- Damien Roy: droy@uottawa.ca
- Daniel Fiorilli: Daniel.Fiorilli@uottawa.ca
- Saban Alaca: SabanAlaca@cunet.carleton.ca

**Speaker:**Daniel Fiorilli (U. of Ottawa, CNRS)**Title:**Variance of primes in progressions**Abstract:**I will discuss some recent work with de la Bretèche as well as some of my past work on Hooley's conjecture on primes in progressions. I will show how these questions are linked with large deviations of random variables.

**Speaker:**Sacha Mangerel (CRM)**Title:**Multiplicative Functions in Short Arithmetic Progressions and Applications**Abstract:**We shall discuss recent work on bounds for the variance over progressions modulo q of the partial sums ∑_{ n≤x, n≡a (mod q)}f(n) where f is a bounded multiplicative function and x/q goes to infinity arbitrarily slowly. We show cancellation in this variance for all but an exceptional set of moduli q of essentially best possible size (unless progress can be made on major open problems), with refinements for q of special types (e.g., smooth or prime), improving in various aspects on work of Hooley and others. We will also discuss some applications of our method to bounding the least integer with exactly 3 prime factors in an arithmetic progression (where our result is as good as what is implied by GRH), results of Bombieri-Vinogradov type and some problems in the function field setting.

(joint work with O. Klurman and J. Teräväinen)

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