The current state of quasi-steady-state approximations: manifolds, time scales, singularities, and stochastic fluctuations

Abstract: Over the past decade, mathematicians have made considerable progress concerning the theory and applicability of quasi-steady-state (QSS) approximations in chemical kinetics. The application of Fenichel theory has revealed that QSS reduction in chemical kinetics is far richer than previously thought, even in low-dimensional systems that do not exhibit oscillatory behavior. In this talk, I will discuss recent discoveries that have emerged in the field of mathematical enzyme kinetics, including methodologies for obtaining perturbation parameters, singular points, dynamic bifurcations and scaling laws. If time permits, I will also discuss the applicability of QSS reductions in stochastic environments, and comment on some open problems in both deterministic and stochastic enzyme kinetics.

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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