Math 583FA
Research in Geometric Analysis

John M. Lee

Spring 2005, Monday/Wednesday 11:30-12:45
Goals: Research in mathematics requires a number of skills. The most obvious one is having creative and original mathematical ideas; this skill requires a certain amount of talent and years of hard work, and probably cannot be taught. But there are several other skills that can be taught, such as reading and absorbing research papers, giving mathematical lectures, and writing mathematical papers. This course aims to give you some directed practice in the latter three skills, in the hope that it will stand you in good stead when you research and write your dissertation, and later when you write research papers of your own. Along the way, you will be introduced to some of the most significant contributions to geometric analysis of the past several decades.

Format: This course will meet twice a week for 75 minutes each. During each meeting, students will give lectures about recent research in geometric analysis. If time permits, I will intersperse these with longer discussion periods during which we can discuss mathematical issues that arise in the lectures. I'll distribute a list of important research papers in geometric analysis from approximately the past 50 years, organized into "themes", with each theme represented by several related papers. Students will work in teams of two to three people. Each team will choose two themes from the list: one during the first half of the quarter, and one during the second half. Each team will give a series of lectures on each of their two themes, and will collaborate on an expository paper about their second theme.

Prerequisites: Topology & Geometry of Manifolds (Math 544/5/6); Geometric Structures (Math 547); Real Analysis or Linear Analysis (524/5 or 554/5); and some familiarity with algebraic topology and partial differential equations is recommended.