【Seminar】A smooth isometric immersion is determined by a framed curve

Abstract:

The work presented in this talk is motivated by the following problem in mechanics: what is the equilibrium shape of an unstretchable, elastic surface subject to prescribed edge conditions? If the elastic surface starts as a rectangular strip and is deformed to obtain a Möbius band, Wunderlich realized that the shape of the deformed surface and its bending energy are determined by a framed curve. Invoking an energy minimization principle, he then reasoned without proof that the equilibrium shape of the deformed surface can be obtained by minimizing the energy over all such framed curves. In this talk, it will be shown that Wunderlich’s idea applies to simply connected, planar reference region with corners. Additionally, it will be shown that the set of isometric immersions acting on such a region are in one-to-one correspondence with a family of framed curves that satisfy certain prescribed conditions, each of which has a clear geometric interpretation.

Biography:

Brian Seguin obtained a B.S. in Engineering Mechanics from the University of Illinois Urbana-Champaign in 2005 and a Ph.D. in Mathematical Sciences from Carnegie Mellon University in 2010. He is currently a faculty member at Loyola University Chicago. Brian is interested in problems coming from applied analysis and geometry. For example, he has worked on projects involving lipid bilayers, liquid crystal theory, soap films, material surfaces, and nonlocal curvature.

Zoom:

Link: https://oist.zoom.us/j/97994143590?pwd=MXZRY0xTSHE4elova0Y5Sm5YRzdVUT09
ID: 979 9414 3590
Passcode: 312250

*Refreshments will be provided after the seminar.