Department of Mathematics
Department of Mathematics
University of Connecticut
341 Mansfield Road U1009
Storrs, CT 06269-1009
In Fall 2022, I am teaching Math 5026 (Generic sets and forcing in computability theory). The course is managed through HuskyCT and you can find details there. My office hours this semester are Monday 11:00-12:00, Friday 9:00-10:00 and by appointment.
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.
Graduate Students, Honors Students and Postdoctoral Fellows
My past PhD students are
- Marie Nicholson, Applications of computability theory to partial and linear orders, 2017
- Shelley Stahl, Computability theoretic results for the game of cops and robbers on infinite graphs, 2017
- Caleb Martin, Computability theory and ordered groups, 2015
- Jacob Suggs, On lowness of isomorphism as restricted to classes of structures, 2015
- Amy Turlington, Computability of Heyting algebras and distributive lattices, 2010
- Matt Jura, Reverse mathematics and the coloring number of graphs, 2009 (jointly advised with Joe Miller)
- Oscar Levin, Computability theory, reverse mathematics and ordered fields, 2009
- Tyler Markkanen, Separating the degree spectra of structures, 2009 (jointly advised with Joe Miller)
- Alex Rogalski, Reverse mathematics on lattice ordered groups, 2007
My past masters students are
- Whitney Patton Turner, Computable linear orders and Turing reductions, 2012
My Honors Thesis students are
- Tristan Knight, The continuum hypothesis and set-theoretic forcing, 2019
- Madeline Tremblay, The Banach-Tarski paradox, 2017
- Nicole Bowen, Hilbert's Tenth Problem, 2014
- Jonathon Lynn (co-advised with Manny Lerman), Common proof techniques and Martin's Axiom in set theory, 2004
The past Postdoctoral Fellows and Visiting Assistant Professors in logic at UConn include
- Eric Astor (2015-2018), Google
- Linda Brown Westrick (2014-15 and 2016-18), Penn State
- Stephen Flood (2013-15), Bridgewater State University
- Johanna Franklin (2011-14), Hofstra University
- Paul Ellis (2008-11), Manhattanville College
- Asher Kach (2007-09 and 2010-11), Google
- Stephen Binns (2004-07), King Fahd University of Petroleum and Minerals, Saudi Arabia
- Bjørn Kjos-Hanssen (2003-06), University of Hawai'i at Manoa
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 2:00-3:30 roughly every other week during the semester.
Other logic seminar in the region include the Harvard logic seminar and a variety of logic seminars at CUNY.