Workshop

New ideas in string theory, in particular D-branes and their relevance to open strings, have in many ways revolutionized modern quantum field theory, but this subject is currently highly heuristic: its formalization and mathematical development has barely begun. The geometric naturality and flexibility of these concepts has fostered rapid development, but their codification is completely open. Orbifolds, gerbes, and stacks are all topics with well-established classical literatures, but the idea that they should be grouped together, and that the various kinds of twistings they manifest are relevant to physics, is a new idea in mathematics. Structure The central purpose of this two week program in Morelia is to introduce these concepts to young research mathematicians from both South and North America. The introductory lectures given during the first week will provide the necessary background; these will be supplemented, primarily during the second week, with lectures by leading researchers on recent progress. The second week of the program serves as the Opening Workshop for the MSRI program, Spring, 2006, in New Topological Structures in Physics. For more information on this program, go to New Topological Structures in Physics. Priority will be given to young applicants from Pan-American institutions and women and minorities from the US and Canada. This workshop is a Pan-American Advanced Studies Institutes Program. Funding is provided by the Office of International Science and Engineering of the National Science Foundation and the Office of Basic Science of the Department of Energy. Trainees Approximately 30 Trainees (postdoctoral fellows and graduate students) will be supported for the entire two week program. They will be provided housing at the Howard Johnson in Morelia. Interested candidates must register on line filling both the registration and application parts of the form. In the box “Additional Information” be sure to indicate that you are applying as a trainee. The deadline for funding applications is October 25; during the first week of November selected trainees will be so notified and provided with a form to register for housing at the Howard Johnson. Researchers All researchers interested in the content of the program are welcome to attend, whether or not they apply for funding. However, if you wish to attend, you must register on line. There are some funds available to provide support for the second week, the “Opening Workshop.” Applications for this support must be submitted by October 25 by completing the application part of the registration form. During the first week of November applicants selected for funding will be informed of their support and all registrants will be given access to a housing registration form. Visas American citizens and permanent residents, as well as nationals from many other countries, need only a "tourist card" to enter Mexico for the workshop. For a list of these countries and information on obtaining a tourist card see: Consular Section of Embassy of Mexico in the United States of America Nationals from countries which require a visa to enter Mexico can find information and a visa application (pdf format) at: http://www.consulmexsf.com/ then select "services to non-Mexican" then select "visa legal framework". If you need documentation supporting your visa application, contact Daniel Juan-Pineda, daniel@matmor.unam.mx. For information about the Instituto de Matematicas, Unidad Morelia, go to http://www.matmor.unam.mx. For local information on Morelia, go to http://www.matmor.unam.mx/turismo/ingles/default.html. Tentative Schedule First Week: January 9-13, 2006 Monday, January 9 • 8:30am - 9:00 Welcome • 9:00am - 10am Introduction to algebraic topology (cell complexes, homology and cohomology, manifolds) B. Uribe • 10:30am -11:30am Introduction to algebraic topology (Transversality, Thom isomorphism) E. Lupercio • 12:00m - 1:00pm Introduction to algebraic topology (K-theory) B. Uribe • 1:00pm - 4:00pm LUNCH • 4:00pm - 5:30pm Discussion session with the lecturers. Tuesday, January 10 • 9:00am - 10am Introduction to algebraic topology (Simplicial complexes) B. Uribe • 10:30am -11:30am Introduction to Algebra (Algebras coming from physics, work of Gerstenhaber) E. Lupercio • 12:00m - 1:00pm Introduction to Algebra (Operads, BV algebras) E. Lupercio • 1:00pm - 4:00pm LUNCH • 4:00pm - 5:30pm Discussion session with the lecturers. Wednesday, January 11 • 9:00am - 10am Twisted K-theory (I) C. Teleman • 10:30am -11:30am String Topology (I) V. Godin • 12:00m - 1:00pm A -algebras (I) J. McClure • 1:00pm - 4:00pm LUNCH • 4:00pm - 4:30pm Discussion session with C. Teleman. • 4:30pm - 5:00pm Discussion session with V. Godin. • 5:30pm - 6:00pm Discussion session with J. McClure. Thursday, January 12 • 9:00am - 10am Loop Groups (I) N. Kitchloo • 10:30am -11:30am Twisted K-theory (II) C. Teleman • 12:00m - 1:00pm A ?-algebras (II) J. McClure • 1:00pm - 4:00pm LUNCH • 4:00pm - 4:30pm Discussion session with N. Kitchloo • 4:30pm - 5:00pm Discussion session with C. Teleman • 5:30pm - 6:00pm Discussion session with V. Godin. Friday, January 13 • 9:00am - 10am String Topology (II) V. Godin • 10:30am -11:30am Loop Groups (II) N. Kitchloo • 12:00m - 12:30pm Discussion session with V. Godin. • 12:30pm - 1:00pm Discussion session with N. Kitchloo. • 1:00pm - 4:00pm LUNCH Second Week: January 16-20 Titles and Abstracts (Adobe PDF file opens in new window, or Right-Click and select "Save Link As…" or "Save Target As…", to save a local copy) Week 2 Tentative Schedule Time Monday Tuesday Wednesday Thursday Friday 9:00-10:00 P. Teichner P. Teichner S. Stolz M. Hopkins M. Hopkins 10:00-10:30 Coffee Break 10:30-11:30 D. Freed D. Sullivan D. Sullivan D. Sullivan C. Telemann 11:45-12:45 U. Tillmann S. Galatius K. Fukaya F. Cohen I. Moerdijk 12:45-15:00 Lunch Break 15:00 - 15:45 E. Getzler N. Wahl EXCURSION E. Lupercio P. Norbury 16:00 - 16:45 J. Devoto V.Godin A. Voronov M. Xicotencatl Parallel sessions         17:00-17:45 C. Westerl and A. Ramirez N. Ganter     C. Douglas V. Gorbounov B. Uribe