# Thesis Defense

## Euclidean Association Schemes

Charles Brittenham

Tuesday, September 20th, 2022
2:30 PM - 4:30 PM
Zoom Meeting ID: 94306351795

We study a particular family of association schemes involving the Euclidean distance” t graphs over finite vector spaces. The spectra of adjacency matrices associated to this scheme are Kloosterman sums which have a plethora of applications in number theory.

We recover known results regarding these sums and situate them in a combinatorial context.

In particular, we show that one can recover known results about the Kloosterman moments by deriving closed formulas using association scheme theory and relate this to the vertical equidistribution of such sums established by N. Katz.

We also investigate some Falconer type problems involving this association scheme and use Delsarte’s linear programming setup to investigate their distributional properties.

Event contact: jonathan dot pakianathan at rochester dot edu