I currently have a temporary assistant professor position in the mathematics department at Queens College, C.U.N.Y. in New York City. I received my Ph.D. in mathematics from Carnegie Mellon University in August 2004. I had a short postdoc at Charles University in Prague from July 2004 to December 2004, followed by a postdoc at Instituto Superior Tecnico in Lisbon, Portugal, that ended August 2009. In Portugal, I was part of the Center for Logic and Computation, working with the project: Continuous Time Computation and Complexity.
Research Summary (A summary of my research)
Research Statement (A more detailed account of my research)
K. Ojakian (with Manuel L. Campagnolo), An improved characterization of computable analysis with differential equations. In preparation.
K. Ojakian (with Manuel L. Campagnolo), Characterizing Computable Analysis with Differential Equations Fifth International Conference on Computability and Complexity in Analysis 2008. Preprint
K. Ojakian (with Manuel L. Campagnolo), The elementary computable functions over the real numbers: applying two new techniques, Archives for Mathematical Logic (46) 2008. Preprint
K. Ojakian (with Manuel L. Campagnolo), Using Approximation to Relate Computational Classes over the Reals, in conference: Machines, Computations, and Universality 2007 , Lecture Notes in Computer Science (4664) 2007. Preprint
K. Ojakian (with Manuel L. Campagnolo), The methods of approximation and lifting in real computation, Third International Conference on Computability and Complexity in Analysis 2006 , Electronic Notes in Theoretical Computer Science (167) 2007. Preprint
K. Ojakian, Upper and lower Ramsey bounds in bounded arithmetic, Annals of Pure and Applied Logic, (135) 2005. Preprint
K. Ojakian, Combinatorics in Bounded Arithmetic. PhD thesis, Carnegie Mellon University, 2004. Supervised by Jeremy Avigad.
Continuous-time versus discrete-time computation over the reals
CUNY Logic Seminar, New York, NY (November 2009)
Computable analysis tutorial
Effective Mathematics of the Uncountable 2009, New York, NY (August 2009)
Characterizing computable analysis with differential equations
CUNY Set Theory Seminar, New York, NY (March 2009)
Slides
The model-theoretic proof of the witnessing theorem of bounded arithmetic (an exposition)
Logic Seminar, Lisbon, Portugal (February 2009)
Characterizing computable analysis with differential equations
Logic and Computation Seminar, Lisbon, Portugal (November 2008)
Characterizing Computable Analysis with Differential Equations
Fifth International Conference on Computability and Complexity in Analysis, Hagen, Germany (August 2008)
Slides
Proving the Church-Turing Thesis?
Logic Seminar, Lisbon, Portugal (March 2008) Slides
Computable Analysis and Analog Computation
Days in Logic, Lisbon, Portugal (January 2008)
Some New Approaches to Characterizing Computable Analysis by Analog Computation
Computability in Europe 2007, Sienna, Italy (June 2007) Slides
Bounded Arithmetic With Bounded Finite Types
26th Weak Arithmetics Days, Seville, Spain (June 2007)
The methods of approximation and lifting in real computation
Third International Conference on Computability and Complexity in Analysis, Gainesville, Florida, USA (November 2006)
The method of approximation in real computation
Computability in Europe 2006, Swansea, Wales, UK (July 2006)
Bounded arithmetic with bounded finite types
25th Weak Arithmetics Days, Clermont-Ferrand, France (June 2006)
Bounded arithmetic with bounded finite types
Logic and Computation Seminar, Coimbra, Portugal (April 2006)
Combinatorics in Bounded Arithmetic
Logic Seminar, Charles University, Prague, Czech Republic (September 2004)
The Probabilistic Method and Ramsey Theory in Bounded Arithmetic
Logic Seminar, Pennsylvania State University, State College, PA (October 2003)
Lower Ramsey Bounds in Bounded Arithmetic
Association for Symbolic Logic Annual Meeting, Chicago, IL (May 2003)
Ramsey Theory in Bounded Arithmetic
Math Logic Seminar, Carnegie Mellon University,
Pittsburgh, PA (January 2003)
The Probabilistic Method in Bounded Arithmetic
Fall school of the Logic seminar, Pec, Czech Republic (September 2002)
A strengthening of a Ramsey result
Fall school of the Logic seminar, Pec, Czech Republic (September 2001)