Varieties of general type are the higher dimensional analogs of Riemann surfaces of topological genus at least 2. The moduli spaces of Riemann surfaces are well understood and have natural compactifications. In this talk I will discuss recent results leading to the construction of compact coarse moduli spaces for varieties of general type of any fixed dimension and fixed canonical volume.

Christopher Hacon is currently a Distinguished Professor at the University of Utah.His main area of research is in the field of Algebraic Geometry which, loosely speaking, is a branch of mathematics that studies the geometric properties of sets defined by polynomial equations. Together with his co-authors, Hacon has proved many foundational results on the geometry of higher dimensional algebraic varieties including the celebrated result on the finite generation of canonical rings.
Hacon is a member of the American Academy of Arts and Sciences (2017), the National Academy of Sciences (2018), the Royal Society (2019) and he has been awarded the Clay research award (2007), the Cole Prize (2009), the Feltrinelli Prize (2011), and the Breakthrough Prize (2018).