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GEOTOP-A | Tropical Geometry of Phylogenetic Tree Space | Anthea Monod

BHV space is a well-studied moduli space of phylogenetic trees that appears in many scientific disciplines, including computational biology, computer vision, combinatorics, and category theory. Speyer and Sturmfels identify a homeomorphism between BHV space and a version of the Grassmannian using tropical geometry, endowing the space of phylogenetic trees with a tropical structure, which turns out to be advantageous for computational studies. In this talk, I will present the coincidence between BHV space and the tropical Grassmannian. I will then give an overview of some recent work I have done that studies the tropical Grassmannian as a metric space and the practical implications of these results on probabilistic and statistical studies on sets of phylogenetic trees.