Noah Snyder : Teaching Statement

Lectures # 5 and 6 : The Prime Number Theorem . Noah Snyder

Riemann used his analytically continued ζ-function to sketch an argument which would give an actual formula for π(x) and suggest how to prove the prime number theorem. This argument is highly unrigorous at points, but it is crucial to understanding the development of the rest of the theory. Notice that log ζ(s) = ∑ p ∑ n 1 np −ns for Re(s) > 1. Letting J(x) = ∑ pk≤x 1 k , notice that log ζ(s) =...

Constructing the extended Haagerup planar algebra by

The ontogeny of social skills: experimental increases in social complexity enhance reproductive success in adult cowbirds

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Groups with a Character of Large Degree Noah

Let G be a finite group of order n and V a simple C[G]-module of dimension d. For some nonnegative number e, we have n = d(d + e). If e is small, then the character of V has unusually large degree. We fix e and attempt to classify such groups. For e ≤ 3 we give a complete classification. For any other fixed e we show that there are only finitely many examples.

Subfactors of index exactly 5

We give the classification of subfactor planar algebras at index exactly 5. All the examples arise as standard invariants of subgroup subfactors. Some of the requisite uniqueness results come from work of Izumi in preparation. The non-existence results build upon the classification of subfactor planar algebras with index less than 5, with some additional analysis of special cases.