Abstracts for some talks (Spring Semester 2010) Tuesday, January 19, 4:00 p.m., VV B139. Brian Street (UW) Multi-parameter singular Radon transforms We discuss singular (and maximal) Radon transforms where the singular kernel has a multi-parameter structure. We discuss operators of the form \[ f\mapsto \psi(x) \int f(\gamma(t,x)) K(t) dt, \] where $\psi$ is a $C^\infty$ cutoff function, $\gamma$ is a smooth function satisfying $\gamma(0,x)=x$, and $K$ is a ``singular kernel'' supported near $t=0$. The goal is to give ``finite-type'' conditions on $\gamma$ under which the above operator is bounded on $L^p$ ($1 2 are obtained for maximal operators over a wide range of hypersurfaces. These estimates are sharp in many situations, including the convex hypersurfaces of finite line type considered by Iosevich, Sawyer, and others. As a corollary, we also give a generalization of the result of Sogge and Stein that for some finite $p$ the maximal operator corresponding to a hypersurface whose Gaussian curvature does not vanish to infinite order is bounded on L^p. Monday, February 22, 4:00 p.m., Colloquium Richard Oberlin (UCLA) A variation-norm Carleson Theorem Abstract: The Carleson-Hunt theorem shows that for every p-integrable function f on the circle, 1