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Title: Algebraic Curves over Finite Fields: Theory and Applications Speaker: Vincenzo Pallozzi Lavorante Universite degli Studi di Modena e Reggio Emilia Time: 2:00pm–3:00pm Place: Zoom Meeting

The study of algebraic curves defined over a finite field has attracted much interest in recent times. The purpose of this talk is to introduce the basic notions related to algebraic curves over finite fields, together with some examples of how it finds a concrete and common application in different research areas. In particular we will explore the connection with coding theory, permutation polynomials and see an interesting application in finite geometry.

No seminar this week.

Title: On the Number of Equivalence Classes of Boolean Functions Speaker: Xiang-dong Hou Time: 2:00pm–3:00pm Place: Zoom Meeting

Two Boolean functions from \(F_{2^n}\) to \(F_2\) are called (affine) equivalent if one can be obtained from the other through an invertible affine transformation of the variables followed by an addition of an affine function. Most coding theoretic and cryptographic properties of Boolean functions are preserved under this equivalence. Let \(N_n\) denote the number of equivalence classes of Boolean functions in \(n\) variables. No explicit formula for \(N_n\) is known. A long-standing open question by MacWilliams and Sloane asks for an asymptotic formula for \(N_n\) as \(n\to\infty\). Recently, we found a solution to this question.