Jeremy Booher's Homepage
**Jeremy Booher**

I am a postdoc in the School of Mathematics and Statistics at the University of Canterbury. Here is my CV.

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, where my advisor was Brian Conrad.

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

My email is jeremy.booher [AT] canterbury.ac.nz

I am in Room 620 of the Jack Erskine building.

**Research**

Iwasawa Theory for p-torsion Class Group Schemes in Characteristic p, with Bryden Cais, submitted. [arXiv] [MAGMA code]

Doubly isogenous genus-2 curves with D_{4}-action, with Vishal Arul, Steven R. Groen, Everett W. Howe, Wanlin Li, Vlad Matei, Rachel Pries, and Caleb Springer, submitted. [arXiv] (MAGMA Computations)

Recovering affine curves over finite fields from L-functions, with José Felipe Voloch, Pacific Journal of Mathematics 314-1 (2021), 1--28. [arXiv] [journal]

G-Valued Crystalline Deformation Rings in the Fontaine-Laffaille Range, with Brandon Levin, submitted. [arXiv]

Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy, with Renee Bell, William Chen, and Yuan Liu, to appear in Algebra & Number Theory. [arXiv]

Recovering Algebraic Curves from L-functions of Hilbert Class Fields, with José Felipe Voloch, Research in Number Theory 6, 43 (2020). [arXiv] [journal]

Realizing Artin-Schreier Covers of Curves with Minimal Newton Polygons
in Positive Characteristic, with Rachel Pries, Journal of Number Theory, Volume 214, (2020) pages 240-250. [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, accepted for publication in INVOLVE. [arXiv]
This incorporates student projects I developed for PROMYS 2019.

a-Numbers in Artin-Schreier Covers, with Bryden Cais, Algebra & Number Theory, Vol. 14 (2020), No. 3, 593–653. [arXiv] [journal] (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]

**Teaching**

#### At the University of Canterbury

EMth 211 (Engineering Linear Algebra and Statistics), 6 weeks in Semester 2 2021.

Math 324 (Cryptography and Coding Theory), 4 weeks in Semester 2 2021.

During summer 2020-2021, I supervised a student research project on covers of non-ordinary curves over finite fields.
#### At the University of Arizona

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).

** 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, in graduate school, and beyond.

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}.