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Research Statement
Research
Shankar Venkataramani
Research Statement
Variational problems and weak convergence methods for Nonlinear PDE
Extended dynamical systems and phase transitions
The formation and dynamics of singularities
Isometric immersions and underdetermined PDEs
Multiple tools for Multiple scales
Outline
Multiple scale analysis
Analysis of Nonlinear PDEs
Collective behavior
Geometry and Topology
Applications of dynamical systems
Stochastic dynamics
Why multiple scale analysis?
Nonlinear PDE
Interacting Nonlinear Dynamical Systems
Multiple tools for Multiple scales
Nonconvex Variational Problems
Energy Concentration and Minimal Obstructions
Generalized Crumpling
Sound propagation in crumpled sheets
Singularities and Microstructure in thin elastic sheets
Singularities with Additional Structure
Oscillations and Multiple Scale Solutions
Global Transitions
Blowup in Parabolic equations and systems
Nonlinear diffusion equations with discontinuities
Fekete points and charge placement on 2D conductors
Pattern formation
Continuum Coupled maps
Vibrated granular layers
Fronts in periodically forced systems
Multiple Scale Behavior, Coarsening and Domain Growth
Nonequilibrium phase transitions : Noise and fluctuations
Existence of smooth Isometric immersions
Convex Integration
Black hole event horizons
Anomalous Diffusion in fluid flows
Dynamical systems with Invariant manifolds
The bubbling transition
On-off intermittency
Bibliography
About this document ...
Department of Mathematics
5734 S. University Ave.
University of Chicago
Chicago, IL 60637
shankar@math.uchicago.edu
