Damir Dzhafarov
University of Connecticut, CT·Mathematics & Statistics
Some mathematical problems cannot be solved by any computer program, and some theorems need stronger logical assumptions to prove than others. Computability theory, which grew out of Alan Turing's 1930s work defining what an algorithm is, asks which problems a computer can solve.
- Fields
Mathematics & Statistics
Computer Science
- Topics
computability theory
reverse mathematics
Ramsey's theorem
- Grants
- 1 known grant, through Aug 2027
What they work on
- 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.
- Analyze the Ginsburg–Sands theorem, a purely topological generalization of Ramsey's theorem, to find how hard it is to compute solutions and which axioms are needed to prove it.
- Develop new techniques and conceptual tools for computable combinatorics that strengthen the links among computability theory, combinatorics and topology.
More about the research
For problems it cannot solve, it measures how far they are from being solvable. Reverse mathematics asks how complicated a theorem is by finding the minimum set of axioms, or starting assumptions, needed to prove it. The two fields are closely linked, and together they reveal hidden connections across mathematics and can lead to more efficient computational methods.
Why it matters
This is basic research in the foundations of mathematics. Measuring the computational and logical strength of Milliken's tree theorem and the Ginsburg–Sands theorem would clarify how combinatorics, topology and computability relate. The new proof techniques could eventually inform other problems in computable mathematics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Uri Andrews
University of Wisconsin-Madison, WI·Mathematics & Statistics
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.
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.
Pablo Soberon Bravo
CUNY Bernard M Baruch College, NY·Mathematics & Statistics·Early-career
Show that high-dimensional mass partition problems, such as the Stone-Tukey theorem on cutting several objects into equal halves at once, are deeply connected to fair partition problems such as envy-free division.
The school
University of Connecticut: 31 labs on PI Pages, $434M a year on research, 360 research doctorates a year.
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