Date

Time

Room

Title

Monday, January 29, 2007

4:005:00 pm

BESC 180

Before the Big Bang: a Novel Resolution of a Profound Cosmological
Puzzle
The second law of thermodynamics says, in effect, that things get more
"random" as time progresses. This tells us that the beginning of the
universe  the "big bang"  must have been an extraordinarily precisely
organized (i.e. very nonrandom) state. What was the particular nature of
this state? How can such a special state have come about? In this talk, a
novel solution is suggested, which involves an examination of what is to be
expected in the very remote future of our universe, with its observed
accelerated expansion. My suggested model depends upon a slightly more
primitive form of spacetime geometry than Einstein's curved metric geometry,
namely conformal geometry in which it is merely the speed of light (in
every direction) that provides the needed strucure. (Note: this type of
conformal geometry also lies at the basis of twistor theory, which is
the subject of the two remaining DeLong Lectures.)

Wednesday, January 31, 2007

4:005:00 pm

DUAN G1B20

Twistor Theory: Old and New
Basic twistor geometry and its description of massless free fields
Twistor theory revives some 19thcentury geometry of Sophus Lie
and Felix Klein, and puts it to use to reexpress and generalize elegant
representations (some put forward at the turn of the 20th century) of some
of the most basic fields of physics. The theory indicates a possibly deep
role for holomorphic concepts (complex manifold structure, holomorphic sheaf
cohomology, complex bundles) in the key equations of physics, relating them
to foundational aspects of quantum theory. Some recent developments will be
outlined, such as the twistorstring theory promoted by Edward Witten and a
novel approach to the resolution of divergences in quantum field theory due
to Andrew Hodges.

Thursday, February 1, 2007

4:005:00 pm

ECCR 245

Twistor Theory: Old and New
On curved twistor spaces, twistorstrings, and the resolution of quantum
divergences
Continuation of Lecture II.

Professor Roger Penrose

Roger Penrose was born in 1931. He obtained his B.Sc. (1952, in
mathematics) at University College London, and his Ph.D. (1957, in
algebraic geometry) at St John's College, Cambridge. He held several
teaching and research positions in the UK and USA, particularly at
Birkbeck College London. Between 1973 and 1998 he was Rouse Ball
Professor of Mathematics at Oxford University and is currently Emeritus
Rouse Ball Professor. Since 1993 he has been Francis and Helen Pentz
Distinguished (visiting) Professor of Physics and Mathematics at Penn
State University. He is married and has four sons.
He was elected Fellow of the Royal Society in 1972 and has also been
elected to four other national scientific organizations including the
National Academy of Sciences. In 1993, he was knighted
for services to science,
and he received the Order of Merit in 2000.
He has received many awards, including Israel's Wolf Foundation Prize for
Physics 1988 (with Stephen Hawking) and the London Mathematical Society's
DeMorgan Medal 2004, as well as fourteen honorary degrees.
His research interests include various aspects of physics and geometry,
with many contributions to general relativity theory and the foundations
of quantum theory, the introduction of a generalized inverse of matrices,
the theory of nonperiodic tilings (including the first examples involving
only two distinct tiles), and the physical basis of consciousness. He
originated twistor theory, a proposal for uniting quantum ideas with
spacetime structure. He has also made contributions to cosmology, most
notably in relation to the geometrical nature of the big bang and its
fundamental role in the second law of thermodynamics.
He has written many scientific papers and several books, including three
technical books, and several semipopular books such as "The Emperor's New
Mind: On Computers, Minds, and the Laws of Physics", which won the 1990
Science Book Prize, "Shadows of the Mind: A Search for the Missing Science
of Consciousness", and the recent book "The Road to Reality: A Complete
Guide to the Laws of the Universe".

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.


