Teaching and Advising:
- MA-518 - Geometry of Curves and Surfaces
Geometry of curves and surfaces in space. Topics include: arclength, torsion, and curvature of curves, Frenet frame and equations; tangent spaces, shape operators, and curvatures of surfaces; metrics, covariant derivatives, parallel transport, geodesics, and Gauss-Bonnet Theorem.
- MA-755 - Introduction to Riemannian Geometry
An introduction to smooth manifolds with metric. Topics include: Riemannian metric and generalizations, connections, covariant derivatives, parallel translation, Riemannian (or Levi-Civita) connection, geodesics and distance, curvature tensor, Bianchi identities, Ricci and scalar curvatures, isometric embeddings, Riemannian submanifolds, hypersurfaces, Gauss Bonnet Theorem; applications and connections to other fields.
Course materials, homework assignments, office hours, and all other information about my classes are posted on https://wolfware.ncsu.edu/
Applied and Computational Differential and Algebraic Geometry
I am a member of the Geometry, Topology, Mathematical Physics group and the Symbolic Computation group.
- Geometric study of differential and algebraic equations.
- Symmetry reduction of differential equations and variational problems.
- Computational invariant theory: differential and algebraic
- Problems of equivalence and
symmetry under group actions.
- Geometric methods in computer image recognition and image
- Geometric modeling.
- Symbolic Computation.
Funded Research Projects
Math Programs for Young People
There are many wonderful programs in Mathematics for talented youth. The following unsorted list is by no means complete. I compiled it from programs that I am more familiar with so I have an easy reference for people asking for a recommendation.
Last updated: January, 2020.
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