황동선 (IBS-CCG)          [연습문제]

- 제목: A guide to normal complex surface singularities 

- 초록: Singularities are unavoidable in current research of algebraic geometry. Among them, normal complex surface singularities form an important class of singularities not only in algebraic surfaces but also in 4-dimensional topology. They also play the role of toy models for higher dimensional singularities. This lecture series will be a guide to normal complex surface singularities for beginning graduate students or non-experts. Topics include the following. 

     1. Toric surface singularities 

     2. Various classes of surface singularities 

     3. Projective contractibility 

     4. Singularities of some projective surfaces

최성락 (연세대학교)          [Lecture1]     [Lecture2]     [Lecture3]     [Lecture4]     [연습문제]

- 제목: Geometry of algebraic fiber spaces: Iitaka Conjecture, etc 

- 초록: An algebraic fiber space can be considered as a relative version of an algebraic variety. It is defined as a surjective morphism  f:X->Y between algebraic varieties X, Y with a general fiber F. Obviously, randomly chosen X,Y, F do not define algebraic spaces and the intertwined relation among X,Y, F still remains to be studied. In this lecture series, we will introduce and study the Iitaka conjecture and some related problems regarding algebraic fiber spaces. We will start by collecting basic definitions and results. And then we delve into the problems.

박경배 (강원대학교)          [Lecture1]     [Lecture2]     [Lecture3]     [Lecture4]     [연습문제]

- 제목: An introduction to low-dimensional topology 

- 초록: The goal of this lecture series is to introduce early graduate students to some basic theories of the low-dimensional topology, the study of manifolds of dimension ≤4. We first introduce classical construction techniques of low dimensional manifolds, Dehn surgery description of closed, oriented 3-manifolds and their trace 4-manifolds. Then we deal with Rohlin’s and Casson’s invariant for homology 3-spheres in homology cobordism group and their applications. Throughout the lectures, examples of 3-manifolds, such as Lens spaces, Seifert fibered spaces, and Brieskorn spheres, will be demonstrated. We assume audiences are familiar with the basic concepts of algebraic topology: the fundamental group, the homology and cohomology theory and the Poincaré duality. A suitable reference of the lecture might be “Lectures on the topology of 3-manifolds” by Nikolai Saveliev. The following is the tentative schedule of lectures.

     Lecture 1: Dehn surgery along a framed link 

     Lecture 2: Kirby moves 

     Lecture 3: Intersection forms of 4-manifolds and Rohlin invariants 

     Lecture 4: Casson invariants