# Geometry: Differential & Algebraic

Researchers at Duke use geometric methods to study:

- the geometry and arithmetic of algebraic varieties;
- the geometry of singularities;
- general relativity and gravitational lensing
- exterior differential systems;
- the geometry of PDE and conservation laws;
- geometric analysis and Lie groups;
- modular forms;
- control theory and Finsler geometry;
- index theory;
- symplectic and contact geometry

## Faculty

#### William K. Allard

###### Professor Emeritus of Mathematics

#### Paul Stephen Aspinwall

###### Professor of Mathematics

**Keywords in this area**

Algebraic Geometry, Mirror Symmetry, Calabi-Yau Varieties, Derived Categories

#### Hubert Bray

###### Professor of Mathematics

**Keywords in this area**

scalar curvature, minimal surfaces, geometric flows, conformal geometry, isoperimetric surfaces

#### Robert Bryant

###### Phillip Griffiths Professor of Mathematics

**Keywords in this area**

differential geometry, holonomy, exterior differential systems, integrability, curvature, Lie groups, symplectic geometry, complex geometry, homology

#### Ingrid Daubechies

###### James B. Duke Distinguished Professor of Mathematics and Electrical and Computer Engineering

**Keywords in this area**

shape space

#### Jayce Robert Getz

###### Associate Professor of Mathematics

**Keywords in this area**

arithmetic geometry

#### Heekyoung Hahn

###### Assistant Research Professor of Mathematics

**Keywords in this area**

Flag varieties and periods

#### Richard Hain

###### Professor of Mathematics

**Keywords in this area**

algebraic geometry, Hodge theory, arithmetic geometry, topology of varieties

#### Mark Haskins

###### Professor of Mathematics

**Keywords in this area**

Special and exceptional holonomy spaces, especially Calabi-Yau 3-folds, $G_2$ holonomy and $Spin_7$ metrics. Calibrated submanifolds and currents in special holonomy spaces: special Lagrangian, associative and coassociative and Cayley submanifolds. Singular calibrated currents especially calibrated cones. Einstein and Ricci-flat metrics.

#### William L. Pardon

###### Professor of Mathematics

**Keywords in this area**

Singular spaces, Quadratic forms

#### Arlie O. Petters

###### Benjamin Powell Distinguished Professor of Mathematics

**Keywords in this area**

geometric lensing, black holes, extra dimensions, singularities

#### Colleen M Robles

###### Associate Professor of Mathematics

**Keywords in this area**

Differential Geometry, Geometric PDE, Hodge theory

#### Leslie Saper

###### Professor of Mathematics

**Keywords in this area**

Locally symmetric spaces, L2-cohomology, geometric analysis of singularities

#### Chadmark L. Schoen

###### Professor of Mathematics

**Keywords in this area**

algebraic cycles, Chow groups, Hodge conjecture, Tate conjecture, Generalized Birch and Swinnerton-Dywer conjecture, algebraic surfaces, algebraic threefolds, varieties over finite fields, Galois representations and cohomology

#### Mark A. Stern

###### Professor of Mathematics

**Keywords in this area**

geometric analysis, Yang Mills theory, Hodge theory, Index theory

#### Hau-Tieng Wu

###### Associate Professor of Mathematics

**Keywords in this area**

spectral geometry