Résumé

Adam Harper

I will talk a little about the Riemann Hypothesis, andhow it can be reformulated as a question about cancellation in the sum of the Mobius function, which only takes values 1, -1, and 0.

Then I will explain what is known and conjectured about the size of this sum, and try to describe the work of various authors on a random analogue of the problem.

There are connections with the Law of the Iterated Logarithm and with large values theory for Gaussian processes, which I will try to sketch.