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i-CMC Workshop

(Interdisciplinary meeting of the CMC members)

 

Date: July 24~25, 2014,           Place: KIAS CMC 4fl.Semiar room  

 
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  [Schedule]




[Title and Abstracts] 

Sungwoon Kim
Title
Bounded cohomology and rigidity theory.
Abstract
Bounded cohomology is very useful to establish rigidity results. In this talk, I will review some definitions and results about bounded cohomology and then explain how to apply bounded cohomology theory to obtain rigidity results. Furthermore, some open questions will be presented.
 
Jinwon Choi
Title
Enumerative geometry and moduli problems
Abstract
Enumerative geometry is a branch of algebraic geometry concerned with counting numbers of solutions to geometric questions. It is an old subject studied and revisited extensively over the past 150 years. In this talk, we introduce elementary enumerative problems and classical/modern approaches by means of the moduli spaces and the intersection theory. The main focus will be on the curve counting theories.

Jaejeong Lee
Title
Introduction to hyperbolic geometry via Klein projective model
Abstract
Using the synthetic method I will explain some of the elementary constructions in hyperbolic geometry, for example, isometries, product of isometries, and moduli of certain group of isometries.


Mario Chan
Title
Holomorphic line bundles on complex manifolds and transcendental methods
Abstract
Holomorphic line bundle is one of the fundamental objects of study in algebraic geometry. Despite being algebraic in nature, applying transcendental methods in the study of this object is often effective in solving some problems around it. In this talk, some typical questions concerning a holomorphic line bundle on a complex manifold as well as how some transcendental methods (namely, solving -  equations with or without singular weight) can be applied to deal with such questions are discussed.


Soyeun Jung
Title
Introduction to the stability of periodic traveling waves
Abstract
Stability of solutions is one of the fundamental topics in PDE. In particular, we focus on the stability of periodic traveling waves (wavetrain). Traveling waves are solutions to partial differential equations that move with constant speed while maintaining their shape. Linearization of the PDEs about a given solution is a natural approach to the study of stability of the solution. In this talk, we introduce pointwise bounds on the Green function of the linear operator by using its spectral information.


Kyungyong Lee
Title
Introduction to canonical bases
Abstract
Algebras that arise in the geometric Langlands program and representation theory often admit canonical bases. These bases are expected to satisfy good algebraic/geometric/topological/combinatorial properties. We introduce the desired properties in elementary languages.