Abstract:  In this talk we introduce a set of conditions a system of polynomial equations in several variables may satisfy, which are encoded in an associated graph, the polynomial graph. We explain a theorem describing the number of solutions to the system in this case, and show how this can be applied to graphical games. Time permitting, we will also describe emergent node tree structures (ENT structures) on games, a new model for games in which the players can be hierarchically decomposed into groups, along with a new solution concept for these games which refines Nash equilibria. We describe how the theorem applies to games with ENT structure.

Dr. Ruchira Datta received her undergraduate education at the California Institute of Technology. She has a M.S. in Computer Science (awarded 2002) and Ph.D. in Mathematics (awarded 2003) from the University of California at Berkeley. Her research interests are in combinatorics, algebra and computer science. Dr. Datta is a faculty candidate in the Department of Mathematical Sciences.