Counting Sign Changes in the Prime Number Theorem

The prime number theorem tells us that the number of primes up to x is asymptotic to li(x), the logarithmic integral function. But which is greater, pi(x) or li(x)? Littlewood showed that the function  pi(x) - li (x) changes sign infinitely many times, and a great amount of work has gone towards finding the first sign change. For this talk, we will focus instead on the average density of sign changes, improving on a method due to Kaczorowski.