## EVENT DETAILS AND ABSTRACT

**Algebraic Geometry Seminar**
**Title:** Ball quotients and Algebraic Geometry

**Speaker:** Eduard Looijenga

**Speaker Info:** University of Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

Some moduli spaces in algebraic geometry come with a Kaehler metric of constant negative holomorphic curvature or more precisely, can be identified (usually via a period map) with a Zariski open subset of a complex ball quotient. About 27 years ago Allcock found a ball quotient of dimension 13, which is intriguing for two reasons: its expected connections with some of the sporadic finite simple groups (such as the Monster group) and the likelihood of it having a modular interpretation. I shall first review the most important known examples of ball quotients with a modular interpretation (all of dimension at most 10) and then describe recent progress on the 'moonshine properties' of the Allcock ball quotient.

**Date:** Wednesday, March 27, 2024

**Time:** 3:00pm

**Where:** Lunt 103

**Contact Person:** Yuchen Liu

**Contact email:** yuchenl@northwestern.edu

**Contact Phone:**

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