Matt Litman

Graduate Student in Mathematics, UC Davis

Email: mclitman@ucdavis.edu Office: 2137 MSB

Graduate Student in Mathematics, UC Davis

Email: mclitman@ucdavis.edu Office: 2137 MSB

I am a fifth year graduate student in the pure mathematics group at UC Davis interested in *computational* number theory, where I investigate number theoretic problems through computer experimentation. Past and present work of mine includes the study of rational approximations via backwards continued fractions, expansions of the Riemann xi function in different orthogonal polynomial bases, distribution of primitive roots modulo different primes, value sets and sums over value sets for integral polynomials over finite fields, the algebraic-geometric dichotomy of higher dimensional integral sphere packings, and the orbital structure of automorphisms acting on graphs arising from surfaces defined by diophantine equations (i.e. Markoff triples). The common thread across all of these topics is the use of computer experimentation to gather evidence, form conjectures, and illuminate possible proof techniques.

My CV can be found by clicking on either use of CV in this sentence.

- A Cryptographic Hash Function from Markoff Triples, joint with E. Fuchs, K. Lauter, and A. Tran, Mathematical Cryptology 1 (1) (2021) pp. 103-121.
- Beyond Expansion II: Achieving or Exceeding the Ramanujan-quality Exponent of Distribution, Arbeitsgemeinschaft: Thin Groups and Super-approximation Workshop Report 2021/50 (2021) pp. 57-61.
- Möbius Disjointness for Skew Products on the Heisenberg Nilmanifold, joint with Z. Wang, Proceedings of the American Mathematical Society 147 (2019) pp. 2033-2043.
- On Consecutive Primitive nth Roots of Unity Modulo q, joint with T. Brazelton, J. Harrington, and S. Kannan, Journal of Number Theory 174 (2017) pp. 494-504.
- Flow Instabilities Due to Interfacial Surfactant/Polar Oil Material in a Hele-Shaw Cell, joint with A. Belmonte and Z. Niroobakhsh. Physical Review Letters E 96 (2017), 053102.

- Residue sums of Dickson polynomials over finite fields , joint with T. Brazelton, J. Harrington, and T.W.H. Wong (2022).
- Orbits on K3 Surfaces of Markoff Type, joint with E. Fuchs, J.H. Silverman, and A. Tran (2022).
- Asymptotic Density of Apollonian-Type Orbits, joint with A. Shedyvasser (2021).
- Error Approximation for Backwards and Simple Continued Fractions, joint with R.C. Bjorklund (2021).
- Sphere Eversion: Analysis of a Veridical Paradox (Senior Thesis).

- Interactive Proof of Hurwitz's Theorem, Mathematica program (2020)
- Backwards Continued Fraction Calculator for ℚ+ℚ(√D) , Mathematica program (2020)
- Zeta Functions and Quadratic Fields: An Introduction to Higher Number Theory, Chapter 13 (Translation), book by Don Zagier (in German, 1981), translation joint with F. Biefel (2020)
- Algebra Prelim Solutions, solutions provided by El Tigre (2020)

- Arbeitsgemeinschaft on Thin Groups and Super-Approximation, Mathematisches Forschunginstitut Oberwolfach, October 2021 -- Talk
- Mid-Atlantic Seminar on Numbers V (MASON V), Virtual, March 2021 -- Talk (slides)
- Number Theory Series in Los Angeles II, Occidental College, February 2020 -- Talk (slides)
- Illustrating Number Theory and Algebra, ICERM, October 2019 -- Lightning Talk
- Geometric Representation Theory and Low Dimensional Topology, ICMS, June 2019
- Graduate Student Combinatorics Conference (GSCC 2019), UPenn/Drexel, April 2019
- Joint Mathematics Meeting, Atlanta, GA, January 2017 -- Poster Presentation
- Mid-Atlantic Seminar on Numbers I (MASON I), Towson University, October 2016 -- Talk (slides)
- Young Mathematicians Conference, The Ohio State University, August 2016 -- Talk (slides)

Past:
Mat 21B (TA and Instructor), Mat 21C, Mat 67,

Mat 115A (TA and Instructor), Mat 125A,

Mat 135A (Discussion Notes), Mat 145 (Instructor),

Mat 150A, Mat 150B, Mat 150C (Discussion Notes),

Mat 167, Mat 185B, Mat 250A