Michelle Chu
University of Minnesota, MN·Mathematics & Statistics·Early-career
A shape and the algebra attached to it carry the same information in two very different languages. Attached to a space is its fundamental group, an algebraic object that records the distinct ways a loop can be drawn in that space; conversely, groups can be studied through the spaces they act on by symmetries.
- Fields
Mathematics & Statistics
Education Research
- Topics
geometric group theory
hyperbolic manifolds
hyperbolic 3-manifolds
- Grants
- 1 known grant, through Aug 2030
What they work on
- Study virtual properties of the fundamental groups of hyperbolic 3-manifolds — properties held by finite-index subgroups, which correspond to finite-sheeted covering spaces of the manifold.
- Extend the study of virtual properties to hyperbolic manifolds in higher dimensions, with emphasis on examples constructed by arithmetic methods from number-theoretic data.
- Investigate virtual properties of broader classes of groups that generalize and extend fundamental groups of hyperbolic manifolds, focusing on their subgroup structure and the geometric actions they admit.
- Build regional mathematical community through a workshop for upper Midwest students and faculty, a seminar series linking geometers and topologists at nearby institutions, and undergraduate support via the Mathematics Project at Minnesota.
More about the research
This project works at the intersection of geometry, topology and algebra, asking how algebraic properties of a group correspond to geometric and topological properties of the spaces on which it acts.
Why it matters
This is pure mathematics: the payoff is a sharper understanding of how the algebra of a group determines the geometry and topology of the spaces it acts on, particularly for hyperbolic manifolds and their finite covers. The regional workshop, seminar series and undergraduate support through the Mathematics Project at Minnesota also broaden participation in geometry and topology in the upper Midwest.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Andrew Putman
University of Notre Dame, IN·Mathematics & Statistics
Extend results on stable homology, the algebraic hole-counting invariants that settle down as groups grow, from mapping class groups and related groups to their finite-index subgroups.
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 Minnesota: 88 labs on PI Pages, $1.4B a year on research, 722 research doctorates a year.
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