This $451,324 National Science Foundation Project Grant supports collaborative research on definability and computability over arithmetically significant fields through The Trustees of the University of Pennsylvania. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), this three-year award will advance understanding of polynomial equations, a foundational mathematical language, through interaction of logic, number theory, algebraic geometry, topology and related areas. Graduate student training and an online collaboration platform will be developed. Principal investigators will study computability and definability in the first-order and existential language of rings over number fields, their rings of integers and infinite algebraic extensions. Outstanding questions concerning extensions of Hilbert's Tenth Problem to rational numbers and rings of algebraic integers will also be considered, as well as definability of valuation rings in function fields over global and local fields. This research at the intersection of multiple mathematical disciplines has the potential to yield new insights in computability theory and number theory.
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