Valentina Harizanov

Research Interests

Most of my research is in computable(recursive) algebra and model theory (see Harizanov's Handbook of Recursive Mathematics chapter), and in computability (recursion) theory, which are subfields of mathematical logic (see Crossley's 2005 tutorial).

Computability theory is the mathematical theory of algorithms. (See computability theory home page.) Problems which can be solved algorithmically are called decidable. Undecidable problems can be more precisely classified by considering generalized algorithms, which require external knowledge. Turing degrees provide an important measure of the level of such knowledge needed. Computable model theory explores algorithmic properties of objects and constructions arising within mathematics.

I am especially interested in computability theoretic complexity of relations (see Hirschfeldt's Bulletin of Symbolic Logic paper) and structures (see Harizanov's Bulletin of Symbolic Logic paper), including their Turing degrees. I am also interested in natural language semantics, philosophy of mathematics, and theoretical computer science (in particular, frequency computations, inductive inference and algorithmic learning theory, and quantum computing).

My research has been supported by the NSF research grants DMS-0502499 (2005–07) and DMS-0704256 (2007–09), as well as by the NSF binational research grants for collaboration with Russia/Kazakhstan (2000–09).

Recent and Future Meetings (Organizer or Speaker)

• European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium, Sofia, Bulgaria, July 31–August 5, 2009, plenary speaker.
• Joint Mathematics Meetings, Washington, D.C., January 5–8, 2009, co-organizer (with Jozef Przytycki) of the Special Session Orderings in Logic and Topology, Schedule and Abstracts, Talks
• BIRS Workshop on Computability, Reverse Mathematics and Combinatorics, December 7–12, 2008, Banff, Alberta; invited participant.
• AMS Meeting, October 11–12, 2008, Wesleyan University, Connecticut, Special Session Computability Theory and Effective Algebra, invited speaker.
• 2008 ASL Annual Meeting, March 27–30, 2008, Irvine, California, Program, Special Session Computability Theory, invited speaker.
• Workshop on Knots and Quantum Computing, University of Texas at Dallas, December 18–20, 2007, invited speaker.
• AMS meeting, Middle Tennessee State University, Murfreesboro, Special Session on Advances in Algorithmic Methods for Algebraic Structures, November 3–4, 2007; invited speaker.
• Model Theory and Computable Model Theory, University of Florida Special Year in Logic, February 5–10, 2007. Organizing Committee: Doug Cenzer, Valentina Harizanov, David Marker and Carol Wood
• 2006–07 ASL Winter Meeting, January 7–8, 2007 (with Joint Mathematics Meetings), New Orleans, plenary speaker.
• AMS meeting, University of Connecticut, Special Session on Computability Theory in Honor of Manuel Lerman's Retirement, October 28–29, 2006; invited speaker.
• AMS meeting, Notre Dame, Special Session on Model Theory and Computability, April 8–9, 2006, invited speaker.
• SouthEastern Logic Symposium, University of Florida, Gainesville, March 10–13, 2006; invited speaker.
• ASL Winter Meeting, January 12–15, 2006 (with Joint Mathematics Meetings), San Antonio. Program Committee: Su Gao, Valentina Harizanov (chair), and Chris Miller
• Workshop on Vaught's Conjecture, University of Notre Dame, May 18–24, 2005, invited speaker.
• SouthEastern Logic Symposium, University of Florida, Gainesville, April 15–17, 2005, invited speaker.
• AMS Meeting, Northwestern University, October 23–24, 2004, invited speaker. Special session Computability Theory and Applications
• ASL Annual Meeting, May 19–23, 2004, Carnegie Mellon University, plenary speaker.
• National Annual Graduate Student Conference in Logic, University of Notre Dame, May 1–2, 2004, participant. Picture with graduate students.
• ASL Winter Meeting, January 9–10, 2004 (with Joint Mathematics Meetings), Phoenix. Program Committee: Valentina Harizanov, John Steel, and Carol Wood (chair)
• Joint Mathematics Meetings, Baltimore, January 15–18, 2003, AMS special session Computability and Models (co-organizer with Doug Cenzer)