Geometry and Topology are branches of mathematics that study of shapes and spaces. In Topology we study the properties of an object that are preserved under continuous deformations such as stretching, twisting, and bending. In Geometry we study properties of spaces such as curvature, and distance.
The modern fields of Geometry and Topology interact heavily with a diverse collection of core areas of Mathematics. Symmetries of a geometric space, and fundamental invariants of topological spaces such as homology are described in the language of Algebra. Differential geometry extends techniques from calculus and linear algebra to study smooth manifolds. There are deep connections to partial differential equations through the modern subject of gauge theory, algebraic geometry through the topology of algebraic varieties, combinatorics through knot theory, and theoretical physics through general relativity and string theory. In addition, Geometry and Topology are increasingly applied to the study of nonlinear phenomena in the sciences and the characterization of structure in complex data. Our faculty collaborate on a broad range of applications including neuroscience, robotics, materials science, ecology, microbiology, and medicine.
The geometry/topology research group at OSU studies:
- Algebraic topology
- Configuration spaces
- Differential geometry
- Discrete Conformal geometry
- Hyperbolic geometry
- Lie groups
- Low-dimensional topology (knots, 3 and 4-manifolds)
- Surgery theory
- Symplectic and contact geometry
- Topological data analysis
- Topological neuroscience
