Date | Time | Room | Title |
---|---|---|---|

Monday, January 29, 2007 |
4:00-5:00 pm | BESC 180 |
Before the Big Bang: a Novel Resolution of a Profound Cosmological PuzzleThe 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 non-random) 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 |
4:00-5:00 pm | DUAN G1B20 |
Twistor Theory: Old and NewBasic twistor geometry and its description of massless free fields Twistor theory revives some 19th-century geometry of Sophus Lie and Felix Klein, and puts it to use to re-express 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 twistor-string 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 |
4:00-5:00 pm | ECCR 245 |
Twistor Theory: Old and NewOn curved twistor spaces, twistor-strings, and the resolution of quantum divergences Continuation of Lecture II. |

## Sir 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 non-periodic 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 space-time 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 semi-popular 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". |

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.

1962-1963 Paul Halmos

1963-1964 Marshall Hall Jr.

1964-1965 Edwin Hewitt

1965-1966 George Polya

1966-1967 Alfred Tarski

1967-1968 John Milnor

1968-1969 Paul Cohen

1969-1970 Jurgen Moser

1970-1971 Mark Kac, Irving Kaplansky

1971-1972 Abraham Robinson

1972-1973 George Mackey

1973-1974 Olga Taussky Todd

1974-1975 Andrew Gleason

1975-1976 Tosio Kato

1976-1977 Hugh Montgomery

1977-1978 Elias Stein

1978-1979 Raoul Bott

1979-1980 Alan Weinstein

1980-1981 Enrico Bombieri

1981-1982 Richard S. Varga

1963-1964 Marshall Hall Jr.

1964-1965 Edwin Hewitt

1965-1966 George Polya

1966-1967 Alfred Tarski

1967-1968 John Milnor

1968-1969 Paul Cohen

1969-1970 Jurgen Moser

1970-1971 Mark Kac, Irving Kaplansky

1971-1972 Abraham Robinson

1972-1973 George Mackey

1973-1974 Olga Taussky Todd

1974-1975 Andrew Gleason

1975-1976 Tosio Kato

1976-1977 Hugh Montgomery

1977-1978 Elias Stein

1978-1979 Raoul Bott

1979-1980 Alan Weinstein

1980-1981 Enrico Bombieri

1981-1982 Richard S. Varga

1982-1983 Charles Fefferman

1983-1984 S.S. Chern

1984-1985 Robert Zimmer

1985-1986 Gerd Faltings

1986-1987 Dennis Sullivan

1987-1988 Stephen Smale

1988-1989 Branko Grunbaum

1989-1990 Ronald Graham

1990-1991 Kenneth Ribet

1991-1992 Michael Atiyah

1992-1993 John H. Conway

1993-1994 John Tate

1994-1995 Vladimir Arnold

1996-1997 Alain Connes

1997-1998 Barry Mazur

1999-2000 Nigel Higson

2000-2001 Jeff Cheeger

2001-2002 Vaughan F. R. Jones

2002-2003 Richard Taylor

2003-2004 Phillip A. Griffiths

1983-1984 S.S. Chern

1984-1985 Robert Zimmer

1985-1986 Gerd Faltings

1986-1987 Dennis Sullivan

1987-1988 Stephen Smale

1988-1989 Branko Grunbaum

1989-1990 Ronald Graham

1990-1991 Kenneth Ribet

1991-1992 Michael Atiyah

1992-1993 John H. Conway

1993-1994 John Tate

1994-1995 Vladimir Arnold

1996-1997 Alain Connes

1997-1998 Barry Mazur

1999-2000 Nigel Higson

2000-2001 Jeff Cheeger

2001-2002 Vaughan F. R. Jones

2002-2003 Richard Taylor

2003-2004 Phillip A. Griffiths

2004-2005 Paul Baum

2005-2006 Isadore M. Singer

2006-2007 Sir Roger Penrose

2007-2008 Maxim Kontsevich

2008-2009 Persi Diaconis

2009-2010 Ieke Moerdijk

2010-2011 Endre Szemerédi

2011-2012 Vitaly Bergelson

2012-2013 Yuval Peres

2013-2014 Benedict H. Gross

2014-2015 Robert Bryant

2015-2016 Magdalena Musat

2017-2018 Michael J. Hopkins

2018-2019 Kristin Lauter

2019-2020 Barry Simon

2005-2006 Isadore M. Singer

2006-2007 Sir Roger Penrose

2007-2008 Maxim Kontsevich

2008-2009 Persi Diaconis

2009-2010 Ieke Moerdijk

2010-2011 Endre Szemerédi

2011-2012 Vitaly Bergelson

2012-2013 Yuval Peres

2013-2014 Benedict H. Gross

2014-2015 Robert Bryant

2015-2016 Magdalena Musat

2017-2018 Michael J. Hopkins

2018-2019 Kristin Lauter

2019-2020 Barry Simon

If you have any questions concerning this lecture series, please contact
Mathematics.