[English]

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102ϊ -- 056Ί, 17:00 -- 18:30

ιΈ (εwεw@Θw€Θ)

Abstract: An MOY graph is a trivalent graph equipped with a balanced coloring. In this talk, we define a version of Alexander polynomial for an MOY graph. This polynomial is the Euler characteristic of the Heegaard Floer homology of an MOY graph. We give a characterization of the polynomial, which we call MOY-type relations, and show that it is equivalent to Virofs gl(1 | 1)-Alexander polynomial of a graph. (A part of the talk is a joint work of Zhongtao Wu)

109ϊ -- 056Ί, 17:00 -- 18:30

Boris Hasselblatt (Tufts University)

Abstract: A refinement of Dehn surgery produces new contact flows that are unusual and interesting in several ways. The geodesic flow of a hyperbolic surface becomes a nonalgebraic contact Anosov flow with larger orbit growth, and the purely periodic fiber flow becomes parabolic or hyperbolic. Moreover, Reeb flows for other contact forms for the same contact structure have the same complexity. Finally, an idea by Vinhage promises a quantification of the complexity increase.

1016ϊ -- 056Ί, 17:00 -- 18:30

Daniel Matei (IMAR Bucharest)

Abstract: We discuss the resonance varieties, encoding vanishing of cohomology cup products, of various classes of finitely presented groups of geometric and combinatorial origin. We describe the ideals defining those varieties in terms spanning trees in a similar vein with the classical matrix tree theorem in graph theory. We present applications of this description to 3-manifold groups and Artin groups.

1023ϊ -- 056Ί, 17:00 -- 18:30

François Fillastre (Université de Cergy-Pontoise)

Abstract: There are many ways to parametrize two copies of Teichmueller space by constant curvature -1 Riemannian or Lorentzian 3d manifolds (for example the Bers double uniformization theorem). We present the co-Minkowski space (or half-pipe space), which is a constant curvature -1 degenerated 3d space, and which is related to the tangent space of Teichmueller space. As an illustration, we give a new proof of a theorem of Thurston saying that, once the space of measured geodesic laminations on a compact hyperbolic surface is identified with the tangent space of Teichmueller space via infinitesimal earthquake, then the length of laminations is an asymmetric norm. Joint work with Thierry Barbot (Avignon).

1030ϊ -- 056Ί, 17:00 -- 18:30

uκ [¬ (HΖεw)

Abstract: In the theory of Teichmüller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally equivalent or not. On the other hand, for Riemann surfaces of topologically infinite type, the situation is rather complicated.

In this talk, after constructing an example which shows the complexity of the problem,
we give some geometric conditions for Riemann surfaces to be quasiconformally equivalent.
Our argument enables us to see a universality of Schottky spaces.

116ϊ -- 056Ί, 17:30 -- 18:30

φ Vκ (€Qεw)

Abstract: A coarse version of negatively-curved spaces have been very well studied as Gromov hyperbolic spaces. Recently we introduced a coarse version of non-positively curved spaces, named them coarsely convex spaces and showed a coarse version of the Cartan-Hadamard theorem for such spaces in a joint-work with Tomohiro Fukaya (arXiv:1705.05588). Based on the work, I introduce coarsely convex spaces and explain a coarse Cartan-Hadamard theorem, ideas for proof and its applications to differential topology.

118ϊ(Ψ) JΓϊ, Ι²ΣΊ³’ -- 056Ί, 10:30 -- 12:00

Michael Heusener (Université Clermont Auvergne)

Abstract: This is joint work with Leila Ben Abdelghani, Monastir (Tunisia). Given a manifold $M$, the variety of representations of $\pi_1(M)$ into $\mathrm{SL}(2,\mathbb{C})$ and the variety of characters of such representations both contain information of the topology of $M$. Since the foundational work of W.P.\ Thurston and Culler \& Shalen, the varieties of $\mathrm{SL}(2,\mathbb{C})$-characters have been extensively studied. This is specially interesting for $3$-dimensional manifolds, where the fundamental group and the geometrical properties of the manifold are strongly related. However, much less is known of the character varieties for other groups, notably for $\mathrm{SL}(n,\mathbb{C})$ with $n\geq 3$. The $\mathrm{SL}(n,\mathbb{C})$-character varieties for free groups have been studied by S.~Lawton and P.~Will, and the $\mathrm{SL}(3,\mathbb{C})$-character variety of torus knot groups has been determined by V.~Munoz and J.~Porti. In this talk I will present some results concerning the deformations of diagonal representations of knot groups in basic notations and some recent results concerning the representation and character varieties of $3$-manifold groups and in particular knot groups. In particular, we are interested in the local structure of the $\mathrm{SL}(n,\mathbb{C})$-representation variety at the diagonal representation.

1113ϊ -- 056Ί, 17:00 -- 18:30

³δ Gr (HΖεw)

Abstract: When a group is acting on a space isometrically, we may consider the "translation distance" of random walks, which is called the drift of the random walk. In this talk we consider mapping class group acting on the Teichmüller space. We first recall several characterizations of the drift. The drift is determined by the transition probability of the random walk. The goal of this talk is to show that the drift varies continuously with the transition probability measure.

1120ϊ -- 056Ί, 17:00 -- 18:30

tδ μη (εwεw@Θw€Θ)

Abstract: There are two filtrations of the Torelli group: One is the lower central series and the other is the Johnson filtration. They are closely related to Johnson homomorphisms as well as finite type invariants of homology 3-spheres. We compare the associated graded Lie algebras of the filtrations and report our explicit computational results. Then we discuss some applications of our computations. In particular, we give an explicit description of the rational abelianization of the Johnson kernel. This is a joint work with Shigeyuki Morita and Masaaki Suzuki.

1127ϊ -- 056Ί, 17:00 -- 18:00

Α‘ {q (εwεw@Θw€Θ)

Abstract: In this talk, we introduce a fixed point property of groups which is a broad generalization of Serre's property FA, and give a criterion for groups to have such a property. We also apply the criterion to show that various generalizations of Thompson's group T have fixed points whenever they act on finite dimensional non-positively curved metric spaces, including CAT(0) spaces. Since Thompson's group T is known to have fixed point free actions on infinite dimensional CAT(0) spaces, it follows that there is a group which acts on infinite dimensional CAT(0) spaces without global fixed points, but not on finite dimensional ones.

124ϊ -- 056Ί, 17:00 -- 18:30

Vincent Florens (Université de Pau et des Pays de l'Adour)

Abstract: We define the slope of a link associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a multivariate generalization of the Kojima-Yamasaki η-function. It is the ratio of two Conway potentials, provided that the latter makes sense; otherwise, it is a new invariant. We present several examples and discuss the invariance by concordance. Joint with A. Degtyarev and A. Lecuona.

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