University of Colorado

Fortieth Annual DeLong Lecture Series

Department of Mathematics

Professor Phillip A. Griffiths

Geometry and Arithmetic Cycles

Algebraic geometry is the study of algebraic varieties defined as the solutions of polynomial equations defined over a field. When the field is the complex numbers, the subject involves a rich interplay between analysis, differential geometry, topology and commutative algebra. The purpose of these lectures will be to discuss how the central problem in complex algebraic geometry, namely the understanding of the configuration of sub-varieties in an algebraic variety, leads necessarily to questions in arithmetic. The combination of geometry and arithmetic required to solve the main problems in the field will certainly turn out to be one of the rich stories in mathematics. These lectures are intended to explain, in generally non-technical terms, what is known in this story and what the central open questions are.

Date	Time	Room	Title
Monday, March 29, 2004	4:00-5:00 pm	BESC 180	How an elementary geometric question leads naturally to arithmetic considerations
Wednesday, March 31, 2004	5:00-6:00 pm	DUAN G125	The two main problems in the study of algebraic cycles
Thursday, April 1, 2004	5:00-6:00 pm	DUAN G125	The infinitesimal structure of the space of algebraic cycles

Phillip A. Griffiths

Phillip A. Griffiths is a Professor in the School of Mathematics at the Institute for Advanced Study. He was the Institute's Director from 1991-2003, Provost and James B. Duke Professor of Mathematics at Duke University from 1983-1991, and Professor of Mathematics at Harvard University from 1972-1983. He has also taught at Princeton University and the University of California, Berkeley. Dr Griffiths teaches mathematics graduate courses at Princeton University and supervises Princeton graduate students. He is Secretary of the International Mathematical Union.

As Chairman of the Sciences Institutes Group, Dr Griffiths leads the Millennium Science Initiative (MSI), whose primary goal is to strengthen the science and technology capacity of developing nations through programs of research and training planned and driven by local scientists. Dr Griffiths serves as special advisor to the Mellon Foundation, and he is a Distinguished Presidential Fellow for International Affairs at the National Academies.

Dr Griffiths received his Ph.D. from Princeton University. He is a member of the National Academy of Sciences, the American Philosophical Society, and the Council on Foreign Relations. He is a Foreign Associate of the Third World Academy of Sciences and of the Accademia Nazionale dei Lincei, and an Honorary Fellow of the Indian Academy of Sciences. He was a member of the National Science Board from 1991-1996. A former member of the Board of Directors of Bankers Trust New York Corporation, Dr Griffiths currently serves on the Boards of Directors of the Oppenheimer Funds and of GSI Lumonics.

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.

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

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