Hubert L. Bray

Greg Galloway

Rafe Mazzeo

Natasa Sesum

This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

Geometric Analysis

Trevor and his sister Farrah are in the fifth and fourth grades. How did they get a time machine? And why does everyone think they are the key to saving the galaxy?"Trevor the Time Traveler" is a fun story, first and foremost, about Trevor, his sister Farrah, and their adventures. However, there is a lot of true science in the book. Even the “science fiction" is as consistent with modern physics as the author could make it. The author is a professor of mathematics and physics at Duke University. He studies black holes, dark matter, and the curvature of space and time. “I wrote this story for my kids to teach them as many of the coolest, mind blowing ideas as I could, as well as how to be a good person. But when I was done, I realized this was a fun book for adults as well. Where else will you find general relativity explained to a fifth grader in a story with wormhole jump ropes, bullies, secret agents, gamblers, dinosaurs, aliens, and a flying unicorn who can talk, read minds, and grant wishes?”This book is the perfect gift for boys and girls to get them interested in science. It is also great for adults who enjoy fantasy, science fiction, and high level discussions of some of the greatest ideas ever discovered. For excerpts from the book, discussions of the science behind the story, and some cool photos of the universe, visit the facebook page for "Trevor the Time Traveler" at www.facebook.com/TrevorTheTimeTraveler.

Hubert L. Bray

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