山口 睦 (大阪府立大学)
Representations of the group represented by the dual Steenrod algebra スライド
We begin this talk by reviewing the definition of representations of group objects in a category with finite products in terms of fibered category. Then, we introduce a notion of "cartesian closed fibered category" which generalizes the notion of cartesian closed category. We show that "cartesian closed fibered categories" enable us to construct (right) induced representations of group objects, which will be applied to study representations of the (topological) affine group scheme represented by the dual Steenrod algebra.
15:50−16:40
南 範彦 (名古屋工業大学)
From the periodic table of chemical elements to Ohkawa's theorem on the Bousfield classes in the stable homotopy category
The famous theorem of late Dr. Tetsusuke Ohkawa states that the Bousfield classes in the stable homotopy category forms a set. This surprising theorem reflects Ohkawa's brilliant talent in abstract mathematics, but, when Ohkawa was a kid, he was a not only a prodigy of mathematics, but also of chemistry. a chemical engineer and he was raised surrounded by chemical literatures. For Ohkawa, the essence of chemistry, the periodic table of elements, was just one of picture books for kids!
In this talk, I shall indicate some similarities between the underlying mathematical structures of the periodic table of chemical elements and Ohkawa's theorem.
17:00−17:50
松岡 拓男
Higher coherence and a generalization of higher categorified algebraic structures スライド
Discovery or recognition of the right kind of algebraic structure is often important in the development of mathematical subjects. We consider algebraic structures in higher categorical contexts, in view of the presence around various subjects, of higher categorical structures such as some related to topological field theories. We show that increase in the categorical dimension leads to possibility of enrichment of structures in quite non-traditional places. A structure to be such a place, naturally generalizing a higher categorified structure, is found as controlling algebraic structures of a specific kind, as an operad does, but is a finer structure in general than a coloured operad, with high categorical dimensionality. The technical basis for these is inductivity embedded in the structure of the coherence for higher associativity. We would like to show how examples arise naturally.
11月13日 (日)
09:00−09:50
内藤 貴仁 (東京大学)
The loop homology of rationally elliptic manifolds
Sullivan introduced a coproduct on the reduced loop homology and showed that the homology has an infinitesimal bialgebra structure with respect to the coproduct and Chas-Sullivan loop product. In this talk, I will talk about the coproduct of rationally elliptic manifolds. I will also introduce based loop space version of the coproduct and discuss triviality or non-triviality of the structure.
10:10−11:00
蔦谷 充伸 (九州大学)
Coincidence Reidemeister trace and its generalization
Reidemeister trace is a homotopy invariant of a self map and a refinement of the Lefschetz number. Lefschetz number was generalized for a coincidence of two maps between manifolds. In this talk, we give a construction of the corresponding Reidemeister trace, which is realized as a homology class of the homotopy equalizer. In the construction, shriek maps appearing in string topology play an important role. We also give a technique to compute the Reidemeister trace using Serre spectral sequences.
11:20−12:10
亀子 正喜 (芝浦工業大学)
On the 4th integral cohomology of the classifying space of a connected Lie group
The 4th integral cohomology of the classifying space $BG$ of a connected Lie group $G$ plays an important role in algebraic and arithmetic geometry. I will talk about some problems in algebraic and arithmetic geometry related with the 4th integral cohomology of $BG$. Starting with the counterexamples for the integral Hodge conjecture by Atiyah and Hirzebruch in 1962 and those for the integral Tate conjecture over finite fields by Colliot-Thélène and Szamuely in 2010, I will talk about recent results on the integral Hodge and Tate conjectures modulo torsion obtained by Pirutka, Yagita, Antieau, Tripathy and myself.
13:30−14:20
Kathryn Lesh (Union College),
Julia E. Bergner (University of California),
Ruth Joachimi (University of Wuppertal),
Vesna Stojanoska (Cambridge),
Kirsten Wickelgren (Georgia Institute of Technology)
Fixed points of $p$-toral subgroups acting on decomposition spaces
Decompositions of complex $n$-space into proper orthogonal subspaces form a (topological) poset with a natural action of the unitary group. I will discuss fixed point spaces of $p$-toral subgroups of $U(n)$ on the nerve of this poset. I will show that most of them are actually contractible. This is recent progress in joint work with Bergner, Joachimi, Stojanoska, and Wickelgren.
14:40−15:30
劉 曄 (北海道大学),
秋田 利之 (北海道大学)
Second mod 2 homology of Artin groups
In this talk, after a survey on known results concerning the $K(\pi,1)$ conjecture and homology of Artin groups, I will introduce a new result, that is a formula of the second mod 2 homology of an arbitrary Artin group, without assuming the $K(\pi,1)$ conjecture is true. This is joint work with Toshiyuki Akita.
15:50−16:40
秋田 利之 (北海道大学)
On the mod p cohomology of Coxeter groups and their alternating subgroups
In this talk, I will introduce our results on vanishing ranges for the mod p cohomology of Coxeter groups and alternating subgroups of finite Coxeter groups. The latter is a joint work with Ye Liu.
17:00−17:50
宮内 敏行 (福岡大学),
向井 純夫 (信州大学),
Marek Golasiński (University of Warmia and Mazury)
Gottlieb groups of some mod 2 Moore spaces
The Gottlieb group is an important subgroup of the homotopy group. In this talk, I will explain how to calculate Gottlieb groups of mod 2 Moore spaces. I will also introduce our results.
11月14日 (月)
09:00−09:50
松下 尚弘 (京都大学)
On the universality problem of the Hom complexes of graphs
A quasitoric manifold is a $2n$-dimensional smooth manifold with a locally standard action of the compact torus $T^n$, for which the orbit space is identified with a simple polytope. For instance, $\mathbb{C}P^n$ is a quasitoric manifold over the simplex $\Delta^n$, and a Hirzebruch surface, a $\mathbb{C}P^1$-bundle over $\mathbb{C}P^1$ defined as the projectivization $P(L\oplus\mathbb{C})$ for some line bundle $L$ over $\mathbb{C}P^1$, is a quasitoric manifold over the square $I^2$. Such ``bundle-type'' quasitoric manifolds, like Hirzebruch surfaces, have been studied by many toric topologists, but not yet been formulated definitely. In this talk, I will establish the notion of bundle-type quasitoric manifold, and give some new classification results on them.
A Hessenberg variety is a subvariety of a flag variety and is defined by some good subset of the root system of the corresponding Lie group. We show an interesting relation between its cohomology ring and the hyperplane arrangement on the Lie algebra of the maximal torus corresponding with the subsets of roots. This relation is interpreted as an extension of Borel's work on the cohomology rings of flag varieties. This is a joint work with T. Abe, T. Horiguchi, M. Masuda, and S. Murai.