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

Monday, October 13, 2014 |
4:00-5:00pm | BESC 180 |
The idea of holonomyThe notion of 'holonomy' in mechanical systems has been around for more than a century and gives insight into daily operations as mundane as steering and parallel parking and in understanding the behavior of balls (or more general objects) rolling on a surface with friction. A sample question is this: What is the best way to roll a ball over a flat surface, without twisting or slipping, so that it arrives at at given point with a given orientation? In geometry and physics, holonomy has turned up in many surprising ways and continues to be explored as a fundamental invariant of geometric structures. In this talk, I will illustrate the fundamental ideas in the theory of holonomy using familiar physical objects and explain how it is also related to group theory and symmetries of basic geometric objects. Following Monday's lecture, there will be a reception in honor of Professor Bryant at the Koenig Alumni Center, 1202 University Avenue (the SE corner of Broadway and University). |

Tuesday, October 14, 2014 |
5:00-6:00pm | BESC 180 |
Convex billiards and non-holonomic systemsGiven a closed, convex curve C in the plane, a billiard path on C is a polygon P inscribed in C such that, at each vertex v of P, the two edges of P incident with v make equal angles with the tangent line to C at v. (Intuitively, this is the path a billiard ball would follow on a frictionless pool table bounded by C.) For 'most' convex curves C, there are only a finite number of triangular billiard paths on C, a finite number of quadrilateral billiard paths, and so on. Obviously, when C is a circle, there are infinitely many closed billiard n-gons inscribed in C, but, surprisingly, the same is true when C is an ellipse. (This is a famous theorem due to Chasles.) The interesting question is whether there are other curves, besides ellipses, for which this is true. In this talk, I'll discuss these phenomena and show how they are related to the geometry of nonholonomic plane fields (which will be defined and described). |

## Robert Bryant |
A North Carolina native, Robert Bryant received his PhD in mathematics in 1979 at the University of North Carolina at Chapel Hill, working under the direction of Robert B. Gardner. After serving on the faculty at Rice University for seven years, he joined the faculty of Duke University in 1987, where he held the Juanita M. Kreps Chair in Mathematics until moving to the University of California at Berkeley in July 2007. He served there on the faculty and as the Director of the Mathematical Sciences Research Institute from 2007 until 2013, after which, he returned to Duke University as the Phillip Griffiths Professor of Mathematics. He has held visiting positions at universities and research institutes around the world. His research interests center on exterior differential systems and the geometry of differential equations as well as their applications in Riemannian geometry, special holonomy, and related areas. He serves on the editorial boards of the Duke Mathematical Journal, Communications in Analysis and Geometry, and the Journal of the AMS. He is currently the President-elect of the American Mathematical Society and will assume the office of the AMS Presidency in February 2015, for a term of 2 years. He is a fellow of the American Academy of Arts and Sciences and a member of the National Academy of Sciences. In his spare time, he enjoys reading, playing the piano, rock climbing, and other physical activities. |

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

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