|August 30, 2014|
Peter Sarnak is the Eugene Higgins Professor of Mathematics at Princeton where he has been a faculty member since 1991. He has had previous appointments at Stanford University and New York University, and has also been a member of the Institute for Advanced Study.
Sarnak has made major contributions to number theory, and to questions of analysis often motivated by number theory. He won the Ostrowski Prize in 2001, SIAM's Polya prize in 1998 and early in his career, received an NSF Presidential Young Investigator Award. He is a member of the National Academy of Sciences and a Fellow of the Royal Society. He gave a plenary lecture at the ICM in Berlin in 1998.
After introducing automorphic L-functions we discuss the problem of their size especially at special points on the critical line. Using techniques of averaging over families (via trace formulae)one can obtain sufficient information about these special values so as to make decisive applications.We will describe these methods as well as some applications to diophantine problems(sums of three integer squares in number fields) and to problems in mathematical physics (specifically quantum chaos).
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