Jason DeVito
University of Tennessee-Martin, TN·Mathematics & Statistics
Manifolds are shapes that look flat up close but can curve and twist on a large scale, like the surface of a sphere seen by someone standing on it. They are central to Einstein's general theory of relativity, which describes spacetime as a curved manifold.
- Fields
Mathematics & Statistics
- Topics
differential geometry
topology
manifolds
- Grants
- 1 known grant, through Jun 2027
What they work on
- Determine which homogeneous spaces and biquotients, spaces built from symmetry groups, carry a double disk bundle structure, made by gluing two disk-shaped families of disks together.
- Use codimension one biquotient foliations, slicings of a space into layers one dimension lower, to probe the Double Soul Conjecture about which curved manifolds split into two disk bundles.
- Construct new examples of manifolds with interesting Riemannian metrics, rules for distance and curvature, by exploiting double disk bundle structures.
More about the research
This project studies a special class called double disk bundles. These are manifolds that can be built by gluing together two simpler pieces, each made of a family of disks arranged over a smaller core shape. The goal is to understand how double disk bundles relate to other important classes of manifolds.
Why it matters
This is pure mathematics. It adds understanding of how a manifold's curvature relates to its overall shape through double disk bundle structures and the Double Soul Conjecture. New examples of manifolds with interesting Riemannian metrics could eventually inform geometry tied to general relativity.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Charles Cifarelli
Stony Brook University, NY·Mathematics & Statistics
Construct new examples of non-compact singularity model geometries, namely Kähler-Ricci solitons and complete non-compact Calabi-Yau metrics, which describe how complex manifolds degenerate.
Matthew Stover
Temple University, PA·Mathematics & Statistics
Use ideas from geometry, topology, algebraic geometry and dynamics to answer open questions, including basic existence problems, about real and complex hyperbolic lattices, which are discrete symmetry groups of curved spaces.
Mark Brittenham
University of Nebraska at Omaha, NE·Mathematics & Statistics
Investigate the L-space conjecture for toroidal 3-manifolds, which links left-orderable fundamental groups, foliations and Floer homology, using the notion of slope detection.
The school
University of Tennessee-Martin: 1 labs on PI Pages.
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