October 17, 2005
|4:00-5:00 pm||BESC 180||
Introduction to Index Theorems
Index theory begins with the study of existence and uniqueness for linear equations. I will explain the Fredholm alternative - when uniqueness implies existence and vice versa - and proceed to define the index of Fredholm operators. A simple example will illustrate the analytic, topological, and geometric character of the index.
I will show why the space of Fredholm operators is a classifying space for K-theory.
October 18, 2005
|4:00-5:00 pm||MUEN E050||
K-theory and Twisted K-theory
I will introduce spin and spinc manifolds via the bundle of Clifford algebras over a manifold, and define Twisted K-theory in terms of bundles of simple algebras. Then I'll discuss the index theorem for families of Dirac operators and recent generalizations.
October 24, 2005
|4:00-5:00 pm||BESC 180||CANCELLED|
Isadore M. Singer
| Isadore M. Singer was born in 1924 in Detroit, and received his undergraduate degree from the University of Michigan in 1944. After obtaining his Ph.D. from the University of Chicago in 1950, he joined the faculty at the Massachusetts Institute of Technology (MIT). Singer has spent most of his professional life at MIT, where he is currently an Institute Professor.
Singer is a member of the American Academy of Art and Sciences, the American Philosophical Society and the National Academy of Sciences (NAS). He served on the Council of NAS, the Governing Board of the National Research Council, and the White House Science Council. Singer was vice president of the American Mathematical Society from 1970 - 1972.
In 1992 Singer received the American Mathematical Society's Award for Distinguished Public Service. The citation recognized his "outstanding contribution to his profession, to science more broadly and to the public good."
Among the other awards he has received are the Bôcher Prize (1969) and the Steele Prize for Lifetime Achievement (2000), both from the American Mathematical Society, the Eugene Wigner Medal (1988), and the National Medal of Science (1983). In 2004, he was awarded the Abel Prize, jointly with Sir Michael Atiyah.
When Singer was awarded the Steele Prize his response, published in the Notices of the AMS, was: "For me the classroom is an important counterpart to research. I enjoy teaching undergraduates at all levels, and I have a host of graduate students, many of whom have ended up teaching me more than I have taught them."
Singer has also written influential textbooks that have inspired generations of mathematicians.
This Lecture Series is funded by an endowment given by Professor Ira M. DeLong, who came to the University of Colorado in 1888 at the age of 33. Professor DeLong essentially became the mathematics department by teaching not only the college subjects but also the preparatory mathematics courses. Professor DeLong was a prominent citizen of the community of Boulder as well as president of the Mercantile Bank and Trust Company, organizer of the Colorado Education Association, and president of the charter convention that gave Boulder the city manager form of government in 1917. After his death in 1942 it was decided that the bequest he made to the mathematics department would accumulate interest until income became available to fund DeLong prizes for undergraduates and DeLong Lectureships to bring outstanding mathematicians to campus each year. The first DeLong Lectures were delivered in the 1962-63 academic year.