Bertrand Guillou
University of Kentucky, KY·Mathematics & Statistics
Imagine every possible way of wrapping a high-dimensional sphere around a lower-dimensional one. Sorting these maps into classes is a central problem in algebraic topology, the branch of mathematics that studies shapes using algebra, and it matters for geometry and physics.
- Fields
Mathematics & Statistics
- Topics
algebraic topology
homotopy theory
stable homotopy groups of spheres
- Grants
- 1 known grant, through Jul 2027
What they work on
- Compute equivariant stable homotopy groups of spheres for the cyclic group of order 2, the Klein four group and the quaternion group of order 8, using motivic and synthetic homotopy theory.
- Run the Bockstein, Adams and slice spectral sequences, step-by-step algebraic tools for computing homotopy groups, using techniques such as Massey products to settle hard steps.
- Establish the height 1 Telescope Conjecture in the R-motivic and cyclic-2-equivariant settings, describing certain periodic families of elements in their stable homotopy groups.
More about the research
This project looks at a special version of the problem: maps that respect certain symmetries of the spheres.
Why it matters
This is pure mathematics. It adds concrete computations of how symmetric spheres map onto each other, and a clearer picture of repeating patterns in these maps. Such results feed into the wider study of shapes and their symmetries in topology, with possible links to geometry and physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Christopher Rogers
University of Nevada-Reno, NV·Mathematics & Statistics
Gather evidence for the Alekseev-Torossian conjecture that the Kashiwara-Vergne group (KRV) equals the Grothendieck-Teichmueller group (GRT), by studying how both act on explicit geometric and topological objects.
Adam Levine
Duke University, NC·Mathematics & Statistics
Investigate knot concordance questions, including homology slice knots, ribbon concordance and piecewise-linear concordance of knots in homology 3-spheres, using Heegaard Floer homology invariants.
Alexander Zupan
University of Nebraska-Lincoln, NE·Mathematics & Statistics
Prove new cases of the smooth four-dimensional Poincaré conjecture, which asks whether sphere-like four-dimensional spaces are truly standard spheres, by connecting four-dimensional handle calculus with Dehn surgery on knots and links.
The school
University of Kentucky: 34 labs on PI Pages, $528M a year on research, 319 research doctorates a year.
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