Dr. Kirill V. Golubnichiy

Texas Tech University

Welcome to my page

I obtained my Ph.D. in 2022 from the University of Washington, Seattle, under the supervision of Kenneth Bube and Michael V. Klibanov.

Research

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.

Teaching

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.

Research Grants

Graduate Students (Includes Co-Supervisions)

Doctoral

Master's

Graduate school Service:

Committee Member

Service/Professional Activities:

Organizer for AIP 2025

  • Minisymposium at the Applied Inverse Problems (AIP) Conference 2025, Rio de Janeiro, Brazil, July 28–August 1, 2025: Inverse Problems for Partial Differential Equations – Advances and Applications.

Research Monographs

  • Tsarai I. Gutsunaev, Aleksandr A. Shaideman, and Kirill V. Golubnichiy. New Euclidon Method of Generating Stationary Vacuum Einstein Fields. World Scientific Publishing Co. Pte. Ltd., Singapore, 2025. World Scientific.

Books

  • Kirill V. Golubnichiy. Higher Mathematics for Colleges. Manual and problem book, Moscow State University of Economics, Statistics, and Computer Science (MESI), Moscow, Russia, 2007. (In Russian.)
  • Kirill V. Golubnichiy, Andrey O. Shishanin, and Edwin R. Benavente. Higher Mathematics. 2nd ed., revised and enlarged, manual and problem book for students of higher technical schools, Peoples' Friendship University of Russia (PFUR), Moscow, Russia, 2009. (In Russian.) Russian State Library.
  • Kirill V. Golubnichiy, Andrey O. Shishanin, and Edwin R. Benavente. Higher Mathematics. 3rd ed., revised and enlarged, manual and problem book for students of higher technical schools, Peoples' Friendship University of Russia (PFUR), Moscow, Russia, 2010. (In Russian.)
  • Galina V. Shadrina and Kirill V. Golubnichiy. Economic Analysis: Textbook for Universities. 4th ed., revised and expanded, Yurait Publishing, Higher Education, ISBN 978-5-534-16899-0, 2023. Yurait.
  • Galina V. Shadrina and Kirill V. Golubnichiy. Financial and Economic Activity Analysis: Textbook for Universities. 4th ed., revised and expanded, Yurait Publishing, Higher Education, ISBN 978-5-534-16888-4, 2025. Yurait.
  • Galina V. Shadrina and Kirill V. Golubnichiy. Managerial and Financial Analysis: Textbook for Universities. 2nd ed., revised and expanded, Yurait Publishing, Higher Education, ISBN 978-5-534-16532-6, 2025. Yurait.
  • Galina V. Shadrina and Kirill V. Golubnichiy. Theory of Economic Analysis: Textbook for Universities. 4nd ed., revised and expanded, Yurait Publishing, Higher Education, ISBN 978-5-534-16535-7, 2025. Yurait.

