WAM 2026
On Superorthogonality
Abstract: How do we check if two vectors are orthogonal? We compute their dot product, which by definition takes two vectors as inputs. How do we check if two functions are orthogonal? We compute their inner product, which by definition takes two functions as inputs. Why only two? What would it mean for 4 functions to be “orthogonal”? Or 8 functions? Or 7 functions? Let’s call this superorthogonality. What can we deduce about collections of functions that are superorthogonal? We will explore how accidental encounters with papers spanning 90 years led to a systematic investigation of these questions, and a way to see that previously “unrelated” theorems in harmonic analysis and number theory share a very interesting structure deep under their surface.