

林 晋 (産総研・東北大オープンイノベーションラボラトリ)

On an explicit example of topologically protected corner states

Abstract: In condensed matter physics, topologically protected (codimension-one) edge states are known to appear on the surface of some insulators reflecting some topology of its bulk. Such phenomena can be understood from the point of view of an index theory associated to the Toeplitz extension and are called the bulk-edge correspondence. In this talk, we consider instead the quarter-plane Toeplitz extension and index theory associated with it. As a result, we show that topologically protected (codimension-two) corner states appear reflecting some topology of the gapped bulk and two edges. Such new topological phases can be obtained by taking a ``product’’ of two classically known topological phases (2d type A and 1d type AIII topological phases). By using this construction, we obtain an example of a continuous family of bounded self-adjoint Fredholm quarter-plane Toeplitz operators whose spectral flow is nontrivial, which gives an explicit example of topologically protected corner states.

11月21日 -- 056号室, 17:00 -- 18:30

境 圭一 (信州大学)

The space of short ropes and the classifying space of the space of long knots

Abstract: We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in R^3. We make use of techniques developed by S. Galatius and O. Randal-Williams to construct a manifold space model of the classifying space of the space of long knots, and we give an explicit map from the space of short ropes to the model in a geometric way. This is joint work with Syunji Moriya (Osaka Prefecture University).

11月28日 -- 056号室, 17:00 -- 18:30

Sang-hyun Kim (Seoul National University)

Diffeomorphism Groups of One-Manifolds

Abstract: Let a>=2 be a real number and k = [a]. We denote by Diff^a(S^1) the group of C^k diffeomorphisms such that the k--th derivatives are Hölder--continuous of exponent (a - k). For each real number a>=2, we prove that there exists a finitely generated group G < Diff^a(S^1) such that G admits no injective homomorphisms into Diff^b(S^1) for any b>a. This is joint work with Thomas Koberda.

12月5日 -- 056号室, 17:00 -- 18:30

川村 一宏 (筑波大学)

Derivations and cohomologies of Lipschitz algebras

Abstract: For a compact metric space M, Lip(M) denotes the Banach algebra of all complex-valued Lipschitz functions on M. Motivated by a classical work of de Leeuw, we define a compact, not necessarily metrizable, Hausdorff space \hat{M} so that each point of \hat{M} induces a derivation on Lip(M). To some extent, \hat{M} may be regarded as "the space of directions." We study, by an elementary method, the space of derivations and continuous Hochschild cohomologies (in the sense of B.E. Johnson and A.Y. Helemskii) of Lip(M) with coefficients C(\hat{M}) and C(M). The results so obtained show that the behavior of Lip(M) is (naturally) rather different than that of the algebra of smooth/C^1 functions on M.

12月12日 -- 056号室, 17:00 -- 18:30

清水 達郎 (京都大学数理解析研究所)

On the self-intersection of singular sets of maps and the signature defect

Abstract: 閉 n 次元有向多様体 M から R^p へのMorin写像と呼ばれるクラスの可微分写像の特異点集合は, M の部分多様体をなすことが知られている. この特異点集合の k 重自己交差が定めるホモロジー類と,M から R^{p+k-1} へのgenericな写像の (Jacobianが) k 階退化した特異点集合が定めるホモロジー類が, 2を法として一致することを示す(ただし n>p+k-2). この事実自体はThom多項式等を用いる方法で間接的に示すことができると思われれるが, 本講演では幾何的な直接の対応を与える. この証明の利点の1つは M が境界を持つ場合に拡張できることである. その応用として3次元多様体の接束の自明化(枠)の不変量である不足符号数と特異点を用いた解釈を与える. ただし,2を法にしている.