James Dilts. Department of Mathematics University of California, San Diego ccom.ucsd.edu/~jdilts

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1 James Dilts Department of Mathematics University of California, San Diego Appointments ccom.ucsd.edu/~jdilts Postdoctoral Scholar and Lecturer, UC: San Diego, July 2015 Present. Education Ph.D. Mathematics, University of Oregon, June Advisor: James Isenberg, J. Dilts. The Einstein Constraint Equations on Asymptotically Euclidean Manifolds. PhD thesis, University of Oregon, 2015 B.S. Mathematics, Brigham Young University, April 2010, GPA 3.85/4 Research Interests General relativity provides not only an accurate model of gravity, but also an abundance of interesting and deep mathematical problems. My research has focused on a system of elliptic equations that arise when considering initial data for the Einstein equations, and the attempt to parameterize all of their solutions. This has included analytic work, as well as some numerical work. I intend to continue this project, as well as to study the existence and genericity of constant mean curvature Riemannian submanifolds in Lorentzian spacetimes. More generally, I am interested in geometric analysis, and the differential equations that arise in that study. I feel it is important to include students in my research. Publications J. Dilts and M. Holst. When do spacetimes have constant mean curvature slices? arxiv: J. Dilts, M. Holst, T. Kozareva, and D. Maxwell. Numerical bifurcation analysis of the conformal method arxiv: James Dilts and James Isenberg. Existence and blowup results for asymptotically euclidean initial data sets generated by the conformal method. Phys. Rev. D, 94:104046, Nov 2016 J. Dilts and D. Maxwell. Yamabe classification and prescribed scalar curvature in the asymptotically Euclidean setting arxiv:1503:04172, accepted by Communications in Analysis and Geometry J. Dilts and J. Leach. A limit equation criterion for solving the Einstein constraint equations on manifolds with ends of cylindrical type. Ann. Henri Poincaré, 16(7): , 2015

2 J. Dilts. The Einstein constraint equations on compact manifolds with boundary. Classical Quantum Gravity, 31(12):125009, 2014 J. Dilts, J. Isenberg, R. Mazzeo, and C. Meier. Non-CMC solutions of the Einstein constraint equations on asymptotically Euclidean manifolds. Classical Quantum Gravity, 31(6):065001, 10, 2014 J. Dilts. A new metacalibration proof of the isoperimetric problem in n-space and on the n-sphere. Rose-Hulman Undergraduate Mathematics Journal, 11(2):34 48, 2010 Teaching and Mentoring Experience Some videos of my teaching are available on my website, ccom.ucsd.edu/~jdilts Mentoring Undergraduate research mentoring, Eric Gelphman (Fall 16 - present). Taught/helped in UCSD Summer Bridge, a program to help disadvantaged students transition to college (Summer 17) Undergraduate research mentoring, Tamara Kozareva (Fall 15 - Spring 17). Is a coauthor on one of my papers. Teaching Assistant for REU group at Brigham Young University (Summer 10) Lecturer: wrote and delivered lectures, oversaw TAs, wrote exams, etc. Intro to Numerical Analysis: Linear Algebra (170A, 200 students), UC: San Diego, 3 times Applied [Advanced] Linear Algebra (102, 150 students), UC: San Diego Intro to Differential Equations (20D, 150 students), UC: San Diego Linear Algebra (18, 200 students), UC: San Diego Calculus (10A-B, 200 non-major students), UC: San Diego Precalculus (3C), UC: San Diego Graduate Teaching Fellow, sole instructor: wrote and delivered lectures, held office hours, wrote and graded quizzes, exams, and homework College Algebra (111), University of Oregon, 4 times Trigonometry (112), University of Oregon, 2 times University Math (106), University of Oregon First year calculus sequence ( ), University of Oregon Second term business calculus (242), University of Oregon Graduate Teaching Fellow, teaching assistant: held help sessions and office hours, graded uniform quizzes and tests. Business calculus series ( ), University of Oregon

