UAlberta Mathematics and Statistics Colloquium: James Lewis

Abstract: We begin with the statement of the Hodge conjecture. Next, we give a precise definition of an arithmetic conjecture. In complex algebraic geometry, either a conjecture arises from analysis, or is arithmetical. Recent work of Voisin shows that Hodge conjecture is arithmetical. Arithmetic conjectures take centuries to resolve. A case at point is Deligne's proof of the Weil conjecture which goes back to Gauss.