On the sum of two reactions

Abstract: It is standard in (bio)chemistry to represent a series of reactions by a single reaction, often called a complex reaction in contrast to an elementary reaction. For example, photosynthesis $6\ \text{CO}_2+6\ \text{H}_2\text{O}\ \to \ \text{C}_6\text{H}_{12}\text{O}_6+6\ \text{O}_2$ is such complex reaction. We introduce a mathematical operation that corresponds to summing two chemical reactions. Specifically, we define an associative and non-communicative operation on the product space $\N_0^n\times \N_0^n$ (representing the reactant and the product of a chemical reaction, respectively). The operation models the overall effect of two reactions happening in succesion, one after the other. We study the algebraic properties of the operation and apply the results to stochastic reaction networks, in particular to reachability of states, and to reduction of reaction networks.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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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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