Research
My research lies at the intersection of geometric model theory (of infinite structures) and finitary discrete mathematics. Mainly, I try to apply technology or ideas, or both, from geometric model theory to structural questions about graphs, relational structures, and matroids and to the theory of efficient algorithms. To carry this out, one has a few options: to amalgamate a class of graphs (or other structures) into an infinite “limit” structure; to work in an ultraproduct of finite structures; or to hunt down the appropriate analogs of concepts from model theory for use in the finitary context. This approach has many interesting applications in (for example) structural Ramsey theory, characterization of zero-one laws, and analysis of asymptotics of definable sets.
Publication list and preprints.
Teaching
Fall 2013
- Calculus I, Part I. (Moodle)
Course Syllabus
Math 121-01
T,Th 2:40PM – 4:00, Exley 141. - Set Theory. (Moodle)
Course Syllabus
Math 241-01
T,Th 10:30AM – 11:50, Exley 139.