Michael Yiasemides

Lattice Points in Function Fields, and Hankel Matrices

In this talk we discuss the function field analogue of lattice points in thin elliptic annuli. We will begin with a general introduction to lattice points in the classical setting, including briefly highlighting connections to physics and various areas of number theory; before introducing the function field analogue and stating our results on the mean and variance of lattice points in elliptic annuli. Our approach is unique to the function field setting, and it translates the problem to one involving Hankel matrices over finite fields. We will summarise this approach, before finishing by highlighting some interesting connections between Hankel matrices and number theory in function fields.