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# What is a moduli space? (Javier Gonzalez Anaya, HMC)

## October 25, 2023 @ 4:15 pm - 5:30 pm

**Title: **What is a moduli space?

**Speaker: **Javier Gonzalez Anaya, Department of Mathematics, Harvey Mudd College

**Abstract**: A natural endeavour in mathematics is to classify objects according to their properties. For example, we can readily identify straight lines in the plane, or recognize different kinds of triangles depending on their symmetries. Less intuitive, however, is that given a class of mathematical objects, it is often possible to construct a geometric space parametrizing those objects. Known as “moduli spaces”, the study of these spaces has been a major driving force of modern geometry. In this talk we will explore some of the main ideas behind moduli theory through examples, ranging from the moduli space of lines in the plane to the one of points on the sphere. We will finish by discussing our ongoing research on the moduli space of points in d-dimensional space.

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. Currently, he holds a position as a visiting assistant professor at Harvey Mudd College, having previously served in a similar role at UC Riverside. Beyond his research, Javier is a committed educator and mentor, having overseen student research projects and taught an extensive range of courses.