Date & Time: Wednesday, January 14, 2015, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: Manoj Gopalkrishnan, TIFR Mumbai
Title: The Geometry of Reaction Networks
Abstract: Biochemical reaction networks are known to exhibit exquisite dynamical behavior. One way of modeling this dynamical behavior is via the Law of Mass Action, as a system of ordinary differential equations. The mathematical field that pursues the systematic study of the class of such ordinary differential equations has come to be known as "reaction network theory." It has attracted a diverse community of researchers from dynamical systems, algebraic geometry, combinatorics, control theory, chemical engineering, systems biology, computer science, category theory, etc. I shall give a mathematical introduction to this area, and argue that the study of reaction networks is of intrinsic mathematical interest. I shall state the Permanence Conjecture, a four-decade old open problem that is surprisingly easy to state, and describe some progress I have made towards this conjecture along with collaborators Ezra Miller (Duke University Math) and Anne Shiu (Texas A&M Math).