Peter Sarnak, Princeton University
“Randomness in geometry - the topology of random real hypersurfaces and percolation”
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.
Reception will be held in DC 1301 - Fishbowl from 4:30 to 6:00pm.