Title: The distribution of primes in short intervals

Abstract: What is the maximum number of primes in an interval of length y?
Here y is no bigger than a small multiple of (log x)^{2}, that is, y is tiny compared to x. We will present several conjectures (for different ranges of y) based on (a couple of) heuristic ideas, and investigate these conjectures with data from calculations of primes. There are one or two surprising issues that arise. This is joint work with Allysa Lumley.