Colloquium

Starts: September 18, 2009 at 3:00 PM
Location: Jones Hall 301
Contact: Chi-Kwong Li

Summary

Speaker: Ka Hin Leung (National University of Singapore)

Full Description

Title: Field Descent Method and Lander's Conjecture

Abstract: Let G be a group of order v. A (v, k, λ)-difference set in G is a subset D consisting of k elements such that any nonidentity element in G is represented exactly λ times of the form xy ^-1 with x,y in D.

The study of difference is related to quite a number of combinatorial objects that find applications in codes, cryptography etc. In this talk, I will highlight some of the main problems researchers interested in the theory of difference set. In particular, I will focus on Lander’s conjecture.

Lander’s conjecture: Let D be a (v, k, λ)-difference set in an abelian group G. Suppose a prime p divides gcd(v, k-λ). Then the p-Sylow subgroup of G is not cyclic.

This conjecture is still open but we made some breakthrough in 2004 in case k-λ is a prime power. The key of the proof is a method developed called field descent method. I will highlight the key ingredients of this method and its application in solving other related problems.