Selected publications

  • Mikhail V. Klibanov and Kirill V. Golubnichiy. Carleman Estimates for Inverse Problems. Submitted, 2026.
  • Mikhail V. Klibanov, Kirill V. Golubnichiy, and Benjamin Jiang. A Semi-Discrete Convexification Method Combined with Deep Learning for Electrical Impedance Tomography. Submitted, 2026. arXiv:2602.18001.
  • Mikhail V. Klibanov, Mikhail Yu. Kokurin, and Kirill V. Golubnichiy. Corruption via Mean Field Games. Journal of Mathematical Analysis and Applications, vol. 566, no. 1, 2026. arXiv:2504.06430. Elsevier.
  • Mikhail V. Klibanov, Aleksander A. Shananin, Kirill V. Golubnichiy, and Sergey Kravchenko. Forecasting of Stock Option Prices via the Solution of an Ill-Posed Problem. Inverse Problems, vol. 38, no. 11, 2022. arXiv:2202.07174. IOP Publishing.
  • Mikhail V. Klibanov, Andrey V. Kuzhuget, and Kirill V. Golubnichiy. An Ill-Posed Problem for the Black-Scholes Equation for a Profitable Forecast of Prices of Stock Options on Real Market Data. Inverse Problems, vol. 32, no. 1, 2016. IOP Publishing.
  • Mikhail V. Klibanov, Kirill V. Golubnichiy, and Andrey V. Nikitin. Quasi-Reversibility Method and Neural Network Machine Learning for Forecasting of Stock Option Prices. Contemporary Mathematics, vol. 784, American Mathematical Society, 2023. arXiv:2111.06642. AMS.
  • Mikhail V. Klibanov and Kirill V. Golubnichiy. Convexification Method in Inverse Problems. Advanced Computational Methods in Engineering and Applied Mathematics, Springer. Accepted, to appear, 2026.
  • Aleksandr A. Shaideman and Kirill V. Golubnichiy. Stationary Multiple Euclidean Solutions to the Vacuum Einstein Equations. Gravitation and Cosmology, vol. 32, no. 2, 2026. arXiv:2502.03675. Springer.
  • Wanchaloem Wunkaew, Yuqing Liu, and Kirill V. Golubnichiy. Using the Newton-Raphson Method with Automatic Differentiation to Numerically Solve Implied Volatility of Stock Option through Binomial Model. Communications on Analysis and Computation, vol. 5, pp. 43–52, 2025. arXiv:2207.09033. AIMS.
  • Kirill V. Golubnichiy. Unique Solvability of an Inverse Problem for a Nonlinear Modified Transport Equation. Lobachevskii Journal of Mathematics, vol. 47, no. 9, pp. 4444–4454, 2026. arXiv:1912.02996.
  • Aleksandr A. Shaideman, Kirill V. Golubnichiy, and J. D. Arias H. An Axially Symmetric Stationary N-Center Solution of Einstein's Vacuum Equations. International Journal of Modern Physics A. Accepted, to appear, 2026. arXiv:2603.10064. World Scientific.
  • Benjamin Jiang, Matthieu Durieux, and Kirill V. Golubnichiy. Solving the Stock Option Forecast Problem by a Numerical Method for the Black-Scholes Equation with Machine Learning Classification Model. Lecture Notes in Networks and Systems, vol. 2, pp. 541–561, 2025. arXiv:2209.03512. Springer.
  • Zheng Cao, Raymond Guo, Wenyu Du, Jiayi Gao, and Kirill V. Golubnichiy. Optimizing Stock Option Forecasting with the Assembly of Machine Learning Models and Improved Trading Strategies. Future of Information and Communication Conference (FICC), vol. 920, pp. 610–620, 2024. arXiv:2211.15912. Springer.
  • Zheng Cao, Wenyu Du, and Kirill V. Golubnichiy. Application of Convolutional Neural Networks with Quasi-Reversibility Method Results for Option Forecasting. Lecture Notes in Networks and Systems, vol. 739, 2023. arXiv:2208.14385. Springer.
  • Kirill V. Golubnichiy, Tianyang Wang, and Andrey V. Nikitin. An Evaluation of Novel Method of Ill-Posed Problem for the Black-Scholes Solution. Preprint, 2020. arXiv:2011.09136.
  • Mikhail V. Klibanov, Kirill V. Golubnichiy, and Kenneth P. Bube. Globally Strictly Convex Tikhonov-Like Functional for a Coefficient Inverse Problem for a 1-D Hyperbolic Equation. In progress.
  • Kirill V. Golubnichiy. Inverse Problems for the Nonlinear Modified Transfer Equation. Preprint, 2019. arXiv:1912.02996.
  • Kirill V. Golubnichiy. On One of the Controllability Problems for Modified Transfer Equation. Proceedings of the Voronezh Winter School of Mathematics under S. G. Krein, Voronezh State University, pp. 87–95, 2008. (In Russian.) VSU.
  • Kirill V. Golubnichiy and Galina V. Shadrina. Basic Methods for Forecast Development of Managing Subject. Scientific Bulletin of the Volgograd Branch of RANEPA, Series: Economy, 2015. Journal PDF.

