Geometry: Differential & Algebraic

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

Paul Stephen Aspinwall

Professor of Mathematics

Keywords in this area

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

Hubert Bray

Hubert Bray

Professor of Mathematics

Keywords in this area

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

Robert Bryant

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

Ingrid Daubechies

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

Keywords in this area

shape space

Jayce Robert Getz

Jayce Robert Getz

Associate Professor of Mathematics

Keywords in this area

arithmetic geometry

Heekyoung Hahn

Heekyoung Hahn

Assistant Research Professor of Mathematics

Keywords in this area

Flag varieties and periods

Richard Hain

Richard Hain

Professor of Mathematics

Keywords in this area

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

Mark Haskins

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.

Sayan Mukherjee

Sayan Mukherjee

Professor of Statistical Science

Keywords in this area

topological data analysis

Lenhard Lee Ng

Lenhard Lee Ng

Eads Family Professor

Keywords in this area

symplectic geometry, contact geometry

William L. Pardon

William L. Pardon

Professor of Mathematics

Keywords in this area

Singular spaces, Quadratic forms

Arlie O. Petters

Arlie O. Petters

Benjamin Powell Distinguished Professor of Mathematics

Keywords in this area

geometric lensing, black holes, extra dimensions, singularities

Joseph D Rabinoff

Joseph D Rabinoff

Associate Professor of Mathematics

Colleen M Robles

Colleen M Robles

Associate Professor of Mathematics

Keywords in this area

Differential Geometry, Geometric PDE, Hodge theory

Leslie Saper

Leslie Saper

Professor of Mathematics

Keywords in this area

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

Chadmark L. Schoen

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

Mark A. Stern

Professor of Mathematics

Keywords in this area

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

Kirsten Graham Wickelgren

Kirsten Graham Wickelgren

Professor of Mathematics

Hau-Tieng Wu

Hau-Tieng Wu

Associate Professor of Mathematics

Keywords in this area

spectral geometry