Instructor in Pure Mathematics

2-308
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139

Office Phone: (617) 324-1507
Fax: (617) 253-4358
18.03 Office Hours: TR 1:00-2:00pm

Research

My research interests are in mathematical logic and computability theory, especially computable probability theory, computable model theory, and formalized mathematics.

My PhD thesis, Models with High Scott Rank, was completed in 2008 under the supervision of Gerald Sacks at Harvard University, and uses methods from higher recursion theory to approach a problem in computable model theory.

A result (with Roy) in computable probability theory provides a computable version of de Finetti's theorem on exchangeable sequences of real random variables, which allows for conditional independence that is implicit in a probabilistic program to be automatically exploited in parallel implementations.

A more recent result (with Ackerman and Roy) shows that there is a pair of computable random variables for which the Halting problem is computable from the regular conditional distribution of one variable given the other.

Publications

The computability of conditional probability, with Nate Ackerman and Daniel Roy.

Computable de Finetti measures, with Daniel Roy, submitted, 2009.

Computable exchangeable sequences have computable de Finetti measures, with Daniel Roy, in Mathematical Theory and Computational Practice, Proceedings of Computability in Europe (CiE 2009), LNCS Vol. 5635, 2009.

Models with High Scott Rank, PhD thesis, Harvard University, 2008.

Logic Seminar

Mia Minnes and I jointly organize the MIT Logic Seminar, which meets most Wednesdays at 4:30 pm.

Courses

Spring 2010: 18.515: Mathematical Logic

Fall 2009: 18.03: Differential Equations
(Office Hours: Tues/Thurs 1-2pm and by appointment in room 2-308)

Spring 2009: 18.575: Model Theory

Fall 2008: 18.03: Differential Equations

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