# 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

###### Philip Griffiths Professor of Mathematics

**Keywords in this area**

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

#### Justin Curry

###### Visiting Assistant Professor of Mathematics

**Keywords in this area**

applied algebraic topology, category theory, Sheaf theory

#### Ingrid Daubechies

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

**Keywords in this area**

shape space

#### Goncalo Marques Fernandes de Oliveira

###### William W. Elliott Assistant Research Professor

**Keywords in this area**

Gauge theory, special holonomy

#### Tingran Gao

###### Visiting Assistant Professor in the Department of Mathematics

**Keywords in this area**

Diffusion Geometry, Information Geometry

#### Jayce Robert Getz

###### Assistant Professor in the Department 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

#### Sayan Mukherjee

###### Professor in the Department of Statistical Science

**Keywords in this area**

topological data analysis

#### William L. Pardon

###### Professor of Mathematics

**Keywords in this area**

Singular spaces, Quadratic forms

#### Arlie O. Petters

###### Benjamin Powell Professor of Mathematics in Trinity College of Arts and Sciences

**Keywords in this area**

geometric lensing, black holes, extra dimensions, singularities

#### Colleen M Robles

###### Associate Professor in the Department 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