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**Title: Lifted Representations of Convex Sets**

**Abstract:** A common theme in many areas of mathematics is to find a simpler representation of an object indirectly by expressing it as the projection of an object in some higher-dimensional space. In 1991 Yannakakis proved a remarkable connection between a lifted representation of a polytope and the nonnegative rank of a matrix associated to the polytope. In recent years, this idea has been generalized to cone lifts of convex sets, with applications in, and tools coming from, many areas of mathematics and theoretical computer science. This talk will survey the central ideas, results, and questions in this field.

**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.

### Previous Hayden-Howard lecturers

- 2019-20, Rekha Thomas, University of Washington
- 2018-19, Laura DeMarco, Northwestern University
- 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