Texas Tech University
I obtained my Ph.D. in 2022 from the University of Washington, Seattle, under the supervision of Kenneth Bube and Michael V. Klibanov.
My research lies at the intersection of partial differential equations (PDEs), inverse and ill-posed problems, mean field games, mathematical finance, machine learning, gravitation, cosmology, and mathematical physics. I develop analytical and computational methods for nonlinear PDEs, with particular emphasis on Carleman estimates, convexification, and regularization techniques for coefficient-recovery and forecasting problems.
A major direction of my work concerns inverse problems arising in physics, including Electrical Impedance Tomography (EIT). In EIT, I study the inverse problem of recovering spatially varying electrical conductivity from boundary measurements for the stationary conductivity equation. My work focuses on globally convergent and stable reconstruction methods based on Carleman estimates, convexification, semi-discrete formulations, and machine learning techniques.
I also work on mean field games, including nonlinear coupled PDE systems describing the collective behavior of large populations of interacting agents. My interests include forward, retrospective, and inverse problems for mean field game systems, parameter and coefficient recovery, stability, and numerical reconstruction methods. I am particularly interested in developing Carleman-estimate and convexification-based approaches for highly nonlinear mean field game models and combining them with computational and machine learning techniques.
My current research in mathematical finance includes inverse problems for the Black–Scholes and Heston equations, as well as statistical and machine-learning methods for financial modeling, including GARCH models and neural networks. I am interested in combining PDE-based models, regularization methods, statistical techniques, and machine learning to improve parameter reconstruction, stability, and forecasting from noisy financial data.
Another direction of my research concerns gravitation, cosmology, and quantum theory. In gravitational physics, I study exact solutions of the Einstein and Einstein–Maxwell equations, including stationary and axially symmetric gravitational fields, black-hole-type solutions, Kerr–NUT geometries, multi-center space-times, and related solution-generating methods. These problems are connected with the mathematical structure of relativistic gravitational fields, black holes, and cosmological models.
More broadly, my goal is to combine rigorous PDE analysis with scientific computing, statistical modeling, and machine learning to address challenging problems in inverse problems, mean field games, quantitative finance, Electrical Impedance Tomography, gravitation, black-hole physics, cosmology, and quantum-related mathematical models.
Spring 2025: MATH 2450-114 and MATH 2450-111 – University Calculus III.
Summer 2025: MATH 3350-D22 – Higher Mathematics for Engineers and Scientists I (Introduction to Differential Equations).
Fall 2025: MATH 2450-113 – University Calculus III.
Spring 2026: MATH 2450-112 – University Calculus III.
Fall 2026: MATH 2450-112 – University Calculus III.
Email: kgolubni@ttu.edu
Office: MA 249, Texas Tech University