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email: c1meier@math.ucsd.edu
Office: AP&M 5824
Education: B.A. (2006) Yale University, Ph.D. (2012) UCSD
CV: Download Here

I use nonlinear functional analysis to study systems of elliptic partial differential equations with an emphasis on applications to the constraint equations of general relativity. I am currently investigating non-uniqueness behavior associated with certain formulations of the constraint equations.

Publications
Mathematical General Relativity

  • Generalized Semilinear Elliptic PDE with Applications to the Lichnerowicz Equation
  • Non-uniqueness of Solutions to the Conformal Formulation (Pending)
  • An Alternative Between Non-unique and Negative Yamabe Solutions to the Conformal Formulation    of the Einstein Constraint Equations (Pending)
  • Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent    Horizon Boundaries (Pending)
  • Non-CMC Solutions of the Einstein Constraint Equations on Asymptotically Euclidean Manifolds    (Pending)
  • Noncommutative Algebra

  • Non-commutative Representations of Families of k2 Commutative Polynomials in 2k2 Commuting    Variables
  • Teaching
    I have been the instructor at UCSD for the following courses:

    • Math 20C (UCSD Spring 2013) Calculus (evaluations)
    • Math 20E (UCSD Winter 2013) Vector Calculus (evaluations)
    • Math 20D (UCSD Fall 2012) Differential Equations (evaluations)
    • Math 10A (UCSD Spring 2011) Calculus (evaluations)
    I have been a TA at UCSD for the following courses:

    • Math 142A (Fall 2011) Introduction to Analysis I
    • Math 130A (Winter 2011) Ordinary Differential Equations I (evaluations)
    • Math 180A (Fall 2010)Introduction to Probability (evaluations)
    • Math 130B (Spring 2010) Ordinary Differential Equations II (evaluations)
    • Math 130A (Winter 2010) Ordinary Differential Equations I (evaluations)
    • Math 110 (Fall 2009) Introduction to Partial Differential Equations (evaluations)
    • Math 20D (Spring 2009)Introduction to Differential Equations (evaluations)
    • Math 140C (Spring 2009) Foundations of Real Analysis III (evaluations)
    • Math 140B (Winter 2009) Foundations of Real Analysis II (evaluations)
    • Math 10B (Winter 2009) Calculus (evaluations)
    • Math 20E (Fall 2008) Vector Calculus (evaluations)

    Other Interests

    • Hiking, Camping, Backpacking
    • Soccer, Rock Climbing


    updated 10.06.13