Title   name
Intensive Lectures:A study on smooth 4-manifolds
  Speaker   Park, Jongil    
  Date 2012-01-20
  Place KAIST
  File  의 1 번째 Real Media 동영상입니다. 의 2 번째 Real Media 동영상입니다.
Abstract : Since the inception of gauge theory - Donaldson theory and Seiberg-Witten theory - in late 20 century, a mystery of smooth 4-manifolds has been unveiled and studying 4-manifolds has been the most active and central research area in geometry and topology. One of the fundamental problems in smooth 4-manifolds is to classify simply connected smooth and symplectic 4-manifolds. Topologists and geometers working on 4-manifolds have obtained many fruitful and striking results in this direction in last 30 years. In this lecture series I'd like to review briefly some classical invariants of 4-manifolds and Seiberg-Witten theory with applications. And then, I'll survey various constructions of smooth 4-manifolds such as a logarithmic transform, fiber-sum and a knot surgery. Especially I'll review a knot surgery in some details which turned out to be a powerful tool in the study of smooth 4-manifolds.