Geometry and Dynamics of Reaction System

Chemical reaction networks are directed graphs in which each edge represents a chemical reaction. The most basic kinetics to assign to reaction networks are those of mass-action, first introduced nearly 150 years ago by Guldberg and Waage: the rate at which each reaction occurs is proportional to the product of the concentrations of its reactants. The systematic study of the resulting polynomial ordinary differential equations began in the 1970s, and in recent years, this area has seen renewed interest, due in part to applications to systems biology. This talk will survey progress on long-standing questions pertaining to the dynamics of reaction systems, particularly their multistationarity and long-term stability, using methods from combinatorics and polyhedral as well as toric geometry.