Students


Co-Supervisor of Spencer Frei with Gantumur Tsogtgerel, McGill University, Summer 2012

Together with Gantumur Tsogtgerel, I helped oversee Spencer's summer research project involving weak convergence methods in PDE.

Courses

McGill University

Math 666 is a course I designed myself in which the students—both from mathematics and mechanical engineering—took turns presenting topics that I had selected in advance. The goal was to learn differential geometry and, at the same time, demonstrate how the tools of differential geometry can be used in continuum mechanics. The topics covered in this course were
Brian Seguin
Math 666 Class Dinner

  1. A Brief Introduction to Continuum Mechanics
  2. The Definition of a Manifold
  3. Tangent and Cotangent Spaces
  4. Applications of Tangent and Cotangent Spaces
  5. Multilinear Algebra
  6. Groups and Manifolds
  7. Lie Bracket and Lie Derivative
  8. Fiber Bundles
  9. Different Constructions of Space-Time
  10. The Material Groupoid
  11. Connections, Curvature, and Torsion
  12. Riemannian Geometry
  13. The Principle of Material Frame-Indifference
  14. Basic Inhomogeneity Theory

Carnegie Mellon University

Seminars And Reading Groups

Organizer, Mathematical Biology Working Group, Spring 2014

This group meets weekly and allows graduate students and postdocs the opportunity to present their current work to other people in the mathematical biology group at the University of Dundee.

Co-Organizer, Geometric Measure Theory Reading Group, Spring 2012

Alexandra Tcheng and I organized a reading group for graduate students and postdocs based on the first few chapters of Geometric Measure Theory by Frank Morgan. We covered some basic properties the space of currents and some of its useful subspaces. We concluded the seminar with a compactness theorem and its application to Plateau's problem.

Co-Organizer, Operator Theory Reading Group, McGill University, Fall 2011

Alexandra Tcheng and I organized a reading group for graduate students and postdocs based on the first few chapters of Principles of Functional Analysis by Martin Scheshter. The two main topics that were covered were Riesz theory for compact operators and Fredholm operators.

Co-Organizer, Graduate Student Seminar, Carnegie Mellon University, 2009-2010

Anne Yust and I started a weekly seminar for graduate students to present whatever they are working on.