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

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

Ingrid Daubechies

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

Keywords in this area
shape space

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 of Statistical Science

Keywords in this area
topological data analysis

Lenhard Lee Ng

Eads Family Professor

Keywords in this area
symplectic geometry, contact geometry

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

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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