Jeremy Booher Jeremy Booher's Homepage

Jeremy Booher

I am a postdoc in the School of Mathematics and Statistics at the University of Canterbury. I am working with Felipe Voloch.

Previously, I was a postdoc at the University of Arizona, working with Bryden Cais. Before that, I was a graduate student at Stanford University. My advisor was Brian Conrad. Here is my CV.

I am interested in algebraic number theory and arithmetic geometry, especially Galois representations and coverings of curves in characteristic p.

My email is jeremy.booher [AT]

I am in Room 616 of the Jack Erskine building.


  • Recovering Algebraic Curves from L-functions of Hilbert Class Fields, with José Felipe Voloch, preprint. [arXiv]
  • Realizing Artin-Schreier Covers of Curves with Minimal Newton Polygons in Positive Characteristic, with Rachel Pries, to appear in the Journal of Number Theory. [arXiv], [journal]
  • Realizing Artin-Schreier Covers with Minimal a-numbers in Positive Characteristic, with Fiona Abney-McPeek, Hugo Berg, Sun Mee Choi, Viktor Fukala, Miroslav Marinov, Theo Müller, Paweł Narkiewicz, Rachel Pries, Nancy Xu, and Andrew Yuan. [arXiv] This incorporates a student project from PROMYS 2019.
  • a-Numbers in Artin-Schreier Covers, with Bryden Cais, to appear in Algebra & Number Theory. [arXiv] (MAGMA computations)
  • G-Valued Galois Deformation Rings when l ≠ p, with Stefan Patrikis, Mathematical Research Letters, Vol. 26, No. 4 (2019), pp. 973-990. [arXiv], [journal]
  • Minimally Ramified Deformations when l ≠ p. Compositio Mathematica, Volume 155 / Issue 1 (2019) pages 1-37. [arXiv], [journal]
  • Producing Geometric Deformations of Orthogonal and Symplectic Galois Representations. Journal of Number Theory, Volume 195, (2019) pages 115-158. [arXiv] [journal]
  • Geometric Deformations of Orthogonal and Symplectic Galois Representations is the paper version of my thesis. It has been broken up into the two papers above for publication.
  • Evaluation of Cubic Twisted Kloosterman Sheaf Sums, with Anastassia Etropolski and Amanda Hittson. International Journal of Number Theory, 6 (2010), pages 1349-1365. [pdf] [journal]

  • Expository Notes and Articles

    Expository writing including my senior thesis, Part III essay, and notes for many of the talks I have given at PROMYS and in graduate school.

    Warning: the ones which came from the summers I spent as a counselor at PROMYS use non-standard notation: taking a quotient of a ring by a principal ideal is denoted by a subscript. In particular, Zp is the integers modulo p, not the p-adic integers. Furthermore, the group of units in Zp is denoted by Up.


    Math 446/546 (Theory of Numbers), Spring 2019.

    Math 313 (Linear Algebra), two sections in Fall 2018.

    Math 432/532 (Topological Spaces), Spring 2018.

    Math 313 (Linear Algebra), two sections in Fall 2017.

    Math 446/546 (Theory of Numbers), Spring 2017.

    Math 129 (Calculus II), Spring 2017.

    Math 125 (Calculus I), Fall 2016.

    While at the University of Arizona, I helped with the Tucson Math Circle. During many summers, I worked at PROMYS (2007, 2008, 2010, 2011) and SUMAC (2013, 2014, 2015, 2016), and helped with SURIM (2012).