Let A be a subset of Zn. A function f which maps A to Zn is called a Freiman homomorphism if f(a) + f(b) = f(c) + f(d) whenever a + b = c + d and a, b, c, d are all in A. This is one of the central notions in the area of additive combinatorics. Conlon and Gowers (arXiv:1603.01734) studied the following question: If A is a random subset of Zn, then is it true that with probability close to 1, every Freiman homomorphism on A extends to a Freiman homomorphism of the whole group Zn? The answer, of course, depends on the size of A, and Conlon and Gowers have very precisely determined the size of A for which the answer is yes. Their proof is very interesting and there are a number of open problems remaining.
Supervisors
Primary Supervisor: Rajko Nenadov
Key qualifications and skills
A/A+ in MATH203, MATH220, MATH240, MATH343
Does the project come with funding
No - Student must be self-funded
Final date for receiving applications
Ongoing
How to apply
Apply by email to primary supervisor
Keywords
Combinatorics, probability
