제 2회 Topology Workshop

 

8월 17일(월)-19일(수)

장소: #1501, E6-1, KAIST

 

Invited Speaker

김태희(건국대) 서동엽(KAIST)

송용진(인하대) 이종범(서강대)

정규락(KIAS) 조윤희(서울시립대)

조장현(경상대) 조진석(서울대) 함지영(서울대)

 

주관: 송용진(인하대학교), 서동엽(KAIST)

 

 

문의:

송용진 : yjsong@inha.ac.kr, HP : 011-477-9294

김윤옥 : yokim@kaist.ac.kr, Tel : 042-350-8111

 

☞ Poster

 

 PROGRAM The second TOPOLOGY WORKSHOP

August 17 -19, 2009, KAIST

 

8월 17일 (월)

 

1:00 – 1:15 등록 및 개회식

1:15 – 2:00 서동엽(KAIST)

Bott towers and cohomological rigidity I

A Bott tower is a sequence of CP1-bundles Bi over Bi-1. Each Bi is a called the i-th stage Bott manifold. One 

can extend this definition to define a generalized Bott tower and manifold to be a sequence of complex space

bundles. One of the interesting question in toric topology asks whether two (generalized) Bott manifolds Bn

and Bn' are homeomorphic (or diffeomorphic) provided their cohomologies are isomorphic as graded rings.

 This is called the cohomological rigidity question} for (generalized) Bott manifolds. In this talk we discuss

some related back ground material from toric theory and some positive results on the question.

2:15 – 3:00 이종범(서강대학교)

Averaging formula for Nielsen numbers I

We show that the averaging formula for Nielsen numbers holds for continuous maps on infranilmanifolds, and

infra-solvmanifolds of type (R). We illustrate by examples how practical the formula is.

3:15 – 4:00 정규락(KIAS)

Derived (or Homotopy) categories and derived functors I

Mathematical invariants may be represented as fuctors from categories to categories but many invariants are

 homotopy invariants. So we consider their derived categories and their derived functors instead. I will explain

 this process and give some examples.

4:15 – 5:00조장현(서강대학교)

Finitely dominated spaces and projective modules I

In this talk, I will survey various results in the topic indicated by the title and introduce its related several

algebraic or topological conjectures. I will also present various topics such as finiteness conditions of groups,

 L2-invariants, and etc.

5:15 – 6:00 조장현(서강대학교)

Finitely dominated spaces and projective modules II

In this talk, I will survey various results in the topic indicated by the title and introduce its related several

 algebraic or topological conjectures. I will also present various topics such as finiteness conditions of

groups, L2-invariants, and etc. 6:30 회식 (Dinner)

 

 

8월 18일 (화)

9:15-10:00 서동엽(KAIST)

Bott towers and cohomological rigidity II

A Bott tower is a sequence of CP1-bundles Bi over Bi-1. Each Bi is a called the i-th stage Bott manifold. One

 can extend this definition to define a generalized Bott tower and manifold to be a sequence of complex space

 bundles. One of the interesting question in toric topology asks whether two (generalized) Bott manifolds Bn

 and Bn' are homeomorphic (or diffeomorphic) provided their cohomologies are isomorphic as graded rings.

This is called the cohomological rigidity question} for (generalized) Bott manifolds. In this talk we discuss

some related back ground material from toric theory and some positive results on the question.

2:15 – 3:00 이종범(서강대학교)

Averaging formula for Nielsen numbers II

We show that the averaging formula for Nielsen numbers holds for continuous maps on infranilmanifolds,

and infra-solvmanifolds of type (R). We illustrate by exampleshow practical the formula is.

11:15-12:00 정규락(KIAS)

Derived (or Homotopy) categories and derived factors II

Mathematical invariants may be represented as fuctors from categories to categories but many invariants are

homotopy invariants. So we consider their derived categories and their derived functors instead. I will explain

 this process and give some examples.

 

12:00-1:00 점심

 

1:00~ 단체 관광 (Excursion) 장소: 부여

 

8월 19일 (수)

9:30-10:15 조진석(서울대학교)

Kashaev invariant

We will briefly overview some basic theory of knots and quantum invariants. As an example of quantum

invariants, we will define the Kashaev invariant of a knot.

 

10:30-11:15 조진석(서울대학교)

Kashaev's volume conjecture Kashaev conjectured that the limit of the Kashaev invariant of a knot gives

the hyperbolic volume of the knot complement. We will overview some geometric meanings of the Kashaev

 invariant following Yokota theory. Some recent improvements in the volume conjecture will be briefly

discussed.

11:30-12:15 조윤희(서울시립대학교)

Problems in extended hyperbolic space I

We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter

space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. We discuss

extended Kleinian model and extended Poincare model. And we discuss the advantages of this new

geometric model as well as some of its applications and problems.

 

12:15-1:45 Lunch

1:45-2:30 김태희(건국대학교)

Reidemeister torsion and homology cylinders I

In these two lectures, we will discuss Reidemeister torsion and its application to homology cylinders over a

 surface. In the first lecture, an algebraic definition of Reidemeister torsion will be given, and we will study its

basic properties. Using these, in the second lecture we will show that the homology cobordism group of

 homology cylinders over a surface has nontrivial abelian quotients, which is joint work with Jae Choon Cha

 and Stefan Friedl.

2:45-3:30 김태희(건국대학교)

Reidemeister torsion and homology cylinders II

In these two lectures, we will discuss Reidemeister torsion and its application to homology cylinders over

a surface. In the first lecture, an algebraic definition of Reidemeister torsion will be given, and we will study

its basic properties. Using these, in the second lecture we will show that the homology cobordism group of

homology cylinders over a surface has nontrivial abelian quotients, which is joint work with Jae Choon Cha

and Stefan Friedl.

3:45-4:30 함지영(서울대학교)

Volumes of hyperbolic cone-manifolds of knot 6_1