Number Theory and Combinatorics

Number theory research in our department predominantly uses an Analytic perspective, with an emphasis on modular forms and L-functions. There is also overlap with work in combinatorial number theory, including multi-dimensional recurrence relations. Much of the combinatorial research we carry out is related to graph theory and discrete geometry, with particular emphasis on problems in spectral graph theory, random walks on graphs, random graph models, and related enumerative constructions. This research group also incorporates the analysis of discrete algorithms, including probabilistic approaches.

Daryl DeFord

http://www.math.wsu.edu/faculty/ddeford/ daryl.deford@wsu.edu Neill 328 My research focuses on applications of combinatorial and algebraic methods to the analysis of social data including political redistricting and social network analysis. Recent projects include the following with more details on Applied Mathematics Statistics and Probability Pure Mathematics Data Analytics Probability and Stochastic Processes Number Theory and Combinatorics

Sample Publications Maximum a Posteriori Inference of Random Dot Product Graphs via Conic Programming ReCombination: A family of Markov Chains for Redistricting

Matthew Hudelson

http://www.sci.wsu.edu/math/faculty/hudelson/ mhudelson@wsu.edu Neill 330 Probabilistic approaches to geometric and combinatorial problems, methods for maximizing content of a j-simplex bounded by the unit d-cube, and random walks on graphs. Pure Mathematics Number Theory and Combinatorics

Sample Publications

Anna Johnston

- jannaston@gmail.com - Cryptography/Cryptanalysis, number theoretic transforms relating to coding theory, and understanding the threat/hype/furor of Cryptographically Relevant Quantum Computers (CRQC) on existing algorithms Linear Algebra Number Theory and Combinatorics

Sample Publications Secure Authenticated Key Exchange Prime Proof Protocol

Sheng-Chi Liu

http://www.math.wsu.edu/faculty/scliu/ shengchi.liu@wsu.edu Neill 207 Analytic number theory, especially on L-functions and analytic theory of automorphic forms on GL(n). Pure Mathematics Number Theory and Combinatorics

Sample Publications The L^2 restriction norm of a Maass form on SL_{n+1}(Z) Rankin-Selberg L-functions and the reduction of CM elliptic curves