Brian Tran

UCSD Mathematics




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I am a graduate student researcher at the UCSD Center for Computational Mathematics. My research focuses on structure-preserving and variational discretizations of field theories arising in physics, such as Lagrangian and Hamiltonian PDEs, with applications to mathematical and theoretical physics. My research is supported by the NSF Graduate Research Fellowship DGE-2038238, by NSF under grants DMS-1411792, DMS-1813635, and by the ARCS Scholar Fellowship.


  • Variational Structures in Cochain Projection Based Variational Discretizations of Lagrangian PDEs (with M. Leok), Foundations of Computational Mathematics, submitted, 2021. Preprint:
  • Multisymplectic Hamiltonian Variational Integrators (with M. Leok), International Journal of Computer Mathematics (Special Issue on Geometric Numerical Integration, Twenty-Five Years Later), accepted, 2021. Preprint:


  • Adjoint Systems via Dirac Structures. XVI Young Researchers Workshop in Geometry, Mechanics and Control. Centre de Recerca Matemàtica, UAB. 2021. Abstract.
  • Multisymplectic Variational Integrators for Hamiltonian PDEs. Zoom for Thought Seminar, UCSD Mathematics. 2021. Abstract.
  • Variational Discretizations of Lagrangian and Hamiltonian Field Theories. Advancement to Candidacy, UCSD Mathematics. 2021. Abstract.
  • Multisymplectic Hamiltonian Variational Integrators. UCSD Center for Computational Mathematics Seminar. 2021. Abstract.
  • Discrete Multisymplectic and Variational Principles of the FEM in Lagrangian Field Theory. UCSD Center for Computational Mathematics Seminar. 2020. Abstract.
  • Structure-Preserving Discretizations of Classical Field Theories. UCSD Center for Computational Mathematics Seminar. 2019. Abstract.

Conferences Attended

Expository Writing

Undergraduate Research

  • Honors Thesis under Prof. Michael Holst and Prof. Melvin Leok. UCSD Center for Computational Mathematics. 2016-2018.
  • Research Assistant under Dr. Fred Spada. UCSD Center for Memory and Recording Research. 2016-2018. 
  • Research Assistant under Prof. Brian Keating. UCSD Cosmology Group. 2015-2016.