The polyhedral structure of the disguised toric locus

Abstract: The disguised toric locus of a reaction network is the set of rate constants for which the associated mass action system is dynamically identical to a complex-balanced mass action system. The starting point of this talk is a recent result from joint work with Boros, Craciun, Jin, and Rojas La Luz (2510.03621), showing that the disguised toric locus is homeomorphic to a prism over the disguised toric flux locus, which is a polyhedral cone with a rich combinatorial structure. This result has both theoretical and practical consequences: it leads to new results on the geometry of the disguised toric locus, and provides a computational strategy for explicitly computing the disguised toric locus for networks that were out of reach with previous methods.

chemical biologychemical kineticsalgebraic 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! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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