The Barrett Lectures 2000

University Of Tennessee Knoxville, Knoxville TN

Investigators

Abstract

Abstract Award: DMS-0080037 Principal Investigator: Alexander S. Freire The Barrett Lectures at the University of Tennessee, Knoxville in May 2000, "New Directions in Differential Geometry" will present four main speakers and a number of additional lecturers. These talks will address a broad spectrum of recent work in the subject, including lecture series by four leading researchers on partial differential equations and analytic methods, minimal surfaces, symmetries and isometries in Riemannian geometry, and Lagrangian cycles in symplectic geometry. The major component of this award will support participation in the lecture series by graduate students and recent Ph.D.s. The Barrett Lectures have been held annually since 1972, covering a variety of topics and attracting a national audience. They are one of the few long standing lecture series in mathematics in the southeastern United States. The subject of these lectures for 2000 is differential geometry, the study of aspects of a space that can be captured by measures of length, angle, surface area, volume, and related notions. Riemannian geometry concentrates on issues related to curvature, the measurable quantity that makes rigorous the notion that a flat plane and a round sphere are distinct even at very small scales of attention. Symplectic geometry concerns an idealization of the structure underlying the Hamiltonian framework for mechanics, a structure that enables measurements of areas and volumes but does not require that length and angles be measurable. Both of these flavors of geometric information have dramatic consequences for problems concerning efficient or optimal placement of objects such as a surface in a three-dimensional space, consequences which are mostly expressed in the language of partial differential equations and related ideas from mathematical analysis.