The Analysis & Geometry research program explores the areas of:
- Differential geometry
- Several complex variables
- Non-commutative geometry
- Harmonic analysis
- Microlocal analysis
- Partial differential equations
- Operator theory, spectral theory
- Convex geometry and statistical learning theory
- Banach algebras
| Project | Status |
|---|---|
| Analytic functions | Potential |
| Computational problems | Potential |
| Dualities in algebra, geometry and physics | Potential |
| Eigenfunction concentration | Potential |
| Geometry of gerbes & D-branes | Potential |
| Gromov-Witten invariants and mirror symmetry | Potential |
| Group actions in complex geometry | Potential |
| Harmonic analysis and operator theory for partial differential equations | Potential |
| Harmonic analysis of differential operators | Potential |
| Hyperbolic geometry | Potential |
| Moduli spaces for Elliptic PDEs from quantum physics and string theory | Potential |
| Nash's papers on game theory | Potential |
| Noncommutative geometry & physic | Potential |
| Nonlinear heat equation | Potential |
| Operators which preserve the spectrum | Potential |
| Scattering theory | Potential |
| Spectral continuity | Potential |
| Wave diffraction | Potential |
| Wavelets | Potential |
