Moduli Spaces Through a Combinatorial Lens (Javier González Anaya, Harvey Mudd College)

Speaker: Javier González Anaya, Visiting Assistant Professor of Mathematics, Harvey Mudd College, Claremont CA

Title: Moduli spaces through a combinatorial lens

Abstract: A natural endeavor in mathematics is classifying objects according to their properties. A remarkable fact is that, for many classes of objects, one can construct a geometric space that parametrizes them. Known as “moduli spaces,” the study of these spaces has been a major driving force in modern geometry. In this talk, we will begin by introducing a central example: the moduli space of points on the sphere. Then, we will discuss two natural generalizations from the literature, with a focus on how combinatorial techniques have helped us better understand these spaces. This research has been part of two collaborations, one with J. Bown’s, as part of their senior thesis, and the other as part of M. Bit and J. Luo’s Summer REU co-led with Prof. Dagan Karp.

Bio: Javier González Anaya, PhD is an algebraic geometer specializing in the study of combinatorial structures and finite generation problems within the field of birational geometry. His research extends to areas such as the theory of polytopes and machine learning. He has been a visiting assistant professor at Harvey Mudd College since last year, having previously served in a similar role at UC Riverside. Beyond his research, Javier is a committed educator and mentor, having overseen several student research projects and taught a wide array of courses.