Christopher Rogers
University of Nevada-Reno, NV·Mathematics & Statistics
Symmetry is a basic tool across mathematics. To find all solutions to a system of equations, for example, one first studies its group of symmetries.
- Fields
Mathematics & Statistics
- Topics
Grothendieck-Teichmueller group
Kashiwara-Vergne group
Alekseev-Torossian conjecture
- Grants
- 1 known grant, through Jul 2027
What they work on
- 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.
- Find new examples of GRT and KRV actions on smooth complex algebraic varieties, shapes defined by polynomial equations, using homotopical and deformation-theoretic methods.
- Use wheeled props and knotted surfaces in 4-dimensional space to construct a Kashiwara-Vergne lift of formality morphisms in deformation quantization, with new insights into Duflo and Rozansky-Witten theory.
More about the research
This project studies two "universal" symmetry groups: the Grothendieck-Teichmueller group (GRT) and the Kashiwara-Vergne group (KRV). Both connect to quantum theory, number theory, the theory of knots and tangles, and motives, which are universal geometric invariants in algebraic geometry. Their structure remains largely mysterious. Alekseev and Torossian proved that KRV contains GRT and conjectured that the two are equal, a question still open.
Why it matters
This is pure mathematics. Clarifying how the Grothendieck-Teichmueller and Kashiwara-Vergne symmetry groups relate would deepen understanding of structures shared by knot theory, algebraic geometry, number theory and quantum theory, and could eventually inform work in mathematical physics such as deformation quantization.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Motohico Mulase
University of California-Davis, CA·Mathematics & Statistics
Develop complex Lagrangian geometry as a general framework for studying mirror symmetry, the hidden duality between symplectic geometry and complex algebraic geometry, and for studying quantization.
Abhishek Mallick
Dartmouth College, NH·Mathematics & Statistics
Establish new structural results for instanton, monopole and Heegaard Floer theories, which are invariants built from physics-inspired equations, in settings where spaces carry symmetries such as rotations or reflections.
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.
The school
University of Nevada-Reno: 11 labs on PI Pages, $194M a year on research, 186 research doctorates a year.
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