Brian K. Tran

  • (he/him/his)
  • Visiting Assistant Professor
photo
Address

ECOT 332

I joined the Department of Applied Mathematics as a visiting assistant professor in Fall 2025. Previously, I was a Marc Kac postdoctoral fellow in applied mathematics at Los Alamos National Laboratory. I completed my Ph.D. in Mathematics at UC San Diego in 2023. 

My research can be broadly described as developing, analyzing, and applying numerical and geometric methods for optimization, differential equations, and mathematical physics; particular areas of interest include adjoint optimization and optimal control, geometric mechanics, time integration, computational radiation hydrodynamics, and structure-preserving numerical methods.

I am teaching Calculus 3 for Engineers (APPM 2350) this semester. I previously taught several courses at UC San Diego. Additionally, I have mentored three graduate students. 

Below is a summary of my research and teaching experience. More detailed information about me, my research, and my teaching experience can be found at my website. 

 

Publications

  • B. K. Tran and B. S. Southworth. Galerkin Formulation of Path Integrals in Lattice Field Theory. Journal of Physics A: Mathematical and Theoretical, Accepted, 2025. DOI. arXiv.

  • B. K. Tran, J. W. Burby and B. S. Southworth. A Geometric Perspective on Kinetic Matter-Radiation Interaction and Moment Systems. Geometric Mechanics, 2(1), 107-158, 2025. DOI. arXiv.

  • B. K. Tran, B. S. Southworth and T. Buvoli. Order Conditions for Nonlinearly Partitioned Runge-Kutta Methods. Electronic Transactions on Numerical Analysis, 63, 171-198, 2025. DOI. arXiv.

  • B. K. Tran and M. Leok. Variational Principles for Hamiltonian Systems. Geometric Mechanics, 2(1), 59-105, 2025. DOI. arXiv.

  • B. K. Tran and M. Leok. A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups. Journal of Dynamical and Control Systems, 31, 8, 2025. DOI. arXiv.

  • B. K. Tran, B. S. Southworth and M. Leok. On Properties of Adjoint Systems for Evolutionary PDEs. Journal of Nonlinear Science 34:95, 2024. DOI. arXiv.

  • B. K. Tran and M. Leok. Geometric Methods for Adjoint Systems. Journal of Nonlinear Science 34:25 (75 pages), 2024. DOI. arXiv. 

  • B. K. Tran and M. Leok. Multisymplectic Hamiltonian Variational Integrators. International Journal of Computer Mathematics (Special Issue on Geometric Numerical Integration, Twenty-Five Years Later), 99(1), 113-157, 2022. DOI. arXiv. 

Papers in Review

  • M. N. Vu†, B. K. Tran†, S. A. Shah, G. Zollicoffer, N. Hoang-Xuan and M. Bhattarai. HalluField: Detecting LLM Hallucinations via Field-Theoretic Modeling. Submitted, 2025. arXiv.

  • B. K. Tran, B. S. Southworth, D. B. Cavender*, S. Olivier, S. A. Shah and T. Buvoli. Nonlinear Splitting for Gradient-Based Unconstrained and Adjoint Optimization. Submitted, 2025. arXiv.

  • B. K. Tran, B. S. Southworth, H. F. Blumhoefer* and S. Olivier. Preconditioning transformations of adjoint systems for evolution equations. Submitted, 2025. arXiv.

  • T. Buvoli, B. K. Tran and B. S. Southworth. Multirate Runge-Kutta for Nonlinearly Partitioned Systems. Submitted, 2025. arXiv.

  • B. K. Tran and M. Leok. Variational Structures in Cochain Projection-Based Variational Discretizations of Lagrangian PDEs. Submitted, 2024. arXiv. 

(* Student mentee co-author)

(† Co-first author)

Conference Proceedings

  • B. K. Tran, J. W. Burby and B. S. Southworth. Geometric Formulation of Three-Temperature Radiation Hydrodynamics. Proceedings of the 16th World Congress in Computational Mechanics, 2024. DOI.

Teaching experience

  • Instructor. APPM 2350: Calculus 3 for Engineers. University of Colorado Boulder Applied Mathematics. Fall 2025.

  • Co-mentor. David Cavender, Graduate Student, UC San Diego. Los Alamos National Laboratory Summer Student Program 2025.

  • Co-mentor. Reid Gomillion, Graduate Student, Virginia Tech. Los Alamos National Laboratory Summer Student Program 2024.

  • Assisting Mentor. Hannah F. Blumhoefer, Graduate Student, Iowa State University. Los Alamos National Laboratory Summer Student Program 2024.

  • Instructor. Math 18: Linear Algebra. UCSD Mathematics. Summer Session 1, 2023.  

  • Instructor. Math 20D: Introduction to Differential Equations. UCSD Mathematics. Summer Session 1, 2022.  

  • Instructor. Math 20E: Vector Calculus. UCSD Mathematics. Fall 2021.

  • Instructor. Math 20A: Calculus for Science and Engineering. UCSD Mathematics. Summer Bridge, 2021. 

  • TA. Math 179/279: Projects in Computational and Applied Mathematics. UCSD Mathematics. Spring 2023. 

  • TA. Math 20E: Vector Calculus. UCSD Mathematics. Summer 2019. 

  • TA. Math 20E: Vector Calculus. UCSD Mathematics. Spring 2019. 

  • TA. Math 150B: Calculus on Manifolds. UCSD Mathematics. Winter 2019. 

  • TA. Math 150A: Differential Geometry. UCSD Mathematics. Fall 2018. 

  • Tutor. Phys 2D: Relativity and Quantum Physics. UCSD Physics. Winter 2018.

  • TA. Math 20B: Calculus for Science and Engineering II. UCSD Mathematics. Fall 2017. 

  • Workshop Facilitator. Math 20E: Vector Calculus and Phys 2C: Fluids, Waves, Thermodynamics, and Optics. UCSD OASIS Learning Center. 2015-2016.