Peter Huxford

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About me

I am a G. C. Evans Instructor at Rice University, and am working with Chris Leininger and Alan Reid.

I completed my PhD in Mathematics at the University of Chicago, and was advised by Benson Farb.

I am interested in topological aspects of spaces that come from algebraic geometry, such as configuration spaces, discriminant complements, and moduli spaces. In particular their fundamental groups are of interest to me, among them braid groups and mapping class groups.

Research

• Generators for the level m congruence subgroups of braid groups [arXiv] [doi]
  (with Ishan Banerjee) J. Algebra (2025)
• Noninjectivity of the monodromy of certain equicritical strata [arXiv] [doi]
  (with Nick Salter) Geom. Dedicata (2025)
• Braid groups, elliptic curves, and resolving the quartic [arXiv] [doi]
  (with Jeroen Schillewaert) Math. Ann. (2025)
• Short presentations of finite simple groups [arXiv]
  Preprint, 2019

Selected talks

• An introduction to holomorphic rigidity
  NZMRI, January 2026
• Classifying holomorphic maps between spaces of polynomials
  58th Spring Topology and Dynamics Conference, March 2025
• Level m congruence subgroups of braid groups
  Rice University Topology Seminar, September 2024
• Braids, elliptic curves, and solving the quartic equation [video (starts 12:04)]
  Banff International Research Station, April 2024
• Rigidity of resolving the quartic and other algebraic constructions
  The University of Auckland, July 2023
• Special configurations in algebraic geometry
  The University of Auckland, May 2021

Fun

• A Modular Sculpture Corresponding to Three Rotations [link]
  (with Shintaro Fushida-Hardy) Bridges Conference Proceedings (2024), pp. 511-514