# Geometry, Topology and Physics

Geometry and physics are two inherently intertwined scientific disciplines. On the one hand, geometric ideas provide the foundations for electromagnetism and relativity, and on the other hand quantum field theory and, more recently, string theory, heavily influence the modern study of geometry and topology.

The Geometry, Topology and Physics project has researchers working in modern and classical areas of geometry, including enumerative algebraic geometry, knot theory, deformation theory, tropical and symplectic geometry. All these areas are closely connected to the physics of string theory, quantum field theory, and classical mechanics.

**Specific projects include questions concerning:**

- The topology of moduli spaces of curves, sheaves, and K 3 surfaces.
- The theory of refined real algebraic invariants.
- 4-dimensional aspects of Chern–Simons theory.
- Graph complexes and homotopy theoy of configuration spaces.
- Geometric optimization.

### Project leader

Rahul Pandharipande