Counting elliptic curves of bounded Faltings height

We give an asymptotic formula for the number of elliptic curves over $\mathbb{Q}$ with bounded Faltings height. Silverman has shown that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in $\mathbb{R}^2$.Comment: 12 pages, 2 figures, 1 table. To be published in Acta Arithmetic

A Universal Approach to Vertex Algebras

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.Comment: To appear in the Journal of Algebr

Classifications of elliptic fibrations of a singular K3 surface

We classify, up to automorphisms, the elliptic fibrations on the singular K3 surface $X$ whose transcendental lattice is isometric to $\langle 6\rangle\oplus \langle 2\rangle$.Comment: 28 page