# 2018-2019 J. C. Eaves Lecture

**2018-19 J.C. Eaves Lecture**

Title: Understanding Symplectic Geometry through Polytopes and Lattice Points

Abstract: Topology is often called ``rubber sheet geometry" and is described as ``floppy" while geometry is more ``rigid". Symplectic geometry, the natural geometry of classical mechanics, is floppier than Riemannian geometry but more rigid than topology. I will give an overview of this floppy/rigid spectrum. We will then explore how the geometry and topology of symmetries in this context relate to properties of polytopes, motivated by many pictures and examples. I will conclude with how some of my recent work, joint with Daniel Cristofaro-Gardiner, Alessia Mandini and Ana Rita Pires, comes to feature continued factions, counting lattice points, and the Philadelphia subway system.

The J.C. Eaves Lecture is supported by the Dr. J.C. Eaves Undergraduate Excellence Fund in Mathematics.

About the J.C. Eaves Speakers SeriesThe J.C. Eaves Undergraduate Excellence Fund brings speakers to campus to participate in the undergraduate mathematics program. The Fund is supported by a generous gift from James C. Eaves, Jr. and Mary Eaves, the son and daughter-in-law of J.C. Eaves. J.C. Eaves was a faculty member in the Department of Mathematics and Astronomy at the University of Kentucky and served as Chair of the Department from 1953 to 1963.

The previous speakers in the J.C. Eaves Speakers Series are:

- Francis Su, Harvey Mudd College, 2017-18
- Ken Ono, Emory University, 2016-17
- Frank Wilczek, MIT, 2015-16
- Mihai Stoicu, Williams College, 2015-16

The photograph of J.C. Eaves from 1965 is provided courtesy of the University of Kentucky Libraries Special Collections Research Center. The original may be found at ExploreUK.

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