The recipe for moments of L-functions and characteristic polynomials of random matrices

In 2005, Conrey, Farmer, Keating, Rubinstein, and Snaith formulated a 'recipe' that leads to precise conjectures for the asymptotic behavior of integral moments of various families of $L$-functions. They also proved exact formulas for moments of characteristic polynomials of random matrices, and observed that these formulas have an almost identical form to their conjectures for the corresponding families of $L$-functions. In this talk, we will discuss recent progress towards their conjectures and survey a few applications of their formulas. These will include joint work with Brian Conrey and Caroline Turnage-Butterbaugh.