Ewan Dalby Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called $\theta=1/2$ barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.
 Sun Woo Park Representations of $GL_n(\mathbb{F}_q)$ I will discuss the irreducible representations of $GL_n(\mathbb{F}_q)$. In particular, I will discuss some ways in which we can understand the structure of representations of $GL_n(\mathbb{F}_q)$ , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.