Robert Kohn

Robert Kohn is a Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University. His research bridges applied mathematics, materials science, and mathematical physics through rigorous analysis of energy-driven systems.

• Specializes in partial differential equations, nonlinear elasticity, and phase transformations
• Active in interdisciplinary collaborations with physics and engineering disciplines
• Key contributions to pattern formation and structural optimization problems

Research focuses on:

• Energy-driven pattern formation in materials (superconductors, martensites, thin films)
• Thin film dynamics and surface relaxation mechanisms
• Phase transitions in crystalline solids and microstructure analysis
• Optimization problems in continuum mechanics and control theory

Key article trends show:

• Developing mathematical frameworks for metamaterials and photonic doping
• Connecting PDE analysis to online learning and game theory
• Establishing energy scaling laws for complex material systems
• Exploring topological constraints in mechanical and electromagnetic systems

His work spans both pure mathematical analysis and applied problems in materials science, with notable contributions to:

• Micromagnetics and magnetic microstructures
• Crystal growth inhibition mechanisms
• Geometrically constrained elastic systems
• Stochastic Allen-Cahn equations and phase separation