Summary:
A soliton is a solitary wave that resists dispersion, maintaining its shape while propagating at a constant speed. Solitons were seen first as water waves in a shallow channel, and lately in the motion of a wave envelopes in optical fibers. They also occur in the study of pseudo-spherical surfaces in 3-space. The theory of solitons has been an active research area for more than fifty years, inspired by many applications in mathematical physics, optical communications, algebraic geometry, differential geometry, and more. This lecture will first give a history of solitons, then explain Uhlenbeck's contributions to soliton theory and integrable systems. She gave a simple and unified geometric framework to explain the symmetries and remarkable properties of soliton equations and showed us how to use techniques from soliton theory to study many global
geometric problems.

Chuu-Lian Terng is a mathematician working within the topics of Geometry and Topology, and Mathematical Visualization. She received her B.S. from National Taiwan University in 1971 and her Ph.D. from Brandeis University in 1976 under the supervision of Richard Palais. She is currently a professor at University of California at Irvine, but has also spent time at Northeastern University, Northeastern, Princeton University, Institute for Advanced Study and the Max-Planck Institute in Bonn, Germany.

This lecture was held at The University of Oslo, May 22, 2019 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations.

Program for the Abel Lecture 2019
1. "Some Thoughts on the Calculus of Variations" by Abel Laureate Karen K. Uhlenbeck, University of Texas at Austin, USA
2. "Solitons in Geometry" by professor Chuu-LianTerng, UC Irvine
3. "Limits, Bubbles, and Singularities: An introduction to the fundamental ideas of Karen Uhlenbeck" by professor Robert Bryant, Duke University
4. "An Attempt to Visualise Minimal Surfaces and Maximum Dimensions" by Matt Parker, Standupmaths

свернуть