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Kyoto Young Topologists Seminar

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

Organizer Organizers: Takahiro Oba (RIMS) , Kenta Okazaki (RIMS), Tatsuro Shimizu (RIMS)
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

Organizer Organizers: Takahiro Oba (RIMS) , Kenta Okazaki (RIMS), Tatsuro Shimizu (RIMS)
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

Organizer Organizers: Takahiro Oba (RIMS) , Kenta Okazaki (RIMS), Tatsuro Shimizu (RIMS)
HP:http://www.kurims.kyoto-u.ac.jp/~shimizu/YTS.html

Date

27th (Mon.) Aug. 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)

Organizer Delphine Moussard(RIMS), Kenta Okazaki(RIMS), Tatsuro Shimizu(RIMS)

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

Organizer Delphine Moussard(RIMS), Kenta Okazaki(RIMS), Tatsuro Shimizu(RIMS)

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).

Organizer Delphine Moussard(RIMS), Kenta Okazaki(RIMS), Tatsuro Shimizu(RIMS)

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