Christopher Davis

Lecturer with Potential Security of Employment
Mathematics Department
University of California, Irvine

Contact Information:

E-mail: daviscj@uci.edu (always the best way to reach me)
Office: Rowland Hall, Room 440J
Website: http://www.math.uci.edu/~davis
Office phone: 949.824.5313

picture
Me in front of the Golden Gate Bridge in San Francisco


About me:

I'm at University of California, Irvine for the second time. From 2010-2013 I was a Visiting Assistant Professor here and now I'm a Lecturer with Potential Security of Employment. This is a teaching-focused position, and I hope to be involved with many different facets of education in the math department. From 2013-2015 I was a postdoc at the University of Copenhagen as part of Lars Hesselholt's Niels Bohr Professorship. I was a graduate student at MIT, where my advisor was Kiran Kedlaya. My mathematical interests lie in the general neighborhood of number theory and algebraic geometry. More specifically, you'll see below that many of my papers involve Witt vectors.

Publications:

arXiv link for many of my papers.

Explicit points on y^2 + xy + (t^d)y = x^3 and related character sums, with Tommy Occhipinti. J. Number Theory. 168 (2016), 13-38. Version of 9/26/2014.

Newton slopes for Artin-Schreier-Witt towers, with Daqing Wan and Liang Xiao. Math. Ann. 364 (2016), no. 3-4, 1451-1468. Version of 10/20/2013.

A characterization of strictly APF extensions, with Bryden Cais and Jonathan Lubin. J. Théor. Nombres Bordeaux. 28 (2016), no. 2, 417-430. Version of 2/20/2014.

Almost purity and overconvergent Witt vectors, with Kiran Kedlaya. J. Algebra. 422 (2015), 373-412. Version of 8/16/2014.

Canonical Cohen rings for norm fields, with Bryden Cais. Int. Math. Res. Not. 2015 (2015), 5473-5517. Version of 12/30/2013.

Integral structure on Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex, with David Zureick-Brown. Math. Res. Lett. 21 (2014), no. 2, 281-288. Version of 5/1/2013.

Which finite simple groups are unit groups?, with Tommy Occhipinti. J. Pure Appl. Algebra 218 (2014), no. 4, 743-744. Version of 8/6/2013.

Which alternating and symmetric groups are unit groups?, with Tommy Occhipinti. J. Algebra Appl. 13 (2014), 12 pp. Version of 7/16/2013.

L-functions of p-adic characters, with Daqing Wan. Nagoya Math. J. 213 (2014), 77-104. Version of 3/30/2013.

On the Witt vector Frobenius, with Kiran Kedlaya. Proc. Amer. Math. Soc. 142 (2014), 2211-2226. Version of 10/1/2012.

Overconvergent Witt vectors, with Andreas Langer and Thomas Zink. J. Reine Angew. Math. 668 (2012), 1-34.

Overconvergent de Rham-Witt cohomology, with Andreas Langer and Thomas Zink. Ann. Scient. Éc. Norm. Sup. (4) 44 (2011), no. 2, 197-262.

The overconvergent de Rham-Witt complex, Ph.D. Thesis, MIT. Advised by Kiran Kedlaya. 2009. You can see it here by clicking on the "Preview, non-printable" link. However, note that the results of the first four sections are improved and expanded in my joint papers with Andreas Langer and Thomas Zink, and the results of the last two sections are improved and expanded in my joint papers with Kiran Kedlaya.

Totally geodesic Seifert surfaces in hyperbolic knot and link complements II (access by subscription), with Colin Adams, Hanna Bennett, Michael Jennings, Jennifer Novak, Nicholas Perry, and Eric Schoenfeld. J. Differ. Geom. 79 (2008), no. 1, 1-23.

Preprints:

On the p-typical de Rham-Witt complex over W(k). Version of June 18, 2017.

Witt vectors with p-adic coefficients and Fontaine's rings, with Kiran Kedlaya. Version of 2/21/11. Much of this material has been moved into our Frobenius paper and our Almost purity paper.

Current Teaching:

Spring 2017: Math 9: Introduction to Programming for Numerical Analysis
Spring 2017: Math 120B: Introduction to Abstract Algebra: Rings and Fields
Spring 2017: Math 140B: Elementary Analysis

Past UCI Teaching:

Winter 2017: Math 120B: Introduction to Abstract Algebra: Rings and Fields
Winter 2017: Math 121A: Linear Algebra
Fall 2016: Math 2D: Multivariable Calculus
Fall 2016: Math 120A: Introduction to Abstract Algebra: Group theory
Spring 2016: Math 2B: Integral Calculus
Spring 2016: Math 9: Introduction to Programming for Numerical Analysis
Winter 2016: Math 2A: Differential Calculus
Winter 2016: Math 9: Introduction to Programming for Numerical Analysis
Fall 2015: Math 9: Introduction to Programming for Numerical Analysis
Fall 2015: Math 13: Introduction to Abstract Mathematics
Spring 2013: Math 180B: Number Theory
Winter 2013: Math 173B: Introduction to Cryptology
Winter 2013: Math 180A: Number Theory
Fall 2012: Math 121A: Linear Algebra
Fall 2012: Math 173A: Introduction to Cryptology
Summer 2012: Math 1A: Pre-calculus
Summer 2012: Math 1B: Pre-calculus
Spring 2012: Math 2A: Differential Calculus
Spring 2012: Math 230C: Abstract Algebra
Winter 2012: Math 120B: Abstract Algebra
Fall 2011: Math 2B: Integral Calculus
Fall 2011: Math 232A: Algebraic Number Theory
Summer 2011: Math 173A: Introduction to Cryptology
Spring 2011: Math 2B: Integral Calculus
Spring 2011: Math 233C: Algebraic Geometry
Winter 2011: Math 233B: Algebraic Geometry
Fall 2010: Math 2B: Integral Calculus
Fall 2010: Math 2J: Linear Algebra and Power Series
Summer 2010: Math 2B: Integral Calculus

Other:

Slides from Freshmen and Sophomore advising, February 2017.
CV as of February 2017.
Lab instructions for Math 173, Introduction to Cryptology.
Sage code for Math 173, Introduction to Cryptology.
Cryptography and Sage. Video from a talk I gave at Sage Education Days 5.
Slides from my 2013 JMM talk on "Base rings for global (phi,Gamma)-modules".