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Applied Mathematics

Organizers: Casian Pantea

Spring 2020

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

Abstract: TBD