# The Abel lectures

Welcome remarks from rector **Svein Stølen**, University of Oslo, ** Hans Petter Graver**, President of the Norwegian Academy of Science and Letters and

**, chair of the Abel committee.**

**Hans Munthe-Kaas****Karen Keskulla Uhlenbeck***,* University of Texas, Austin:

*,*

**The Abel lecture**

**Chuu-LianTerng, **UC Irvine

**Solitons in Geometry:**

**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 globalgeometric problems.

**Robert Bryant, **Duke University:

**Limits, Bubbles, and Singularities: An introduction to the fundamental ideas of Karen Uhlenbeck**

**Limits, Bubbles, and Singularities: An introduction to the fundamental ideas of Karen Uhlenbeck**

**Summary:**

Ever since the Greeks, the challenges of understanding limits and infinities have fascinated us, ultimately leading to the development of calculus and much of modern mathematics. When does a limit exist and in what sense? How do we capture these notions in geometric and intuitive ways? Professor Uhlenbeck's work provides fundamental ideas for how to interpret situations in which one would like to take a limit of a set of geometric objects and interpret the result in useful ways. I will try to give a sense of what the challenges are and how Uhlenbeck's ideas provide answers to questions that mathematicians and physicists have been asking for many years. At the end, I will give a sense of how influential her work has been and continues to be.

**Matt Parker**, Standup Mathematician:

**Matt Parker**,

**Popular lecture: An Attempt to Visualise Minimal Surfaces and Maximum Dimensions**

**Popular lecture: An Attempt to Visualise Minimal Surfaces and Maximum Dimensions**

**Summary:**

Much of Karen Uhlenbeck ground-breaking work involved abstract mathematical concepts which are beyond our normal human intuition. And even though there may be practical applications of the results of her work, that does not make minimal surfaces in higher dimensions any less esoteric. Matt Parker will attempt to provide visual demonstrations of both minimal surfaces and higher dimensions (although, probably not at the same time) to allow a small glimpse into the scope of Uhlenbeck's work and achievements.