## Reed Solomon Associate Professor Department of Mathematics

### Contact Information

Office: 214 MSB
Phone: 860-486-2341
Email: david DOT solomon AT uconn DOT edu
University of Connecticut, U-3009
Department of Mathematics
Storrs, CT 06269-3009

### Teaching

For Fall 2015, I am teaching Math 2142 (Advanced Calculus II) and Math 5260 (Mathematical Logic). I will post my office hours for this semester soon. However, I am around almost every day, so feel free to contact me if you cannot come to my regular office hours.

### Research

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 and Postdoctoral Fellows

My past PhD students are

Alex Rogalski, Reverse mathematics on lattice ordered groups, 2007
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).
Amy Turlington, Computability of Heyting algebras and distributive lattices, 2010.
Caleb Martin, Computability theory and ordered groups, 2015
Jacob Suggs, On lowness of isomorphism as restricted to classes of structures , 2015

The past Postdoctoral Fellows and Assistant Professors in Residence in Logic at UConn include

Bjoern Kjos-Hanssen (2003-06), University of Hawai'i at Manoa
Stephen Binns (2004-07), King Fahd University of Petroleum and Minerals, Saudi Arabia
Asher Kach (2007-09 and 2010-11), Google.
Paul Ellis (2008-11), Manhattanville College.
Johanna Franklin (2011-14), Department of Mathematics, Hofstra University.
Linda Brown Westrick (2014-15), Victoria University, Wellington.

### Logic Seminars

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 MIT logic seminar and a variety of logic seminars at CUNY.