Date

Time

Room

Title

Monday, March 28, 2005

4:005:00 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.

Wednesday, March 30, 2005

4:005:00 pm

ECCR 1B40

What is KTheory 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
Ktheory) is taken up. Finally, the connection of Ktheory to the
RiemannRoch 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.

Friday, April 1, 2005

4:005:00 pm

ECCR 1B40

Trees, Buildings, Symmetric Spaces, and KTheory 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
BaumConnes conjecture on the Ktheory 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 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 195859 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 Ktheory 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 BaumConnes 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 BaumConnes 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.


