Abstract: In this talk I will discuss computing knot Floer homology of satellites with arbitrary companions and patterns from a few families of (1,1)-patterns. I'll show how to compute $\tau$ and $\epsilon$ of satellites with these patterns in terms of $\tau$ and $\epsilon$ of the companion and show that there is an infinite subfamily of winding number 1 patterns (generalizing the Mazur pattern) that do not act surjectively on the smooth concordance group. I will also discuss determining the genus and fiberedness of these patterns (and their twisted relatives) in the solid torus. Some of this is based on joint work with Subhankar Dey.
