- National Science Foundation, Project Title “FRG: Collaborative Research: Definability and Computability over Arithmetically Significant Fields”, July 2022- June 2025. This grant is a part of a Focused Research Group Grant. Other members of the group are Valentina Harizanov, Barry Mazur, Jennifer Park, Florian Pop, Karl Rubin
- National Science Foundation, Project Title "Problems of Definability and Decidability over Algebraic Fields", June 2012 – May 2015, Principal Investigator
- John Templeton Foundation, Project Title “First-Order Models and Definitions of
**Z**over Large Subrings of Number Fields”, September 2008 – May 2010. Principal Investigator - National Science Foundation, Project Title “Definability and Decidability over Algebraic Extensions of Product Formula Fields”, June 2007 – May 2010, Principal Investigator
- National Science Foundation, Project Title "Existential Definability over Product Formula Fields", June, 2004 - May, 2007, Principal Investigator
- National Science Foundation, Project Title "Diophantine Definability and Decidability over Algebraic Extensions of Global Fields", August, 2000 - July, 2003, Principal Investigator
- National Security Agency Mathematical Sciences Research Program, Project Title: "Some Problems Concerning Logic of Algebraic Fields", 1998-2000, Principal Investigator.
- National Security Agency Mathematical Sciences Research Program, Project Title: "Some Problems Concerning Logic of Global Fields" 1996-1998, Principal Investigator.
- National Security Agency Mathematical Sciences Research Program, Project Title: "Extensions of Hilbert's Tenth Problem", 1992-94, Principal Investigator.

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