Complex proofs of real theorems.

The title refers to Painlevé’s and Hadamard’s famous dictum, “the shortest and best way between two truths of the real domain often passes through the imaginary one.” I’ll discuss examples from my research on this theme. By ‘complexifying’ a problem the goal is to make it, in fact, less complex. Often, one can achieve a surprising level of simplicity this way. Topics include quasiconvexity problem in calculus of variations, bilipschitz rotational multifractal spectra and limit shapes of random Young tableaux.