Date and Time: 4:00 - 4:55pm, Monday, November 14, 2005 Room: 121 Little Hall Refreshments: After the lecture in LIT 339   OPENING REMARKS by Krishnaswami Alladi Chair, Department of Mathematics

Abstract: The maximum principle is a basic tool in the study of second order elliptic equations. Various forms of the principle will be discussed, including the Hopf Lemma. Applications to symmetry, monotonicity and to geometry will be presented. These lead to the need for new forms of the Hopf Lemma. The talk will be expository.

 ^* Louis Nirenberg is one of the outstanding analysts of the twentieth century. He has made fundamental contributions to the understanding of linear and nonlinear partial differential equations and their application to complex analysis and geometry.

Nirenberg received the AMS Bocher Prize in 1959 for his work on partial differential equations. In 1982 he was the first recipient in mathematics of the Crafoord Prize, established by the Royal Swedish Academy of Sciences in areas not covered by the Nobel Prizes. In 1995 he received the National Medal of Science, the United States' highest honor for contributions to science. (from Notices of the AMS, 4/2002)

For more biographical information on Professor Nirenberg see the Notices of the AMS, April 2002, vol. 49, Number 4.

This years Ulam Colloquium is part of the Special Year in Probability and Analysis