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.