● Invited Speakers
-김 상 현 (KAIST)
-박 재 석 (연세대)
-변 양 현 (한양대)
-송 용 진 (인하대)
-윤 기 헌 (성신여대)
-조 철 현 (서울대)
-최 수 영 (오사카시립대)
-최 영 기 (서울대)

● 일정 및 장소
-2010년 8월 3일 ~4일
-KAIST 자연과학동 E 6-1(#3433)

● 주관자
-서 동 엽 (KAIST)
-송 용 진 (인하대)

● 주최
-대한수학회, 대수구조 및 응용연구센터

※ 참가하는 학생들에게 숙식을 제공합니다.
※ 대학원생들을 위한 강의 및 대학원생들의 발표 위주로 프로그램이 구성됩니다.

발표내용

김상현 (KAIST)

Introduction to Non-Positively Curved Groups I, II
We will survey applications of non-positive curvature to group theory. The first lecture will deal with the geometry of non-positively curved spaces; this includes Cartan--Hadamard theorem, π1-injectivity and Gromov's criteria for non-positive curvature of metric cell complexes. The second lecture will have more group theoretic questions in mind. As a key example of non-positively curved groups, we study right-angled Artin groups (RAAGs). Using techniques developed in the first lecture, we will investigate hyperbolic 2- and 3-manifold subgroups in RAAGs.

박재석 (연세대학교)

Quantum homotopy theory I, II
Physicists assume that the physical reality is governed by quantum principle such that any classical physical entity is just an approximated or derived notion.
In this philosophy the essential properties of classical world should have quantum origin and, thus, be explained via quantum prospective.
The similar viewpoint could be adapted, and may proved to be useful, to study certain mathematical structure, provided that it can be described by the mathematics of certain classical physics admitting certain mathematically well-defined quantization. In this lecture homotopy theory shall be such an example.

Math Background: Prof. Cheolhyun's lectures on Homological vector field and
algebraic structures.
Phys Background: Nothing specific.

박희숙(KAIST)

Introduction to the theory of bounded cohomology
We introduce the theory of bounded cohomology and compare it with ordinary cohomology. We also investigate some known facts on bounded cohomology.

변양현 (한양대학교)

An Introduction to ASD instantons and holomorphic Structures
이 강의는 connection의 정의로부터 출발하여 ASD 인스탄톤을 소개하는 것으로부터 시작한다. 이어서 복소다양체 위의 complex 벡터 번들의 holomorphic 구조를 partial connection이라는 도구를 통해 소개하고, 2차원 Kahler 다양체 위에서 ASD 인스탄톤과 holomorphic 구조와의 관계를 소개함으로써 이 강의가 목표로 하는 기본지식의 소개를 마친다. 강의의 맺음말은 최근에 수학자들이 관심을 두고 있는 이 분야의 문제를 하나 소개하는 것으로 한다.

윤기헌 (성신여자대학교)

Lefschetz fibration and symplectic 4-manifolds
Lefschetz fibration과 symplectic 4-manifold의 관계를 살펴본 후, Lefschetz fibration을 이용하여 4차원 위상수학에서 얻은 결과들을 소개한다.

조철현 (서울대학교)

Homological vector fields and algebraic structures
Algebraic structures such as associative algebras, Lie algebras and their modules is known to correspond to certain vector fields Q with the property [Q,Q]=0. In fact, such framework provide naturally generalized notions such as homotopy algebras, Lie algebroids and so on. We give an elementary introduction of such correspondence. If time remains, the relation between the de Rham theory and homology theories of these algebraic structures such as Hochschild or Chevalley-Eilenberg homology theory will be explained.

조철현 (서울대학교)

Orbibundle and Multisection
Euler class of a vector bundle can be given by the zero set of a
generic (transversal) section. Multisections were introduced to resolve transversality issues for orbifold vector bundles, as the equivariancy and transversality cannot be satisfied at the same time in many cases. We give a basic introduction to these notions.

최수영 (오사카시립대학)

Real Bott manifolds and acyclic digraphs
A real Bott manifold is a closed smooth manifold obtained as the total space of an iterated RP^1-bundles starting with a point, where each RP^1-bundle is the projectivization of the Whitney sum of two real line bundles. The diffeomorphism types of real Bott manifolds can be completely characterized in terms of three simple matrix operations on square binary matrices symmetrically permutable to strict upper triangular form.
This characterization can be visualized combinatorially in terms of graph operations on directed acyclic graphs. Using this combinatorial interpretation, we prove that the decomposition of a real Bott manifold into a product of indecomposable real Bott manifolds is unique up to permutations of the indecomposable factors, and prove that the toral rank conjecture holds for almost free torus action on real Bott manifolds.
This talk is based on a part of joint work with M. Masuda(OCU) and S. Oum(KAIST).

최영기 (서울대학교)

Homotopy theoretic view point of based loop space and free loop space
The relationship between the closed geodesic of compact Riemannian manifold M and the homology of the loop spaces of ¬M was developed by Marston Morse around 1930. Ever since it has become the main topic in the algebraic topology.
The purpose of this talk is to discuss the (co)homology and the homotopy type of based loop space and free loop space of compact Lie groups and homogeneous spaces.

김병천(인하대학교)

Homotopy Three-fold branched covering spaces over a disk

김동희(연세대학교)

Maurer-Cartan equation

김선화 (서울대학교)

Yokota theory on ideal triangulation and volume of hyperbolic knot