Number Theory Seminar: The Mathieu group M_23 is a Galois group over Q

Name: Number Theory Seminar: The Mathieu group M_23 is a Galois group over Q
Start: 2026-09-16T15:00:00-04:00
End: 2026-09-16T16:00:00-04:00
Location: Science Center 507

NUMBER THEORY

When: September 16, 2026

3:00 pm - 4:00 pm

Where: Science Center 507

Address: 1 Oxford Street, Cambridge, MA 02138, United States

Speaker: Bjorn Poonen (MIT)

Researchers realized 25 of the 26 sporadic finite simple groups as Galois groups over Q during 1984-1989, all but the Mathieu group M_23, a group of order 10200960. I will explain the rigidity method for realizing Galois groups in general, explain why it does not quite work for M_23, and explain how we were able to realize M_23 anyway, exploiting a “miracle” for which we are still seeking a conceptual explanation. This is joint work with Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee, Rachel Pries, and Shaowu Zhang.