Christopher Davis
Associate professor of teaching Mathematics Department University of California, Irvine
Contact Information:
Email: 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 


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 20102013 I was a Visiting Assistant Professor here and now I'm an Associate professor of teaching in the math department. This is a teachingfocused position, and I hope to be involved with many different facets of education in the math department. From 20132015 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.
On the ptypical de RhamWitt complex over W(k). Alg. Number Th. 13 (2019) 15971631. Version of April 21, 2019.
Explicit points on y^2 + xy + (t^d)y = x^3 and related character sums, with Tommy Occhipinti. J. Number Theory. 168 (2016), 1338. Version of 9/26/2014.
Newton slopes for ArtinSchreierWitt towers, with Daqing Wan and Liang Xiao. Math. Ann. 364 (2016), no. 34, 14511468. 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, 417430. Version of 2/20/2014.
Almost purity and overconvergent Witt vectors, with Kiran Kedlaya. J. Algebra. 422 (2015), 373412. Version of 8/16/2014.
Canonical Cohen rings for norm fields, with Bryden Cais. Int. Math. Res. Not. 2015 (2015), 54735517. Version of 12/30/2013.
Integral structure on MonskyWashnitzer cohomology and the overconvergent de RhamWitt complex, with David ZureickBrown. Math. Res. Lett. 21 (2014), no. 2, 281288. Version of 5/1/2013.
Which finite simple groups are unit groups?, with Tommy Occhipinti. J. Pure Appl. Algebra 218 (2014), no. 4, 743744. 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.
Lfunctions of padic characters, with Daqing Wan. Nagoya Math. J. 213 (2014), 77104. Version of 3/30/2013.
On the Witt vector Frobenius, with Kiran Kedlaya. Proc. Amer. Math. Soc. 142 (2014), 22112226. Version of 10/1/2012.
Overconvergent Witt vectors, with Andreas Langer and
Thomas Zink. J. Reine Angew. Math. 668 (2012), 134.
Overconvergent de RhamWitt cohomology, with Andreas
Langer and Thomas Zink.
Ann. Scient. Éc. Norm. Sup. (4) 44 (2011), no. 2, 197262.
The overconvergent de RhamWitt complex, Ph.D. Thesis, MIT. Advised by Kiran Kedlaya. 2009. You can see it
here by clicking on the "Preview, nonprintable" 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, 123.
Preprints:
Witt vectors with padic 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:
Past UCI Teaching:
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".