For Fall 2014, I am teaching Math 2141 (Advanced Calculus I) and Math 5026 (Set Theory). My office hours this semester are Monday 1:15-2:45 and Wednesday 10:45-12:15.
My research is in mathematical logic, specifically in computability theory and reverse mathematics. I have a number of papers and preprints available in electronic format. I also have a somewhat random collection of lecture notes and slides.
Computability theory is the study of computational properties of sets and functions on the natural numbers. In addition to studying sets and functions which are computable, one is interested in definitions of relative computability. That is, we study various notions of when a set or function is simpler than (or can be computed given knowledge of) another set or function. Under suitable codings, these notions can be used to study effectiveness in areas of mathematics such as algebra, combinatorics, analysis and so on. One of my main research interests is in effective algebra and combinatorics in this sense.
In reverse mathematics, one tries to isolate the smallest fragment of set theory required to prove a particular theorem of classical mathematics. The set theoretic background is typically second order arithmetic and in this context, there are close connections between computability theory and the subsystems of set theory that arise. I study theorems in algebra and combinatorics in this setting.
My past PhD students are
The past Postdoctoral Fellows and Assistant Professors in Residence in Logic at UConn include
There are several logic seminars both regionally and at UConn. The Connecticut Logic Seminar is a regional seminar regularly attended by faculty and graduate students from UConn, Wesleyan, Vassar and UMass-Dartmouth. The seminar meets Mondays 4:45-6 at Wesleyan University, Exley Science Center 618 (directions).
We have an interdisciplinary UConn Logic Group composed of faculty and graduate students in mathematics, philosophy and linguistics. We run a seminar which meets at Friday 2:00-4:00 roughly every other week during the semester.
Other logic seminar in the region include the MIT logic seminar and a variety of logic seminars at CUNY.