Lecture Outline 3. Evaluation of Lattice Sums via Telescoping over Topographs. The final lecture will focus on telescoping techniques, demonstrating how they can be used to evaluate intricate lattice sums—such as the one above—with geometric meaning.

Lecture Outline 2. Class Number Formula and Summation over Topographs. Building on the first lecture, we will explore the class number formula and how summation identities arise naturally from the structure of topographs.

Lecture Outline 1. Introduction to Binary Quadratic Forms and Conway’s Topographs. We will begin with the basics of binary quadratic forms and their classification, followed by an introduction to Conway’s topographs—a visual and geometric framework for understanding them.

In this talk, aimed at a general audience, we will describe recent results on the characterization of norm forms—a classical object in algebraic number theory—in terms of their values at integer points. These results answer natural questions and are related to still-open conjectures of Littlewood (from 1930) and of Cassels and Swinnerton-Dyer (from 1955). The proofs rely on studying the actions of maximal tori of algebraic groups on homogeneous spaces of arithmetic origin.