# Seminari di Algebra

Il Dipartimento di Matematica organizza i seminari dei ricercatori e ricercatrici di Algebra che hanno preso servizio nel 2022.

**ore 16:00 MARCO CALDERINI ** ** **

**APN functions, crooked functions and exceptional functions among them**

**Abstract: **APN and crooked functions are discrete functions of particular interest in the context of cryptography and combinatorics. In this talk, we will give an overview of the constructions and known infinite families of these functions. Then, we will focus on functions which are APN or crooked over infinite extensions of a field of characteristic 2, that is, on exceptional APN and exceptional crooked functions. We will discuss some recent results on these maps.

**ore 16:45 ALESSIO MENEGHETTI** ** **

**Isomorphisms between computationally-hard algebraic problems for Post-Quantum Cryptography**

**Abstract: **In 1977, Berman and Hartmanis formalised the concept of polynomial-time reduction between computational problems, and then they formulated a conjecture on the equivalence between NP-complete problems. A related problem is the construction of explicit reductions between NP-hard problems. In the context of cryptography, the Maximum Likelihood Decoding Problem and the Multivariate Quadratic Problem are two of the most investigated algebraic problems since they are strictly related to the security of Code-Based and Multivariate-Based Post-Quantum Cryptosystems. In this talk we show the equivalence of the two problems by presenting polynomial-time reductions, and then we briefly discuss the result from a cryptographic point of view.

**ore 17:30 MIMA STANOJKOVSKI** ** **

**Vertices of balls: orders, codes, and tropical geometry**

**Abstract: **Balls in the tropical metric are a particular example of polytropes, namely tropical polytopes that are at the same time convex in the usual sense. Moreover, tropical balls can also be seen as one-apartment slices of balls in Bruhat-Tits buildings. So balls in this context have vertices and we will see how these vertices play an important role in applications to representation theory and algebraic coding theory. I will be reporting on joint work with Yassine El Maazouz, Marvin Hahn, Gabriele Nebe, and Bernd Sturmfels.