Spiral Galaxy NGC 4603, credit NASA
email: jdilts AT ucsd DOT edu
Office: SERF 435
Education: B.S. (2010) Brigham Young University, Ph.D. (2015) University of Oregon
CV: Download Here

My research is focused on the Einstein constraint equations, a coupled system of non-linear elliptic equations, and related geometric problems, such as the (conformally) prescribed scalar curvature problem. The main goal is a complete parametrization of the set of solutions of the constraint equations.

Publications

  • When Do Spacetimes Have Constant Mean Curvature Slices?
  • Numerical Bifurcation Analysis of the Conformal Method
  • Existence and Blowup Results for Asymptotically Euclidean Initial Data Sets Generated by the Conformal Method
  • The Einstein Constraint Equations on Asymptotically Euclidean Manifolds (PhD Dissertation)
  • Yamabe Classification and Prescribed Scalar Curvature in the Asymptotically Euclidean Setting
  • A Limit Equation Criterion for Applying the Conformal Method to Asymptotically Cylindrical Initial Data Sets
  • Non-CMC Solutions of the Einstein Constraint Equations on Asymptotically Euclidean Manifolds
  • The Einstein Constraint Equations on Compact Manifolds with Boundary
  • A Metacalibration Proof of the Isoperimetric Problem
  • My Teaching

  • Teaching Statement
  • Short video of me teaching
  • Full lecture
  • Course Websites

  • Math 170A: Intro to Numerical Analysis: Linear Algebra. Fall 2017
  • Math 3C: Precalculus. Summer Bridge 2017
  • Math 170A: Intro to Numerical Analysis: Linear Algebra. Summer 2017
  • Math 10B: Calculus II. Spring 2017
  • Math 10A: Calculus I. Winter 2017
  • Math 18: Linear Algebra. Fall 2016
  • Math 20D: Introduction to Differential Equations. Spring 2016
  • Math 102: Applied Linear Algebra. Winter 2016
  • Math 170A: Intro to Numerical Analysis: Linear Algebra. Fall 2015
  • Blog

  • I run a blog on advanced math for lay people, called Infinity Plus One!
  • Photos

  • My family and me (Dec 2016, by Brianne Cartwright)


  • updated 12/27/16