“An introduction to the BSD conjecture via conics”
Giovedì 29 Gennaio 2026, ore 11:00 Mercoledì 28 Gennaio 2026, ore 14:00 - Aula 2AB45 2BC60 - Michele Fornea (Dipartimento di Matematica “Tullio Levi-Civita”)
Abstract
Elliptic curves are smooth projective curves described by simple cubic equations of the form $y^2=x^3+ax+b$. The Birch and Swinnerton-Dyer (BSD) conjecture – one of the Millenium Prize Problems – posits a deep and surprising relation between the arithmetic of elliptic curves and special values of $L$-functions. Roughly speaking, it relates the number of rational solutions to the average number of solutions modulo primes.
In this talk we will give an introduction to the main ideas surrounding the conjecture by examining the arithmetic of the affine conic of equation $x^2+y^2=1$.
