A personal perspective on some of the work of Bourgain and Tao (Craaford Prize Symposium, Lund May 2012)

The Sylvester-Gallai Theorem (PIMS-UBC Distinguished Colloquium, Vancouver September 2012)

Looking for patterns in the prime numbers (Royal Society Public Lecture, October 2012)

Hadamard Lectures on Nilsequences, IHES, May/June 2014.

Lecture 1 (90 minutes) Why is classical Fourier analysis insufficient for many problems in additive number theory?

Lecture 2 (70 minutes) Definition of nilsequences. Detailed statement of the inverse theorem for the Gowers norms.

Lecture 3 (80 minutes) Derivatives of nilsequences. Why are nilsequences obstructions to Gowers uniformity?

Lecture 4 (90 minutes) Quantitative equidistribution results concerning nilsequences.

Lecture 5 (85 minutes) Szemeredi's theorem and variants. Conjecture of Bergelson-Host-Kra.

Lecture 6 (85 minutes) Applications of the preceding to linear configurations of primes.