Abstract:  
Birational geometry is the study of algebraic varieties up to adding/removing closed algebraic subsets. Rational curves play a critical role in understanding the birational geometry of varieties. Free curves are the easiest to work with, but on Fano varieties that are even mildly singular, it remains an open question whether these free rational curves exist. In this talk, we discuss free curves of higher genus. We show that any klt Fano variety has these higher-genus free curves. We then discuss some applications, including the existence of free rational curves in terminal Fano threefolds, the lengths of extremal rays of the cone of curves, and studying the fundamental group of the smooth locus of a terminal variety. This is joint work with Eric Jovinelly and Brian Lehmann.

Bio-Sketch: 

Eric Riedl is an Associate Professor in the Math Department at the University of Notre Dame, specializing in birational geometry and the study of curves on varieties. He received his Ph.D. from Harvard University in 2015 under the direction of Joe Harris, then spent three years as a postdoc at the University of Illinois at Chicago before moving to Notre Dame in 2018.