Geometric PDE, relativity, and fluid dynamics
Elliptic and geometric PDE, scalar and boundary mean curvature problems, Einstein constraint equations, and fluid equations, including stability and reconstruction questions from partial observations.
Academic homepage
Цогтгэрэлийн Гантөмөр
I work on analysis, numerical methods, geometry, and mathematical physics, with interests in continuous models and their approximation, computation, and structure.
Монгол
Сайн байна уу. Энэ хуудсанд миний судалгаа, хичээл, тэмдэглэл, мөн Монгол хэлээрх сургалтын материалуудын холбоос багтана.
Current Directions
All researchNumerical analysis and geometric discretization
Adaptive finite and boundary element methods, finite element exterior calculus, discrete exterior calculus, wavelet coordinates, and structure-preserving approximation of differential operators.
Approximation theory, adaptivity, and neural realization
Nonlinear approximation, adaptive and multilevel methods, refinable systems, subdivision schemes, and exact neural-network realization of refinement algorithms.
Quantum fields and computational regularization
Dynamical lattice regulators and computational approaches to quantum field theory, with attention to continuum symmetries, locality, positivity, and computable regularization.
Mathematical exposition, teaching, and computational tools
Expository notes, bilingual teaching projects, calendar computations, and small computational tools for mathematics, physics, and scientific visualization.
Selected Recent Work
Bibliography- Exact ReLU realization of tensor-product refinement iterates arXiv:2605.03917 (2026).
- Exact Loop Controllers for ReLU Realization of Homogeneous Curve Refinements arXiv:2605.01655 (2026).
- Regularity of solutions of the Navier-Stokes-alpha-beta equations with wall-eddy boundary conditions 2025. Zeitschrift für angewandte Mathematik und Physik, Accepted for publication in Zeitschrift für angewandte Mathematik und Physik. arXiv
- Rotationally invariant dynamical lattice regulators for Euclidean quantum field theories J. High Energ. Phys. 2026, 36 (2026). arXiv · journal · DOI
Teaching and Notes
The teaching archive includes past McGill courses, selected notes, and Mongolian-language material where appropriate.
Software and Tools
This homepage is the academic hub. Interactive tools, animations, calendars, and small computational projects are kept separately, with Sol as the organizing project for lightweight tools.
Contact and Profiles
gantimur -at- gmail.com