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 differential equations arising in physics and engineering, such as adjoint systems and classical field theories, with applications to control, optimization, and mathematical physics. My research is supported by the NSF Graduate Research Fellowship DGE-2038238, by NSF under grants DMS-1411792, DMS-1813635, DMS-1345013, and by the ARCS Scholar Fellowship.

For the 2022-2023 academic year, I am organizing the Computational Geometric Mechanics Research Seminar.

Papers

  • Geometric Methods for Adjoint Systems (with M. Leok), Journal of Nonlinear Science, submitted, 2022. arXiv
  • Variational Structures in Cochain Projection Based Variational Discretizations of Lagrangian PDEs (with M. Leok), Journal of Nonlinear Science, submitted, 2022. arXiv
  • Multisymplectic Hamiltonian Variational Integrators (with M. Leok), International Journal of Computer Mathematics (Special Issue on Geometric Numerical Integration, Twenty-Five Years Later), 99(1), 113-157, 2022. arXiv. DOI

Talks and Presentations

  • Title TBD. Foundations of Computational Mathematics 2023, Workshop in "Geometric Integration and Computational Mathematics". Sorbonne University. 2023 (Upcoming). Abstract.
  • Geoemtric Methods for Adjoint Systems. JMM 2023, AMS Contributed Paper Session on Topics in Analysis and Control Theory. Boston, MA. 2023 (Upcoming). Abstract.
  • Geometric Integration of Multisymplectic Hamiltonian PDEs. Trends in Soliton Dynamics and Singularity Formation for Nonlinear Dispersive PDEs. Texas A&M University. 2022. Abstract.
  • Geometric Methods for Adjoint Systems. Computational Geometric Mechanics Research Seminar, UCSD. 2022. Abstract.
  • Geometric Integration of Adjoint DAE Systems. UCSD Center for Computational Mathematics Seminar. 2022. Abstract.
  • Geometric Methods for Adjoint Systems. Symmetries, Invariants, and their Applications. Dalhousie University. 2022. Poster.
  • 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 (see 2016-2017) 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.