Elliptic curves and complex dynamics

In the last decade, an exciting program has emerged connecting the arithmetic of elliptic curves to classical questions in complex algebraic dynamics; that is, the study of iteration of maps on complex algebraic varieties.  We will discuss this program and the fruit it has yielded, providing a new and surprising approach to fundamental questions about the interaction between geometry and arithmetic of elliptic curves. 

About the speaker

Born and raised near Chicago, Dr Holly Krieger completed the undergraduate mathematics honors program at University of Illinois at Urbana-Champaign. She went on to gain a master's degree and a Ph.D. from the University of Illinois at Chicago, with initial research interests during graduate school primarily in arithmetic and Diophantine geometry. Under the guidance of Laura DeMarco and Ramin Takloo-Bighash, her thesis work focused on the emerging field of arithmetic dynamics, which studies the relationship between dynamics of one complex variable and the arithmetic geometry of abelian varieties.
Holly followed her PhD work with an NSF postdoctoral fellowship at MIT under the supervision of Bjorn Poonen, during which time she became particularly interested in problems of unlikely intersections in complex dynamics. Since 2016, she has been the Corfield Lecturer at the University of Cambridge as well as a Fellow at Murray Edwards College. She is also well known for her popular mathematics Numberphile YouTube videos.

Dr. Krieger's talk is supported by The Mahler Lectureship, organised by AustMS and AMSI. The Mahler Lectureship is awarded every two years to a distinguished mathematician who preferably works in an area of mathematics associated with the work of Professor Mahler.