Tata Institute of Fundamental Research
A Geometric Approach to the Global Attractor Conjecture
Seminar
Speaker:
Manoj Gopalkrishnan
Organiser:
Manoj Gopalkrishnan
Date:
Monday, 12 May 2014, 16:00 to 17:00
Venue:
D-405 (D-Block Seminar Room)
(Scan to add to calendar)
Abstract:
Abstract: We tackle one of the most fascinating problems in reaction network theory: the Global Attractor Conjecture, which has been an open question for four decades now. In this paper, we do not quite prove the conjecture, but we prove a significant special case. We obtain a surprisingly crisp combinatorial understanding of the dynamics. On one hand there is this monstrous system of Ordinary Differential Equations with arbitrary degree non-linear terms on the right-hand side which seems hopeless to understand. On the other hand, there is this geometric diagram, much easier to work with. Remarkably, this simple geometric diagram reveals a surprising amount of information about the non-linear Ordinary Differential Equation system (this is joint work with Ezra Miller, and Anne Shiu and was published in SIAM J. Appl. Dyn. Syst., 13(2), 758–797. (40 pages).
http://epubs.siam.org/doi/abs/10.1137/130928170
arxiv.org/abs/1305.5303
| Speaker: | Manoj Gopalkrishnan |
| Organiser: | Manoj Gopalkrishnan |
| Date: | Monday, 12 May 2014, 16:00 to 17:00 |
| Venue: | D-405 (D-Block Seminar Room) |
(Scan to add to calendar)
Abstract:
Abstract: We tackle one of the most fascinating problems in reaction network theory: the Global Attractor Conjecture, which has been an open question for four decades now. In this paper, we do not quite prove the conjecture, but we prove a significant special case. We obtain a surprisingly crisp combinatorial understanding of the dynamics. On one hand there is this monstrous system of Ordinary Differential Equations with arbitrary degree non-linear terms on the right-hand side which seems hopeless to understand. On the other hand, there is this geometric diagram, much easier to work with. Remarkably, this simple geometric diagram reveals a surprising amount of information about the non-linear Ordinary Differential Equation system (this is joint work with Ezra Miller, and Anne Shiu and was published in SIAM J. Appl. Dyn. Syst., 13(2), 758–797. (40 pages).
http://epubs.siam.org/doi/abs/10.1137/130928170
arxiv.org/abs/1305.5303
http://epubs.siam.org/doi/abs/10.1137/130928170
arxiv.org/abs/1305.5303