Randomness in geometry - the topology of random real hypersurfaces and percolation
Peter Sarnak, Princeton University and Institute for Advanced Study (IAS)
Abstract: The behavior of many arithmetic and geometric objects are apparently dictated by models from statistical physics. For example, the topologies of the connected components of the zero sets of random real projective hypersurfaces of high degree follow a universal law of distribution. We explain this (and a more general phenomenon for random band limited functions), its source and some possible connections to percolation. Joint work with I. Wigman.
Speaker biography: Born in South Africa, Peter Sarnak received his PhD from Stanford University in 1980, and is presently a professor at Princeton University and the Institute for Advanced Study. He has received numerous awards, including the prestigious Wolf Prize in 2014. Like his advisor, Paul Cohen, Peter's vision of mathematics is broad, and his work connects many areas of mathematics. He has made fundamental and influential contributions to number theory, automorphic forms, spectral theory, geometry, and graph theory, often uncovering deep connections between different areas of mathematics. He is, all at once, a theory builder with a vast view of the landscape of mathematics, a problem solver of tremendous technical ability, and a problem poser with an uncanny ability to ask questions that open up whole new directions of research. He has also been very influential as a teacher and advisor, having supervised around 60 PhD students and dozens of postdoctoral fellows.
Reception to follow in William G. Davis Computer Research Centre (DC) room 1301 (Fishbowl).