Research Interests

Most of my research is in computable (recursive) algebra and computable model theory (see my Chapter 1 in Handbook of Recursive Mathematics), and in computability (recursion) theory, which are subfields of mathematical logic (see Crossley's  tutorial).

Computability theory is the mathematical theory of algorithms. (See computability resource page.) Problems which can be solved algorithmically are called decidable. Undecidable problems can be more precisely classified by considering generalized algorithms, which require external knowledge. Turing degrees provide an important measure of the level of such knowledge needed. Computable model theory explores algorithmic properties of objects and constructions arising within mathematics.

I am especially interested in computability-theoretic complexity of relations on structures (see Hirschfeldt's paper in the Bulletin of Symbolic Logic), complexity of structures (see my paper in the Bulletin of Symbolic Logic), and complexity of isomorphisms (see our paper with Fokina and Turetsky in the Annals of Pure and Applied Logic). I also study orders on magmas (see our co-authored paper in JKTR). I am also interested in theoretical computer science, in particular, complexity theory, approximate computations, quantum computing, and inductive inference and algorithmic learning theory. My other interests include philosophy of mathematics and linguistic analysis (see our chapter with Kaufmann and Condoravdi in The Expression of Modality book).

Conferences I Help Organize

 

GW Knots in Washington Conferences I Helped Organize

        (co-organized with Jozef Przytycki and Alex Shumakovitch)

        (co-organized with Jozef Przytycki, Yongwu Rong, Alex Shumakovitch, Hao Wu, and
        Radmila Sazdanovic, NCSU)