Special Number Theory Seminar

We will discuss a graph that encodes the divisibility properties of integers by primes. We will prove that this graph has a strong local expander property almost everywhere. We then obtain several consequences in number theory, beyond the...

While conducting a series of number-theoretic machine learning experiments, He, Lee, Oliver, and Pozdnyakov noticed a curious oscillation in the averages of Frobenius traces of elliptic curves over Q.  If one computes the average value of a_p(E) for...

Suppose that Σ⊂ℂ is compact and symmetric about the real axis and is a finite union of rectangles and real intervals with transfinite diameter dΣ greater than 1. Suppose that μ is a H older arithmetic probability distribution on Σ defined in our...

The lecture will discuss a joint work with Gregorio Baldi and Bruno Klingler.  Given a polarized Z-VHS over a complex, smooth quasi-projective variety S, we describe some properties of the Hodge locus, a countable union of algebraic subvarieties of...