2 citations · 6 across the 6 of their papers we have counts for
9 papers
Tropical Count of Curves on Abelian Varieties
Lars Halvard Halle, Simon Rose
We investigate the problem of counting tropical genus g curves in g-dimensional tropical abelian varieties. For g = 2, 3, we prove that the tropical count matches the count provide…
Quasi-modularity of generalized sum-of-divisors functions
Simon Rose
In 1919, P. A. MacMahon studied generating functions for generalized divisor sums. In this paper, we provide a framework in which to view these generating functions in terms of Jac…
Introduction to Modular Forms
Simon Rose
We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their app…
Introduction to Gromov-Witten Theory
Simon Rose
The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk…
Elliptic Calabi-Yau threefolds over a del Pezzo surface
Simon Rose, Noriko Yui
We consider certain elliptic threefolds over the projective plane (more generally over certain rational surfaces) with a section in Weierstrass normal form. In particular, over a d…
Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms
Simon Rose
In this paper we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surfaces using the crepant resolution conjecture an…