Prevalence of deficiency zero for random reaction networks

Abstract: In the study of reaction networks, there is usually a strong connection between the network structure and the qualitative behavior of the dynamical system. Certain network structures such as deficiency zero ensure many desirable behaviors of the dynamical systems including existence and stability of equilibrium.

In this talk, I will attempt to address a natural question: how prevalent these structures (in particular deficiency zero) are among random reaction networks. To answer this question, it is important to have a framework to generate random reaction networks. I will present two such frameworks: an Erdos-Renyi framework, and a stochastic block model framework-which is essentially a more generalized version of Erdos-Renyi. Next, I will examine the scaling limit (as the number of species goes to infinity) of the probability that a random reaction network has deficiency zero.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom!

The organizers.

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