Wilhelm Schlag
Yale University, CT·Mathematics & Statistics
In 1834 John Scott Russell followed a single hump of water for miles along a canal, moving without changing shape. Such solitary waves, now called solitons, are studied rigorously at the meeting point of mathematics and physics.
- Fields
Mathematics & Statistics
Physics
- Topics
solitons
nonlinear partial differential equations
nonlinear PDE
- Grants
- 1 known grant, through May 2027
What they work on
- Determine whether the kink soliton of the phi-4 model is asymptotically stable, extending a long-range scattering theory for potentials that have a threshold resonance.
- Develop the spectral theory of the non-selfadjoint matrix operator that governs small disturbances of Ginzburg-Landau vortices, toward proving their asymptotic stability.
- Describe bubbling, where energy concentrates at tiny scales, in the harmonic map heat flow by combining continuous-in-time bubbling results with a modulation theory.
- Analyze quasiperiodic symplectic cocycles that arise in condensed matter models such as graphene, using non-perturbative methods from the spectral theory of disordered systems.
More about the research
For some special wave equations, mathematicians know how solitons collide, when they are stable, and how a complicated wave eventually breaks into solitons plus spreading ripples. The same tools describe how electrons move through materials, which matters in quantum physics, quantum chemistry and materials science.
Why it matters
This is basic mathematics. It aims to strengthen the theory behind how waves break into stable pieces and how electrons move through ordered and disordered materials. Over time, such results could inform models used in quantum physics, quantum chemistry and materials science, including models of graphene.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Andrew Lawrie
University of Maryland, MD·Mathematics & Statistics
Work toward proving the soliton resolution conjecture, which predicts that generic solutions split into finitely many solitons plus radiation, without symmetry assumptions, beginning with the harmonic map heat flow in two dimensions.
Gong Chen
Georgia Institute of Technology, GA·Mathematics & Statistics·Early-career
Determine whether multi-solitons, solutions made of several solitary waves at once, are stable and unique in nonlinear dispersive equations, using PDE, harmonic analysis and spectral theory.
Sung-Jin Oh
University of California-Berkeley, CA·Mathematics & Statistics·Early-career
Prove a forward-in-time scattering criterion for initially outgoing solutions of the energy-critical wave maps and hyperbolic Yang-Mills equations, as a step toward the soliton resolution conjecture in the one-soliton regime.
The school
Yale University: 73 labs on PI Pages, $1.5B a year on research, 438 research doctorates a year.
Reach out
A start for your email. Fill in the brackets.