## Kyoto Young Topologists Seminar

Date

22th (Mon) July, From 2:00 p.m., 2019

Speaker

David Leturcq (Institut Fourier, Universite Grenoble Alpes)

Title

**
Knot invariants from counting diagrams
**

Abstract

A long knot is an embedding from R into R^3 which follows the z-axis outside a ball. Two such long knots psi and psi' are isotopic if there exists a smooth family (psi_t) of long knots such that psi_0= psi and psi_1=psi'. In this talk, we will explain how to define a long knot isotopy invariant z_2 counting some diagrams with four vertices. The obtained invariant is a Vassiliev invariant and is then connected to the Alexander polynomial. We will explain how to get this relation directly from the diagram counting definition. In the remaining time, we will present the generalization of these objects, methods, and results to higher dimensions or to higher number of vertices.

Venue

Room 206

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Date

19th (Fri.) July, From 3:00 p.m., 2019

Speaker

Tomonori Fukunaga (Kyushu Sangyo University)

Title

**
On convexity of simple closed frontals
**

Venue

Room 006

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Date

3rd July (Wed.) From 1:30 p.m., 2019

Speaker

Toru Yoshiyasu (Kyoto)

Title

**
On Lagrangian embeddings of closed non-orientable 3-manifolds
**

Abstract

I will give new examples of closed non-orientable Lagrangian submanifolds in the standard symplectic 6-space. These Lagrangians are constructed by concatenating a Lagrangian filling and a Lagrangian cap. The existence of a Lagrangian cap is a consequence of Eliashberg-Murphy’s h-principle. The main part of the proof is to construct a Lagrangian filling of a loose Legendrian torus in the standard contact 5-space. After reviewing basics on the h-principle, I will explain the construction.

Venue

Room 402

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Date

28th Feb. and 1st Mar., 2019

Speaker

Koji Yamazaki (Tokyo Tech)

Title

**
Engel Manifolds and Contact Structures
**

Abstract

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.

Speaker

Nobuo Iida(univ. of Tokyo)

Title

**
Bauer-Furuta type refinement of Kronheimer-Mrowka's invariant for
four-manifolds with contact boundary
**

Abstract

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.

Timetable:

28th Feb.

14:00-15:30 Yamazaki(1)

16:00-17:30 Iida(1)

1st Mar.

10:00-11:30 Yamazaki (2)

13:00-14:30 Iida (2)

Venue

Room 110

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Date

13th Feb.(Wed.) From 1:00 p.m., 2019

Speaker

Katsumi Ishikawa (RIMS)

Title

**
Quandle coloring conditions and zeros of the Alexander polynomials
of Montesinos links
**

Abstract

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.

Venue

Room 206

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Date

7th (Fri.) Dec. From 3:00 p.m., 2018

Speaker

Hironobu Naoe (Tohoku univ.)

Title

**
Shadows and Milnor fibrations of divides
**

Abstract

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.

Venue

Room 110

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Date

27th (Mon.) August, 2:30 p.m.-- , 2018

Speaker

Delphine Moussard (RIMS)

Title

**
Torsions of 4-manifolds from trisection diagrams
**

Abstract

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.

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Venue

#478(4th floor of the Research Building no.2 in Yoshida Main campus)

Date

23th (Mon.) July, 2:15 p.m.-- , 2018

Speaker

Sakie Suzuki (Tokyo Tech)

Title

**
Factorizations of the universal R matrix and the universal quantum
invariant for framed 3-manifolds
**

Abstract

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.)

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Venue

110 @RIMS main building

Date

25th(Mon.) June, 13:00 -- , 2018

Speaker

Yusuke Inagaki(Osaka)

Title

**
Anosov representations and their deformation spaces
**

Abstract

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.

HP：http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Venue

Room #478(4th floor of the Research Building no.2 in Yoshida Main campus).