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

Wednesday, January 15, 2014 |
5:00-6:00 pm | RAMY C250 |
The rank of elliptic curvesThe problem of finding rational solutions to cubic equations is central in number theory, and goes back to Fermat. I will discuss why these equations are particularly interesting, and the modern theory of elliptic curves that has developed over the past century, including the Mordell-Weil theorem and the conjecture of Birch and Swinnerton-Dyer. I will end with a description of some recent results of Manjul Bhargava on the average rank. Following Wednesday's lecture, there will be a reception in honor of Professor Gross at the Koenig Alumni Center, 1202 University Avenue (the SE corner of Broadway and University). |

Thursday, January 16, 2014 |
5:00-6:00 pm | RAMY C250 |
The arithmetic of hyperelliptic curvesHyperelliptic curves over Q have equations of the form y, where ^{2} = F(x)F(x) is a polynomial with rational coefficients which has simple roots over the complex numbers. When the degree of F(x) is at least 5, the genus of the hyperelliptic curve is at least 2 and Faltings has proved that there are only finitely many rational solutions. In this talk, I will describe methods which Manjul Bhargava and I have developed to quantify this result, on average. |

## Benedict H. Gross |
Benedict (Dick) Gross is the George Vasmer Leverett Professor of Mathematics at Harvard University. Before he joined the Harvard mathematics faculty, Professor Gross taught at Princeton University, the University of Paris, and Brown University. He is a member of the American Academy of Arts and Sciences and the National Academy of Sciences. Gross's research interests are primarily in number theory and representation theory. Together with Don Zagier, he proved a formula relating the heights of Heegner divisors to the first derivatives of Rankin L-functions at s=1. Their work provided some insight into the conjecture of Birch and Swinnerton-Dyer, and was awarded the Cole Prize in Number Theory of the American Mathematical Society. Dick has had over 30 PhD students, and has enjoyed working jointly with many of his students and colleagues. Over the past two years he has been collaborating with Manjul Bhargava on the arithmetic of hyper elliptic curves. |

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

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

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