New developments in Frobenius manifolds

In this talk we will present new aspect of Frobenius manifolds. 
The Frobenius manifolds play a significant role in mirror symmetry and affects various domains of mathematics such as:
- quantum cohomology
- the moduli space of solutions to Maurer--Cartan equations appearing in the Barannikov-Kontsevich theory, related to Gerstenhaber-Batalanin-Vilkoviskiy algebras 
- Saito manifolds.
Recent developments have allowed to go beyond this, namely with the discovery that Frobenius manifolds interfere in information theory and in $p$-adic number theory.