[English]

Tea: 16:00 -- 16:30 コモンルーム

世話係

河野 俊丈

河澄 響矢

逆井 卓也

4月8日 -- 056号室, 16:30 -- 18:00

正井 秀俊 (東京大学大学院数理科学研究科)

Abstract: By work of Thurston, it is known that if a hyperbolic fibred 3-manifold M has Betti number greater than 1, then M admits infinitely many distinct fibrations. For any fibration ω on a hyperbolic 3-manifold M, the number of fibrations on M that are commensurable in the sense of Calegari-Sun-Wang to ω is known to be finite. In this talk, we prove that the number can be arbitrarily large.

4月15日 -- 056号室, 16:30 -- 18:00

内藤 貴仁 (東京大学大学院数理科学研究科)

Abstract: Chataur and Menichi initiated the theory of string topology of classifying spaces. In particular, the cohomology of the free loop space of a classifying space is endowed with a product called the dual loop coproduct. In this talk, I will discuss the algebraic structure and relate the rational dual loop coproduct to the cup product on the Hochschild cohomology via the Van den Bergh isomorphism.

5月13日 -- 056号室, 16:30 -- 18:00

足助 太郎 (東京大学大学院数理科学研究科)

Abstract: Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class with respect to the family. The derivative is known to be represented in terms of the projective Schwarzians of holonomy maps. In this talk, we will study transverse projective structures and connections, and show that the derivative is in fact determined by the projective structure and the family.

5月20日 -- 056号室, 16:30 -- 18:00

黒木 慎太郎 (東京大学大学院数理科学研究科)

Abstract: A torus manifold is a compact, oriented 2n-dimensional T^n- manifolds with fixed points. This notion is introduced by Hattori and Masuda as a topological generalization of toric manifolds. For a given torus manifold, we can define a labelled graph called a torus graph ( this may be regarded as a generalization of some class of GKM graphs). It is known that the equivariant cohomology ring of some nice class of torus manifolds can be computed by using a combinatorial data of torus graphs. In this talk, we study which torus action of torus manifolds can be extended to a non-abelian compact connected Lie group. To do this, we introduce root systems of (abstract) torus graphs and characterize extended actions of torus manifolds. This is a joint work with Mikiya Masuda.

5月27日 -- 056号室, 16:30 -- 18:00

藤川 英華 (千葉大学大学院理学研究科)

Abstract: We explain recent developments of the theory of infinite dimensional Teichmüller space. In particular, we observe the dynamics of the orbits by the action of the stable quasiconformal mapping class group on the Teichmüller space and consider the relationship with the asymptotic Teichmüller space. We also introduce the generalized fixed point theorem and the Nielsen realization theorem. Furthermore, we investigate the moduli space of Riemann surface of infinite type.

6月3日 -- 056号室, 16:30 -- 18:00

高倉 樹 (中央大学・理工学部)

Abstract: A multiple weight variety is a symplectic quotient of a direct product of several coadjoint orbits of a compact Lie group G, with respect to the diagonal action of the maximal torus. Its geometry and topology are closely related to the combinatorics concerned with the weight space decomposition of a tensor product of irreducible representations of G. For example, when considering the Riemann-Roch index, we are naturally lead to the study of vector partition functions with multiplicities. In this talk, we discuss some formulas for vector partition functions, especially a generalization of the formula of Brion-Vergne. Then, by using them, we investigate the structure of the cohomology of certain multiple weight varieties of type A in detail.

6月10日 -- 056号室, 14:40 -- 16:10

Sergei Duzhin (Steklov Institute of Mathematics)

Abstract: We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology thus proving a conjecture raised in 1987 by J.Przytycki. A knot is said to be bipartite if it has a "matched" diagram, that is, a plane diagram that has an even number of crossings which can be split into pairs that look like a simple braid on two strands with two crossings. The conjecture was that there exist knots that do not have such diagrams. I will prove this fact using higher Alexander ideals. This talk is based on a joint work with my student M.Shkolnikov.

6月10日 -- 056号室, 16:30 -- 18:00

小鳥居 祐香 (東京大学大学院数理科学研究科)

Abstract: Milnor introduced a family of invariants for ordered oriented link, called $\bar{\mu}$-invariants. Polyak showed a relation between the $\ bar{\mu}$-invariant of length 3 sequence and Conway polynomial. Moreover, Habegger-Lin showed that Milnor's invariants are invariants of string link, called $\mu$-invariants. We show that any $\mu$-invariant of length $\leq k$ can be represented as a combination of HOMFLYPT polynomials if all $\mu$-invariant of length $\leq k-2$ vanish. This result is an extension of Polyak's result.

6月17日 -- 002号室, 16:30 -- 18:00

松田 能文 (青山学院大学)

Abstract: Burger，Iozzi，Wienhardは連結かつ向き付けられた有限型の穴あき曲面の基本群 の円周への作用に対して有界オイラー数を定義した．有界オイラー数を含むMilnor-Wood型 の不等式が成立しその最大性はフックス作用を準共役を除いて特徴付ける．被覆を考えること により有界オイラー数の定義は2次元軌道体群の作用に対して拡張される．Milnor-Wood型の 不等式およびフックス作用の特徴付けはこの場合にも成立する．この講演では，モジュラー群 などのいくつかの2次元軌道体群のフックス作用の持ち上げがいつ有界オイラー数により特徴 づけられるかについて記述する．

6月24日 -- 056号室, 17:10 -- 18:10

野坂 武史 (九州大学数理学研究院)

Abstract: 本講演では, 群とその群同型の組から定まるカンドルを扱い, 以下の結果を紹介 する. まず, その際Inoue-Kabaya鎖写像が, カンドルホモロジーから群ホモロ ジーへの写像とし, 定式化される事を見る. 例えば, 有限体上のAlexander quandleに対し, 望月3-コサイクル全ては, 当写像を通じ, 或る群コホモロジー から導出され, 殆どがトリプルマッセイ積で解釈できる事をみる. 加えてカンド ルの普遍中心拡大に対し, Inoue-Kabaya鎖写像が３次において(或る捩れ部分を 除き)同型となる. なお講演内容は当週にある集中講義の聴講を仮定しない.

7月1日 -- 056号室, 16:30 -- 18:00

今城 洋亮 (Kavli IPMU)

Abstract: There are interesting invariants defined by "counting" geometric objects, such as instantons in dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do the counting in a sensible way, however, we have to care about singularities of the geometric objects. Special Lagrangian submanifolds seem very difficult to "count" as their singularities may be very complicated. I'll talk about simple singularities for which we can make an analogy with instantons in dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do it I'll use some techniques from geometric measure theory and Lagrangian Floer theory, and the Floer-theoretic part is a joint work with Dominic Joyce and Oliveira dos Santos.

7月8日 -- 056号室, 16:30 -- 18:00

Ingrid Irmer (JSPS, 東京大学大学院数理科学研究科)

Abstract: A family of curve graphs of an oriented surface S

7月22日 -- 056号室, 16:30 -- 18:00

Jesse Wolfson (Northwestern University)

Abstract: In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.

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