Some Applications of Modular Forms

The theory of modular forms and especially the so-called Ramanujan Conjectures have recently been applied to resolve problems in combinatorics, computer science, analysis, and number theory. Professor Sarnak begins by developing the necessary background material in modular forms. He then considers in detail the solution of three problems: the Rusiewisz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs, e.g. expander graphs and Ramanujan graphs; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares.

• Based on public lectures at Yale, therefore not too technical, and of broad interest
• Very well-known author, who was invited speaker at this year's Int Congress of Maths (all the flyers we prepared were taken)
• Interest to number theorists and combinatorialists