Jeremy Booher

Jeremy Booher

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I am a postdoc in the Mathematics Department at the University of Arizona. My mentor is Bryden Cais. 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 algebraic geometry in characteristic p.

My email is jeremybooher [AT] math.arizona.edu

My office is 315 in the math department.

Research

  • a-Numbers in Artin-Schreier Covers, with Bryden Cais. Submitted. [arXiv] (MAGMA computations)

  • G-Valued Galois Deformation Rings when l ≠ p, with Stefan Patrikis, to appear in MRL. [arXiv]

  • 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.

    Teaching

    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.

    I was a graduate student TA at Stanford. During the summers, I worked at PROMYS (2007, 2008, 2010, 2011) and SUMAC (2013, 2014, 2015, 2016), and helped with SURIM (2012).

    Other Activities

    I am organizing the Algebra and Number Theory Seminar at the University of Arizona.

    I help with the Tucson Math Circle.