Terence Tao

Bounded gaps between primes
Laudatio by Charles Fefferman
Minerva Lectures 2013
Progress in additive prime number theory
Structure and randomness in the prime numbers
Short presentation, perhaps 2017

Bounded gaps between primes

 Part 1   Part 2   Part 3

Minerva Lectures 2013

 Sets with few ordinary lines
Polynomials expanders
Wigner random matrices