SM: West Coast Algebraic Topology Summer School

University Of Oregon Eugene, Eugene OR

Investigators

Abstract

The PIs, Ralph Cohen and Dev Sinha, will be program organizers for a one-week summer school program in algebraic topology, to be hosted at the University of Oregon in the summer of 2010. This summer school will focus on the interface between algebraic topology and algebraic geometry, in particular on moduli spaces. We will bring thirty graduate students and early-career mathematicians together for an introduction to an area which is ripe for investigation, and whose techniques will inform and inspire developments throughout topology. Among other topics, students will learn about mapping class groups, stability theorems, operad actions and other loopspace machinery, cobordism spectra, singularity theory, cobordism categories, and topological field theories. Calculations will be emphasized whenever they are relevant. This summer school will use a unique blend of pedagogical tools, combining elements which have been successful in other settings. Younger researchers will be involved with both organizing and giving talks. Attendees will be encouraged to work problems, fill in background, and do reading together in addition to attending lectures. A full effort will be made to recruit a broad and diverse group of participants. The west coast topology summer school will significantly strengthen the knowledge base of topologists and others who use topology. In its role as a basic study of shape, topology has significant ramifications in other areas of mathematics, from basic counting problems (combinatorics) to solutions of equations (algebra) to applications and extensions of the calculus (analysis). More broadly, knowledge of topology is essential for example in studying the structure of the early universe, in designing a robot arm with a minimal number of controllers, and in searching large data sets for meaningful groupings as successfully done recently for study of breast cancer. The summer school will be structured to highlight ramifications in geometry and algebra, and thus strengthen the ties between basic areas of theoretical mathematics. Mathematicians from underrepresented backgrounds will be vigorously recruited. Graduate students and post-docs will gain hands-on experience with some of the most important developments of contemporary mathematics, preparing them to be future leaders of the field. Participants will enlarge their professional networks, which is especially critical given the geographical distances faced by mathematicians in the western half of North America. Organizers and participants will also have the opportunity to reflect upon the array of pedagogical tools employed, and might employ some themselves in training graduate students and undergraduates or reaching out to fellow scientists and the general public.