Matthew Stover
Temple University, PA·Mathematics & Statistics
How rigid is a curved space, and how much can it be bent or deformed? This research studies that tension between rigid geometry and topological flexibility.
- Fields
Mathematics & Statistics
- Topics
geometric topology
low-dimensional topology
hyperbolic geometry
- Grants
- 1 known grant, through Jul 2027
What they work on
- 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.
- Study profinite properties of discrete subgroups of Lie groups, meaning what their finite quotients reveal, and whether hyperbolic 4-manifolds can admit symplectic structures.
- Clarify how complex hyperbolic lattices lie between the flexibility of hyperbolic manifold groups and the higher-rank rigidity described by Margulis.
More about the research
Topology studies the properties of shapes that survive stretching. The work connects geometry and topology with algebraic geometry and number theory, which study the solutions of polynomial equations, and with dynamics, the study of how systems change over time. Many of its objects were central to classical mathematics in the work of Klein, Picard, Poincaré and E. Cartan.
Why it matters
This is pure mathematics. Its value is a deeper understanding of curved spaces and their symmetry groups, especially hyperbolic lattices, where basic existence questions remain open. Answers could inform several connected fields, including geometry, topology, number theory and dynamics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Richard Canary
University of Michigan, MI·Mathematics & Statistics
Study the metric completion of the Hitchin component, a higher Teichmüller space of surface group representations, with respect to a pressure metric that generalizes the Weil-Petersson metric.
Michelle Chu
University of Minnesota, MN·Mathematics & Statistics·Early-career
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.
Jeremy Kahn
Brown University, RI·Mathematics & Statistics
Determine whether three or four definitions of a surface subgroup being "closely aligned" with an sl_2(R) subgroup, inside lattices of semi-simple Lie groups, are mathematically equivalent.
The school
Temple University: 22 labs on PI Pages, $315M a year on research, 238 research doctorates a year.
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