3 Graduate Teaching Fellow, grader. Fourier Analysis (422/522), University of Oregon General Relativity (Physics ), University of Oregon Differential Geometry (433/533), University of Oregon Differential Equations (420/520), University of Oregon Co-taught graduate seminar on metacalibrations", Brigham Young University ( 09) Tutor at Brigham Young University undergraduate math lab ( 06) Public Outreach Math blog at infinityplusonemath.wordpress.com Conferences Organized Special session on Mathematical Relativity and Differential Geometry, at the Joint Mathematics Meetings, San Diego, January st Pacific Coast Gravity Meeting, University of Oregon, March 2015 Invited Presentations The Conformal Method on Asymptotically Euclidean Manifolds, in Focus Program on 100 Years of General Relativity, Fields Institute, May 2015 Selected Presentations When do Spacetimes Have Constant Mean Curvature Slices?, in AMS Special Session, Joint Mathematical Meetings, San Diego, January 2018 (invited) The Conformal Method Gives a Poor Parameterization of Initial Data, in Geometric Analysis and General Relativity, Banff International Research Station, July 2016 The Conformal Constraint Equations on Asymptotically Euclidean Manifolds, in Mathematical Aspects of General Relativity, Mathematisches Forschungsinstitut Oberwolfach, July 2015 The Einstein Constraint Equations on Asymptotically Euclidean Manifolds, in General Relativity and Gravitation: A Centennial Perspective, Pennsylvania State University, June 2015 The Einstein Constraint Equations on Asymptotically Euclidean Manifolds, in Pacific Coast Gravity Meetings, University of Oregon, March 2015 Prescribed Scalar Curvature on Asymptotically Euclidean Manifolds, in Geometric Analysis seminar, University of Oregon, May 2014 Yamabe Classes on Asymptotically Euclidean Manifolds, in NSF Focused Research Group meeting, UC San Diego, February 2014

4 The Einstein Constraint Equations, in Pacific Coast Gravity Meetings, UC Davis, April 2013 The Limit Equation on Asymptotically Euclidean Manifolds, in Geometric Analysis seminar, University of Oregon, March 2013 Metacalibration and a Proof of the Double Bubble Theorem, in Graduate Student Topology & Geometry Seminar, Lansing, April Received travel grant of $700. An Introduction to Metacalibration and its Application to Multiple Bubble Problems, in Queen Dido Workshop on Isoperimetry, Tunis, Tunisia, May Received travel grant of $1000. The Double Bubble in R n, in AMS Special Session, Joint Mathematical Meetings, San Francisco, January 2010 (invited) Metacalibrations in Geometric Optimization, in Student Poster Session, Joint Mathematical Meetings, San Francisco, January 2010 A New Metacalibration Proof of the Isoperimetric Inequality, in Mathematics Education Special Session at the 2009 College of Physical and Mathematical Sciences Spring Research Conference, Brigham Young University, March 2009 Workshops Attended ESI-EMS-IAMP Summer School on Mathematical Relativity: 99 years of General Relativity, Erwin Schödinger Institute, Vienna, July 2014 Mathematical General Relativity Program, Mathematical Sciences Research Institute, August-December 2013 Workshop on Geometric Analysis and Nonlinear PDEs, Rutgers University, May 2013 Mathematical General Relativity, Mathematical Sciences Research Institute, July 2012 International Conference on the Isoperimetric Problem of Queen Dido and its Mathematical Ramifications, Tunisia, May 2010 Journals Reviewed For Canadian Journal of Physics Journal of Differential Equations Other Skills Mathematica, AUTO bifurcation software Some programming (python, etc.) experience Speak/write/read Serbocroatian fluently Awards Johnson Award, $1200, University of Oregon, 2015

5 Johnson Award, University of Oregon, 2011 MEG Undergraduate Research Grant, Brigham Young University, 2010 Membership in Professional Organizations American Mathematical Society (AMS) American Physical Society (APS) International Society on General Relativity & Gravitation (ISGRG)