Topology Atlas | Conferences

Knots in Washington XXXVI
May 3-5, 2013
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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"Knots, Links and Geometry"
by
Herman Gluck
University of Pennsylvania
Coauthors: Dennis DeTurck, Rafal Komendarczyk, Paul Melvin, Haggai Nuchi, Liu-Hua Pan, Clayton Schonkwiler, David Shea Vela-Vick, Peter Storm

The trajectory of my mathematical life began with knots and low-dimensional topology, then moved into differential geometry, and in recent years is once again involved with knots and links, but this time from the perspective of geometry, and with application to molecular biology, topological fluid dynamics and plasma physics.

I will survey this most recent chapter of my work.

Some key words and phrases: knot theory in the presence of curvature, Gauss linking integral, writhing of knots, helicity of vector fields, upper bounds for the writhing of DNA, lower bounds for the energy of magnetic fields, the search for higher order helicities, link homotopy, generalized Gauss maps for three-component links, Lipschitz minimality of Hopf maps and vector fields.

Date received: April 11, 2013

Copyright © 2013 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbhe-03.