Motivic Filtrations

In my sabbatical year, I plan to focus on two major research projects and two book projects. The research projects are in the areas of algebraic K-theory and higher Brauer groups. The books are on derived algebraic geometry and the geometry of filtrations. I intend to be based largely in Chicago so as to focus on writing and to work with Akhil Mathew on algebraic K-theory research, possibly with official term-long visiting positions at the University of Chicago and/or Northwestern. To support the research and writing projects, I will visit David Gepner at Melbourne for one month to work on higher Brauer groups and Thomas Nikolaus at Münster for one month to work on algebraic K-theory. Additionally, several smaller visits are planned, including to Edinburgh to discuss the geometry of filtrations with Clark Barwick and Arend Bayer, to Paris to work on K-theory with Matthew Morrow, and to Toulouse to discuss derived algebraic geometry with Bertrand Toën.