Summer School on Probabilistic Methods
- 06/26/2017 - 06/30/2017
Sang-il Oum, KAIST
Five-Day Lecture Series by Prof. Joel Spencer
Prof. Joel Spencer (Courant Institute, New York University) http://cs.nyu.edu/spencer/
10 Lectures + 5 Exercise Sessions for 5 Days
Tentative Schedule of Regular Days
2 Morning Lectures + Long Break + 1 Exercise Session before the dinner
(Monday: Starting at 11am)
The Probabilistic Method is a powerful technique developed by the legendary Paul Erdős. To show the existence of a combinatorial object one defines a random object and shows that with positive probability it has the desired properties. Erdős deduces that the object must exist. In homage, we refer to this idea as Erdős Magic. Closely aligned is the study of random structures perse. Throughout we deal with large structures and asymptotic analysis permeates all of the lectures.
The specific lectures should be regarded as tentative. We will have two lectures each day but the material given may take more or less than one lecture period. Also, new material may be added and old material deleted. Expect the actual lectures to be these descriptions times 1 ± o(1).
Lecture I: What is Erdős Magic?
Lecture II: More Erdős Magic
Lecture III: Asymptopia
Lecture IV: Random Graphs
Lecture V and VI: The Erdős-Rényi Phase Transition
Lecture VII: Games Mathematicians Play
Lecture VIII: Needles in Exponential Haystacks
Lecture IX: Zero-One Laws
Lecture X: Gems