Conference Papers and Abstracts

  • Kirill V. Golubnichiy. Klibanov’s Method of Ill-Posed Problem for the Black-Scholes Equation Solution and Machine Learning. Conference Devoted to the 75th Anniversary of the Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia, June 30–July 9, 2021 (online). Abstract, p. 55.
  • Kirill V. Golubnichiy. About One Theorem for Nonlinear Transport Equation. SIAM Front Range Student Conference, 2015.
  • Kirill V. Golubnichiy and Galina V. Shadrina. About One Theorem for Nonlinear Transport Equation. Anniversary Meeting of the MAA Rocky Mountain Section, Colorado Springs, 2014.
  • Kirill V. Golubnichiy. About One Theorem for Nonlinear Transport Equation. International Conference on Differential and Difference Equations and Applications (CDDEA 2012), Strečno, Slovak Republic, June 2012.
  • Kirill V. Golubnichiy. About Two Theorems for Nonlinear Transfer Equation. International Conference on Differential and Difference Equations and Applications (CDDEA 2010), Strečno, Slovak Republic, June 21–25, 2010.
  • Kirill V. Golubnichiy. About the Theorem for the Nonlinear Transfer Equation. Voronezh Winter School of Mathematics under S. G. Krein, Voronezh, January 2010. Book of Abstracts, Voronezh State University, pp. 165–166.
  • Kirill V. Golubnichiy. About a Theorem for the Modified Nonlinear Transfer Equation. XLV Russian Conference on Mathematics, Information Science, Physics, and Chemistry Problems, Peoples' Friendship University of Russia, Moscow, 2009. Book of Abstracts, pp. 24–25. (In Russian.)
  • Kirill V. Golubnichiy. On One of the Controllability Problems for the Modified Transfer Equation. International Conference on Differential and Difference Equations and Applications (CDDEA 2008), Strečno, Slovak Republic, June 23–27, 2008. Abstract, p. 24.
  • Kirill V. Golubnichiy. The Controllability Problems for the Modified Transfer Equation. Differential Equations and Topology Dedicated to the Centennial Anniversary of Lev Semenovich Pontryagin (1908–1988), Moscow, June 17–22, 2008. Abstracts, Moscow State University, p. 118. (In Russian.)
  • Kirill V. Golubnichiy. The Controllability Problems for the Modified Transfer Equation. XLIV Russian Conference on Mathematics, Information Science, Physics, and Chemistry Problems, Peoples' Friendship University of Russia, Moscow, 2008. Book of Abstracts, p. 4. (In Russian.)
  • Kirill V. Golubnichiy. The Controllability Problems for the Modified Transfer Equation. Voronezh Winter School of Mathematics under S. G. Krein, Voronezh, January 2008. Book of Abstracts, Voronezh State University, p. 41. (In Russian.)
  • Kirill V. Golubnichiy. The Controllability Problems for the Modified Transfer Equation. 3rd International Conference Dedicated to the 85th Anniversary of Corresponding Member of the Russian Academy of Sciences Prof. L. D. Kudriavtsev, Functional Spaces, Differential Operators and Their Applications, General Topology, MIPT and PFUR, Moscow, 2008. Abstracts, p. 247. (In Russian.)
  • Kirill V. Golubnichiy. The Controllability Problems for the Modified Transfer Equation. International Conference Differential Equations and Related Topics, dedicated to the memory of I. G. Petrovskii, XXII Joint Session of the Moscow Mathematical Society and I. G. Petrovskii Seminar, Moscow, May 21–26, 2007. Book of Abstracts, Moscow State University, p. 106. (In Russian.)
  • Kirill V. Golubnichiy. The Controllability Problems for the Modified Transfer Equation. XLII Russian Conference on Mathematics, Information Science, Physics, and Chemistry Problems, Peoples' Friendship University of Russia, Moscow, 2007. Book of Abstracts, p. 11. (In Russian.)

