Uri Andrews
University of Wisconsin-Madison, WI·Mathematics & Statistics
Mathematical logic asks what lies at the foundations of mathematics. It has three main branches.
- Fields
Mathematics & Statistics
Computer Science
- Topics
mathematical logic
computability theory
computable model theory
- Grants
- 1 known grant, through Jun 2027
What they work on
- Reduce the spectrum problem for strongly minimal theories, which asks which dimensions of their models are computable, to the locally modular case, which is geometrically tame and closely related to groups.
- Determine concretely which sets can be computable spectra of locally modular strongly minimal theories.
- Develop a theory of computable reductions on equivalence relations, analogous to set-theoretic embeddings of 2-dimensional sets but requiring computability.
- Use computable reductions on equivalence relations to classify algebraic decision problems more finely than Turing degrees, which group natural problems coarsely.
More about the research
Model theory studies mathematical structures through the formal languages that describe them. Computability theory asks which objects and problems can be computed by an algorithm. Set theory derives objects from the basic axioms of mathematics. This project links computability theory with the other two branches. One question is how two structures can look identical in a formal language when one can be computed and the other cannot. Another is how to measure the complexity of classification problems when the comparisons themselves must be computable.
Why it matters
This is pure mathematics. It aims to clarify where computation fits within the logical foundations of mathematics, including a 1970s-era open problem. A finer yardstick for algebraic decision problems could eventually inform how mathematicians and theoretical computer scientists classify the difficulty of algorithmic questions in algebra.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Damir Dzhafarov
University of Connecticut, CT·Mathematics & Statistics
Determine the computability-theoretic and reverse-mathematical strength of Milliken's tree theorem, a generalization of Ramsey's theorem from structural Ramsey theory, by resolving fundamental open questions about it.
Andrew Marks
University of California-Berkeley, CA·Mathematics & Statistics
Investigate Weiss's question on whether amenability implies hyperfiniteness, meaning whether actions of orderly groups can be built from finite pieces, using Gromov's theory of asymptotic dimension, with applications to topological dynamics and operator algebras.
Bhargav Narayanan
Rutgers University-New Brunswick, NJ·Mathematics & Statistics·Early-career
Study up-sets and down-sets in the Boolean hypercube from a probabilistic viewpoint, where they encode events of interest in probabilistic combinatorics and statistical physics.
The school
University of Wisconsin-Madison: 91 labs on PI Pages, $1.9B a year on research, 854 research doctorates a year.
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