Braxton Osting
University of Utah, UT·Mathematics & Statistics
Many physical behaviors, such as how light travels, how structures vibrate and how liquids slosh, are governed by eigenvalues. These are special numbers that come from differential equations and set, for example, the natural frequencies of a system.
- Fields
Mathematics & Statistics
Physics
- Topics
extremal eigenvalue problems
spectral optimization
Steklov eigenvalue
- Grants
- 1 known grant, through Jun 2028
What they work on
- Develop computational methods to maximize a Steklov eigenvalue over smooth metrics on a compact Riemannian surface with boundary, while handling topological constraints on the surface.
- Design topological photonic crystals with large shared spectral bandgaps whose adjacent dispersion surfaces have prescribed topological invariants, such as the Chern number computed from Berry curvature.
- Create analytical and computational tools for enforcing geometric and topological constraints in extremal eigenvalue optimization problems.
More about the research
Changing a material or the shape of a domain shifts these numbers. Engineers often want to design shapes or materials that push an eigenvalue as high or low as possible. This collaborative project develops and analyzes computational methods for these 'extremal eigenvalue' problems, with a focus on hard geometric constraints.
Why it matters
Better methods for optimizing eigenvalues could help engineers design materials and shapes with useful vibration or optical properties. One example is topological photonic crystals that control light in robust ways, which may benefit photonics and device design. The work also advances computational mathematics and mathematical physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Daniel Stern
Cornell University, NY·Mathematics & Statistics
Use new constructions of extremal metrics for Laplacian and Steklov eigenvalues, the natural vibration frequencies of a shape, to produce many new minimal surfaces of prescribed topology in low-dimensional spheres and balls.
Cheikh Ndiaye
Howard University, DC·Mathematics & Statistics
Develop a full degree theory and Morse theory to prove existence of solutions to Q-curvature type equations, which describe angle-preserving reshaping of curved spaces to a prescribed curvature.
Roman Shterenberg
University of Alabama at Birmingham, AL·Mathematics & Statistics
Analyze mathematical models of almost-periodic operators from quantum mechanics to explain the mechanism of electrical conductivity in modulated, non-repeating crystals.
The school
University of Utah: 58 labs on PI Pages, $789M a year on research, 366 research doctorates a year.
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