David Ellis

I am a Junior Research Fellow in Pure Mathematics at St John's College, Cambridge, and a member of the Combinatorics Group in the Department of Pure Mathematics and Mathematical Statistics (DPMMS).
My college webpage, containing a description of my research for non-specialists, can be found here.
My CV can be found here; a list of my publications can be found here.


I work on a variety of problems in combinatorics. I am particularly interested in connections between combinatorics and other areas of mathematics. Recently, I have been working mainly on the inferface between combinatorics, Fourier analysis, representation theory / group theory and probability theory. Here are some selected publications and papers:
Here are the slides from some selected talks:

Algebraic methods in combinatorics (Graduate course, Lent 2011)

In the last fifty years, algebraic methods have been used with striking success in combinatorics. This course explores these methods, and some of their most beautiful applications. There are connections with combinatorial geometry, probability theory, and theoretical computer science. Please find lecture notes below. To all: comments are most welcome! If you have any suggestions of alternative proofs, or other insights on the material you feel could be included, please email me, at D.Ellis at dpmms dot cam dot ac dot uk.

Algebraic methods in combinatorics: an overview (Lecture 1)

The Frankl-Wilson theorem and some consequences in Ramsey theory and combinatorial geometry (Lectures 2-5)

Exact intersections (Lecture 6)

Saturated and weakly saturated hypergraphs (Lectures 6-7)

The Polynomial Method (Lectures 8-10)
Eigenvalue methods in extremal combinatorics: an overview (Lectures 11-12)

The expansion of random regular graphs (Lectures 13-14)

Sparse superconcentrators (Lecture 14)

Eigenvalues, random walks, and Ramanujan graphs (Lectures 15-16)