# Tyler Evans

## Professor & Chair

Dr. Evans joined the mathematics faculty at Humboldt in 2001.

#### Specialty Area

Restricted Lie algebra representations and cohomology. Applications of group theory to discrete mathematics Algebraic (finite) cellular automata.

#### Teaching

Twenty-four years of university classroom experience teaching a wide variety of courses including elementary and intermediate algebra, college algebra, precalculus, elementary statistics, calculus, advanced calculus, differential equations, linear algebra, logic, number theory, abstract algebra, real analysis, knot theory, topology and graph theory.

#### Education

#### Courses Taught

#### Research

Restricted Lie algebra cohomology, group valued finite cellular automata, algebraic combinatorics, undergraduate mathematical research.

#### Publications

14. "On the cohomology of restricted Heisenberg Lie algebras" (with A. Fialowski and Y. Yang), *Linear Algebra and its Applications*, Vol. 699, pp. 295 - 309, 2024.

13. "Central Extensions of Restricted Affine Nilpotent Lie Algebras $n_+(A^{(1)}_1)(p)$" (with A. Fialowski), Journal of Lie Theory, 33 (2023), No. 1, pp. 195-215.

12. “Cohomology of Restricted Filiform Lie Algebras $m^\lambda_2 (p)$" (with A. Fialowski), SIGMA 15 (2019), 095, 11 pages. arXiv:1901.07532 https://doi.org/10.3842/SIGMA.2019.095

11. “Restricted One-dimensional Central Extensions of the Restricted Filiform Lie Algebras $m^\lambda_0 (p)$" (with A. Fialowski). *Linear Algebra and its Applications*, Vol. 565, pp. 244 -257, 2019.

10. “Restricted One-dimensional Central Extensions of Simple Restricted Lie Algebras" (with A. Fialowski). *Linear Algebra and its Applications*, Vol. 513, pp. 96 - 102, 2017.

9. “Restricted Cohomology of Modular Witt Algebras" (with A. Fialowski and M. Penkava). *Proceedings of the American Mathematical Society*, Vol. 144, pp. 1877 - 1886, 2016.

8. “The Chinese Remainder Theorem" (with E. Burroughs). *Mathematics Teaching in the Middle School*, Vol. 14, No. 7, pp. 436-439, March 2009.

7. “Exploiting Symmetry in Pascal's Triangle Modulo a Prime,"* PascGalois Abstract Algebra Classroom Resources, MathDL - The MAA Mathematical Sciences Digital Library*, July 2008, http://mathdl.maa.org/mathDL/47/?pa=content&sa=viewDocument&nodeId=2636.

6. “Discovering binomial identities with PASCALJE,"*PRIMUS*, Vol. 18, No. 4, pp. 361-369, July 2008, Taylor and Francis, UK. DOI: 10.1080/10511970701299492.

5. “A complex for the cohomology of restricted Lie algebras" (with D. Fuchs), *Journal of Fixed Point Theory and Applications*, Vol. 3, No. 1, pp. 159-179, May 2008, Birkhauser Verlag, Basel/Switzerland. DOI 10.1007/s11784-008-0060-y.

4. “Graph adjacency matrix automata" (with J. Abbott, P. Chinn and A. Stewart), *Congressus Numerantium*, Vol. 188, pp. 143-149, 2007.

3. “On some generalizations of Fermat's, Lucas's and Wilson's theorems," *Ars Combinatoria*, Vol. 79, pp. 189-194, April 2006.

2. “Deriving divisibility theorems with Burnside's theorem" (with B. Holt),* Integers: Elec. J. Comb. No. Thy.*, Vol. 5(1), #A26, 2005.

1. “On the restricted Lie algebra structure of the Witt Lie algebra in finite characteristic" (with D. Fuchs), *Funct. Anal. Appl.*, Vol. 36, No. 2, pp. 140-144, April-June, 2002.