## The 2018-19 Hayden-Howard lecture

**Speaker**: Laura DeMarco Department of Mathematics, Northwestern University**Time and location**: Thursday, 11 April 2019, 3:30 pm. 106 Whitehall Classroom Building**Title:** Complex Dynamics and Arithmetic Equidistribution

**Abstract:** I will explain a notion of arithmetic equidistribution that has recently found application in the study of complex dynamical systems. It was first introduced about 25 years ago, by Szpiro-Ullmo-Zhang, to analyze the geometry and arithmetic of abelian varieties. In 2011, Matt Baker and I used the theory to study periodic points of maps on P^1. In this talk, I will explain some dynamical questions that were inspired by questions about elliptic curves, and then how the dynamical results allowed us to solve problems in the original setting of abelian varieties. The new results are joint with Holly Krieger and Hexi Ye.

### Previous Hayden-Howard lecturers

- 2017-18, Mike Hill, University of Califormia, Los Angeles
- 2016-17, Carlos Castillo-Chavez, Arizona State University and Yachay Tech University, Ecuador.
- 2015-16, Yitang Zhang, University of New Hampshire
- 2014-15, Robert Lazarsfeld, State University of New York at Stony Brook
- 2013-14, Jill Pipher, Brown University
- 2012-13, Michelle Wachs, University of Miami
- 2011-12, Doug Ravenel, University of Rochester
- 2010-11, Luis Vega, Universidad del Pais Vasco
- 2009-10, David Eisenbud, University of California at Berkeley
- 2008-09, Carlos Kenig, University of Chicago
- 2007-08, Joachim Rosenthal, University of Zurich
- 2006-07, John Neuberger, University of North Texas
- 2005-06, Fang-hua Lin, New York University
- 2004-05, Gang Tian, Princeton University and MIT
- 2003-04, Doron Zeilberger, Rutgers University
- 2002-03, Craig Huneke, University of Kansas
- 2001-02, Craig Evans, University of California at Berkeley
- 2000-01, Richard Stanley, MIT

### About the Hayden-Howard lecture

The Hayden-Howard lecture was inaugurated in the spring of 2001 by a generous contribution from a friend of the Department of Mathematics. The lecture series was established in honor of mathematics professors Thomas Hayden and Henry Howard. Each year, the lecture series brings a research mathematician of international stature to the University of Kentucky.