University of Colorado Boulder

Forty-First Annual DeLong Lecture Series

Department of Mathematics

Professor Paul Baum

An Introduction to K-Theory

March 28, 2005
4:00-5:00 pm BESC 180 Mathematical Impossibilities
This is mainly about the impossibility (within the rules of Greek geometry) of angle trisection. Some other impossibilities - solution of fifth and higher degree equations by a radical formula, the Fermat problem - will be briefly mentioned. This lecture begins with the quadratic formula and should be understandable to anybody with a reasonable high school education.
March 30, 2005
4:00-5:00 pm ECCR 1B40 What is K-Theory and what is it good for?
This lecture begins with the definition of K(A) via idempotent matrices, where A is a ring with unit. The basic example of the idempotent matrix which "is" the Möbius band is then explained. Next, the vector fields on spheres problem (which was solved by J.F. Adams using K-theory) is taken up. Finally, the connection of K-theory to the Riemann-Roch problem is briefly indicated. This lecture should be comprehensible to people who are familiar with basic definitions such as ring, abelian group, continuity, matrix multiplication, holomorphic function.
April 1, 2005
4:00-5:00 pm ECCR 1B40 Trees, Buildings, Symmetric Spaces, and K-Theory for Group C* algebras
This lecture begins with a list of problems in various parts of mathematics. The point is then made that all of these problems are contained in the Baum-Connes conjecture on the K-theory of group C* algebras. The lecture concludes by stating the relevant problem, and giving some indication of the proposed solution. This lecture should be comprehensible to people with some additional mathematical background to that needed for Lecture II. For example, the definitions of Hilbert space and topological group will be assumed.

Paul Baum

Paul Baum

Paul Frank Baum is Evan Pugh Professor of Mathematics at Penn State University. He previously taught at Brown University and Princeton University.

He received his undergraduate degree from Harvard College (1958) and his Ph.D. from Princeton University (1963). For the academic year 1958-59 he was an "élève étranger" at the École Normale Supérieure in Paris. His Princeton Ph.D. thesis was written under the direction of John Moore and Norman Steenrod.

Professor Baum's work in mathematics has been interdisciplinary, ranging from algebraic geometry to K-theory of operator algebras. In 1980 he began the joint effort with Alain Connes that led to the formulation of the conjecture now known as the Baum-Connes conjecture. This conjecture is unusual in that it cuts across several different areas of mathematics and reveals connections between problems that earlier appeared to be totally unrelated.

During 2004 Professor Baum lectured on the Baum-Connes conjecture at universities and research institutes in Europe and the USA. He had visiting appointments at IHES (Institut des Hautes Études Scientifiques) and at IAS (Institute for Advanced Study). He gave the 2004 Kemeny Lectures at Dartmouth College. In 2005 he will give invited lecture series in India (Tata Institute for Fundamental Research), Japan (Keio University), and Poland (Stefan Banach Institute).

DeLong Lecture Series

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.

Previous DeLong Lecturers