The Mandelbrot set M is a fascinating fractal that encodes in one image the dynamical complexity of the quadratic family z^2 + c. We will wander around M, trying to make sense of its bubbles and their bifurcations, explain how baby Mandelbrot sets are born and where the herds of elephants march, along with various other observable features of M. Despite its enormous complexity, there is a good chance of obtaining a precise topological and geometric description of M. It depends, though, on confirming a long-standing “MLC Conjecture” (on the local connectivity of M) and building up several “Renormalization Theories” that control the small-scale structure of this set.

I will review connections between random matrix theory and statistical properties of the Riemann zeta-function, including recent developments relating to extreme values of the zeta function on the critical line.

One would assume that during the French and American wars in Vietnam, the impoverished guerrillas of the Viet Minh and NLF must have been badly outmatched on the purely technical side of warfare, including cryptography. However, the truth was more complex. In joint work with Phan Duong Hieu (of Limoges, France) we investigate the strengths and weaknesses of all sides in communications intelligence.