Dear all,

I would like to announce the following online seminar that will take place next week via the Zoom platform. Best regards, Maurizia Rossi

*Tuesday, Jan 19 - 4:30pm *(Rome time zone) Speaker: *Arturo Jaramillo Gil* (*CIMAT -* Centro de Investigación en matemáticas, Mexico) Title: *Quantitative Erdös-Kac theorem for additive functions*

Summary: The talk will take as a starting point the celebrated Erdös-Kac theorem; a result of great importance in probabilistic number theory, which establishes that the fluctuations of the number of prime factors in a uniform sample over {1,..., n} are asymptotically Gaussian. Naturally, after the publication of this result, many quantitative versions of it have been studied. LeVeque conjectured that the optimal rate was asymptotically equivalent to loglog(n)^(-1/2). This was later proved by Turan and Rényi by means of an ingenious manipulation of the underlying characteristic function. Unfortunately, up to this day, all the perspectives for solving LeVeque's conjecture are based on the use of non-trivial complex analysis tools, while the probabilistic perspective has been only successfully applied to obtain suboptimal rates of convergence. In this talk, we will give a purely probabilistic proof of LeVeque's conjecture which will allow us to address the problem in a general fashion by means of Stein's method techniques.

*Link Zoom* https://us02web.zoom.us/j/88100676046?pwd=NTFjdlAyVjdSTE8rVnBmUGVWelFPdz09

*Meeting ID*: 881 0067 6046 *Passcode*: 680246

- - - Maurizia Rossi

Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca