BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Diego Rojas La Luz (University of Wisconsin-Madison) DTSTART:20240208T163000Z DTEND:20240208T170000Z DTSTAMP:20260421T124323Z UID:MoRN/88 DESCRIPTION:Title: Un veiling Surprising Connections Between the Classical Theory of Reaction Ne tworks and Generalized Lotka-Volterra Systems\nby Diego Rojas La Luz ( University of Wisconsin-Madison) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe explore the relationship between React ion Networks and Population Dynamics\, with a specific focus on Generalize d Lotka-Volterra systems. Surprisingly\, we find strong analogies between classical Mass Action Kinetics results (like the Horn-Jackson theorem and the deficiency-zero theorem) and new counterparts in Generalized Lotka-Vol terra systems\, hinting at a deep connection\, where previously none was k nown. Notably\, in the Generalized Lotka-Volterra setting\, we can prove t hat “complex-balanced” equilibria (properly defined) are globally attr active (which corresponds to the “global attractor conjecture" in the Re action Networks setting). As an example\, we show how to apply this new th eory to characterize global stability for a large class of cooperative Gen eralized Lotka-Volterra systems. We can also extend our results to analyze the properties of variable-k systems\, an area not fully explored in the context of Generalized Lotka-Volterra systems. This exploration unlocks un tapped insights into the mathematical foundations of these systems\, shedd ing light on their connections and paving the way for new avenues of resea rch and discovery in this field. This is joint work with Gheorghe Craciun and Polly Yu.\n LOCATION:https://researchseminars.org/talk/MoRN/88/ END:VEVENT END:VCALENDAR