The Best Possible Shapes of Surfaces

About the lecture

Abstract:  Much of classical mathematics involves finding a configuration or shape that provides an optimum solution to a problem.  For example, it has long been known (though a rigorous proof took quite a while to find) that the surface of least area enclosing a given volume is a round sphere.  There are many other ways to measure surfaces, though, and finding 'the' surface that optimizes a given 'measurement' (subject to some given constraints) remains a challenging problem that has motivated some of the deepest recent work in the mathematics of geometric shapes. 
In this talk, I will explain some of the classic ways to measure shapes of surfaces and relate this to classical problems involving surface area (soap films and bubbles) and total curvature as well to as recent progress by myself and others on these important optimization problems.

Speaker

Robert Bryant

Duke University, US

  • Prof. Robert L. Bryant is the Phillip Griffiths Professor of Mathematics at Duke University.
  • His research involves geometric partial differential equations (calculus on curved objects) and its applications to a wide variety of problems in differential geometry, integrable systems, and algebraic geometry.  
  • He has served on the faculties of Rice University, the University of California at Berkeley, and Duke University and has also served as the director of the Mathematical Sciences Research Institute in Berkeley, California and as the president of the American Mathematical Society.

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