Kyoto Young Topologists Seminar
28th Feb. and 1st Mar., 2019
Koji Yamazaki (Tokyo Tech)
Engel Manifolds and Contact Structures
A completely non-integrable 2-distribution on a 4-manifold is called an Engel structure. An Engel manifold is a manifold equiped with an Engel structure. Engel manifolds are very similar and closely related to contact manifolds. In this seminar, we follow R. Montgomery's tequniques with the characteristic foliation, the Cartan prolongation and the development map. Moreover, we give the later application of that including my result.
Nobuo Iida(univ. of Tokyo)
Bauer-Furuta type refinement of Kronheimer-Mrowka's invariant for four-manifolds with contact boundary
The Seiberg-Witten invariant is an invariant for closed
4-manifolds and there are many variants of it.I construct a new variant of
the Seiberg-Witten invariant based on two previous works. First, Bauer and
Furuta refined the Seiberg-Witten invariant, and made an invariant called
the stable cohomotopy invariant, which is an S^1-equivariant stable
homotopy map obtained by Furuta's finite dimensional approximation of the
Seiberg-Witten map. Second, Kronheimer and Mrowka defined a variant of the
Seiberg-Witten invariant for 4-manifolds with contact boundary. I combine
these two variants of the Seiberg-Witten invariant; that is, using
Furuta's finite dimensional approximation, I refine Kronheimer-Mrowka's
invariant for 4-manifolds with contact boundary.
10:00-11:30 Yamazaki (2)
13:00-14:30 Iida (2)
13th Feb.(Wed.) From 1:00 p.m., 2019
Katsumi Ishikawa (RIMS)
Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links
We give a simple condition for the existence of a nontrivial quandle coloring on a Montesinos link, which describes the distribution of the zeros of the Alexander polynomial. By this condition, we show the existence of infinitely many counterexamples for Hoste's conjecture.
7th (Fri.) Dec. From 3:00 p.m., 2018
Hironobu Naoe (Tohoku univ.)
Shadows and Milnor fibrations of divides
A’Campo introduced a divide as a generalization of real morsified curves of complex plane curve singularities. A’Campo showed that the link of a connected divide is fibered, moreover such a fibration comes from the “boundary” of a Lefschetz fibration. We interpret them in terms of Turaev' s shadows. This is a joint work with Masaharu Ishikawa.
27th (Mon.) Aug. 2:30 p.m.-- , 2018
Delphine Moussard (RIMS)
Torsions of 4-manifolds from trisection diagrams
We will see how to compute the (non-)twisted homology, the
(non-)twisted intersection form and the abelian torsions of a 4-manifold
from a trisection diagram. This is a joint work with Vincent Florens.
#478(4th floor of the Research Building no.2 in Yoshida Main campus)
23th (Mon.) July, 2:15 p.m.-- , 2018
Sakie Suzuki (Tokyo Tech)
Factorizations of the universal R matrix and the universal quantum invariant for framed 3-manifolds
Take the Drinfeld double D(B) of the Borel subalgebra B of the
quantized enveloping algebra Uq(sl2) of sl2. We consider two embeddings of
D(B) as an algebra, into a double of Heisenberg double and into a quantum
torus algebra. With both embeddings, each image of the universal R matrix
has a factorization into a product of four elements each satisfying a
pentagon relation. This setting leads us to the Kashaev invariant of links
and to quantum Teichmuller* theory . In this talk I will explain these
situations and show our trials to unify these studies in a view point of
the universal S tensor and framed 3-manifolds. This talk includes a joint
work with Y. Terashima.
(*: "u" is u-Umlaut.)
110 @RIMS main building
25th(Mon.) June, 13:00 -- , 2018
Anosov representations and their deformation spaces
Anosov representations are representations of Gromov hyperbolic
groups into higher rank Lie groups with a dynamical property. These
representations have been introduced by Labourie, and studied in the
viewpoint of a generalization of Kleinian groups. In this talk, we review
the definition and remarkable properties of Anosov representations, and
discuss examples of their deformation spaces, called Hitchin components.
Room #478(4th floor of the Research Building no.2 in Yoshida Main campus).