Course No.：2805Z
Period：10
Credits：0.5
Course Category：Lecture
Primary Coverage:
Talk 1. Probabilistic Methods in Combinatorics
The probabilistic method is a powerful tool in graph theory and combinatorics, which proves the existence of a configuration by creating a suitable probability space and by showing a positive probability that the random configuration meets the desired criteria. In this talk I will present some basic techniques of probabilistic combinatorics, along with applications in computer science, discrete geometry, and number theory.
Talk 2. A Tour in Random Graphs
Theory of random graphs was introduced by Erdos and Renyi, and later developed into an active research area with significant connections and applications in computer science, statistical physics, engineering and operations research. This talk is a survey on the major results in the classical Erdos-Renyi random graphs, as well as various models of random graphs.
Talk 3. Searching Games with Errors -- Coping with Liars
This is the Ulam’s searching game considered in the framework of two-person perfect information games. We present the solution of such games with a fixed number of errors, which involves a mixture of techniques in information theory, packing, finite field, and probabilistic methods.
Talk 4. Algebraic Methods in Enumerative Combinatorics
This is a survey on the fundamental ideas and results of enumerative combinatorics. I will present various algebraic tools, including formal power series, sieve methods, partially ordered sets, and Mobius functions.
Talk 5. Parking Functions: Algebra, Combinatorics, and Probability
Parking function is a subject lying in the heart of combinatorics. It is originated from computer science, and has connections to many combinatorial structures. In this talk I will present some interesting results from algebraic, combinatorial, and probabilistic points of view.
Author：HUafei Yan
