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Title: Phase Transitions in Chase-Escape with Death

Abstract: Chase-escape with death is a competitive random growth model which takes place on a graph occupied by red and blue particles. Red particles can spread to adjacent, unexplored sites, and blue particles can expand to adjacent, red sites. Red particles can also die, leaving the site uninhabitable. We study the process on the $d$-ary, rooted tree and are interested in the impact of varying two parameters: the expansion speed of red particles and the death rate of red particles. Our recent work shows the existence of two phase transitions and gives connections between this process and several combinatorial objects, including weighted Catalan numbers and continued fractions. This is joint work with Keisha Cook, Nicole Eikmeier, Sarai Hernandez-Torres, and Matthew Junge.