Organizers: Casian Pantea
Algebraic aspects of deterministic chemical systems
Polly Yu | University of Wisconsin-Madison
Friday, March 6 4 – 5 p.m. at ARM 403
Abstract: Deterministic mass-action systems, one of the most common models in biochemistry, are polynomial systems built out of directed graphs. Unsurprisingly then, algebraic structures are common in these models. In this talk, we introduce mass-action kinetics, its applicability in relation to physics, chemistry and biology, and how its positive steady states form a toric variety. Finally, for generalized mass-action systems, we will see how existence and uniqueness of its steady states are related to intersection of varieties, as well as bijectivity of exponential maps.
Dynamic aspects of deterministic chemical systems
Balázs Boros | University of Wisconsin-Madison
Monday, March 9 4 – 5 p.m. at ARM 403
Abstract: Mass-action dynamical systems are probably the most common mathematical models in biochemistry, cell biology, and population dynamics. Moreover, they represent a large class of polynomial dynamical systems that are important both theoretically and from the point of view of applications. In this talk, we give an introduction to the asymptotic stability of positive steady states of mass-action systems, as well as to the more global dynamical properties like persistence, boundedness, permanence, and global asymptotic stability. We conclude by presenting some recent results on the dynamics of generalized mass-action systems.
Seminar with Abhishek Deshpande
Abhishek Deshpande | University of Wisconsin-Madison
Thursday, March 9 4 – 5 p.m. at ARM 315