Pascal Lecture 2018
Professor Peter Sarnak (Princeton)
" Integer points on affine cubic surfaces"
Abstract: A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions. There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems. Joint works with Bourgain/Gamburd and with Ghosh
Peter Sarnak is a South African-born mathematician who has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, and is also on the permanent faculty at the School of Mathematics of the Institute for Advanced Study. He is known for his work in analytic number theory. Peter is the recipient of many prestigious prizes, such as the George Pólya Prize (1998), the Ostrowski Prize (2001), the Levi L. Conant Prize (2003), the Cole Prize (2005) and the Wolf Prize (2014).