Jeremy Booher's Homepage
**Jeremy Booher**

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 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, Z_{p} is the integers modulo p, not the p-adic integers. Furthermore, the group of units in Z_{p} is denoted by U_{p}.

**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.