Symposium

  • Talk, Colloquium, Department of Mathematics, The University of Alabama, Tuscaloosa, Alabama, USA, November 20, 2026.
  • Talk, SIAM Texas–Louisiana Sectional Meeting, URL , October 30–November 1, 2026.
  • Talk, The New York-New Jersey-Pennsylvania Section of SIAM Annual Meeting 2026, URL , October 23–October 25, 2026.
  • Talk, Colloquium, Department of Mathematics and Statistics, UNCC, Charlotte, NC, USA, October 15, 2026.
  • Talk, Monterrey Institute of Technology and Higher Education (Technological Institute of Monterrey, ITESM), Monterrey, Nuevo León, Mexico, September 21, 2026.
  • Talk, International Biweekly Online Seminar on Analysis, Differential Equations and Mathematical Physics, URL online, May 7, 2026.
  • Talk, Workshop: On operator theory and harmonic analysis and their applications, Institute of Mathematics of NAS RA, Yerevan, Armenia, April 26-30, 2026.
  • Talk, Seminar: Analysis, Texas Tech University, Lubbock, TX, USA, April 22, 2026.
  • Talk, Seminar: Mathematical Finance Seminar, Texas Tech University, Lubbock, TX, USA, April 17, 2026.
  • Talk, Colloquium, South Dakota State University, Brookings, SD, USA, October 8, 2025.
  • Talk, Minisymposium at the Applied Inverse Problems (AIP) Conference 2025, Rio de Janeiro, Brazil, July 28–August 1, 2025.
  • Talk, Seminar: Mathematical Finance Seminar, Texas Tech University, Lubbock, TX, USA, November 22, 2024.
  • Talk, Seminar: Analysis, Texas Tech University, Lubbock, TX, USA, November 18, 2024.
  • Talk, Colloquium, The George Washington University, Washington, DC, USA, March 15, online, 2024.
  • Talk, Colloquium, Umeå University, Umeå, Sweden, March 8, online, 2024.
  • Talk, Colloquium, The University of Akron, Akron, OH, USA, February 13, 2024.
  • Talk, Colloquium, Texas Tech University, Lubbock, TX, USA, January 24, online, 2024.
  • Talk, Quasilinear Equations, Inverse Problems and Their Applications, MIPT, Moscow, Russia, December 4-6, online, 2023.
  • Talk, The Canadian Mathematical Society (CMS), Winter Meeting, Montréal, Quebec, Canada, December 1-4, 2023.
  • Talk, Fin-ML 5th Anniversary, HEC Montréal, Quebec, Canada, November 7-8, 2023.
  • Talk, Colloquium, Department of Mathematics and Statistics, UNCC, Charlotte, NC, USA, October 6, 2023.
  • Talk, BIRS Workshop on "Nonlinear Inverse Problems", Banff International Research Station, Alberta, Canada, July 16-21, 2023.
  • Talk, The Canadian Mathematical Society (CMS), Summer Meeting, University of Ottawa, Ottawa, Ontario, Canada, June 2-5, 2023.
  • Talk, Annual Alberta Mathematics Dialogue (AMD) 2023, Pacific Institute for The Mathematical Sciences, Calgary, Alberta, Canada, May 4-5, 2023.
  • Talk, Colloquium, Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, December 6, 2022.
  • Talk, Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis–2021, Moscow Institute of Physics and Technology, Moscow Region, Dolgoprudny, Russia, June 30–July 9, online, 2021.
  • Talk, MATH+X Symposium on Inverse Problems and Deep Learning in Space Exploration, Rice University, Houston, TX, USA, January 23-25, 2019.
  • Talk, MATH+X Symposium on Data Science and Inverse Problems in Geophysics, Rice University, Houston, TX, USA, January 24-26, 2018.

Workshop

  • WORKSHOP OTHA SPRING 2026 on operator theory and harmonic analysis and their applications, Yerevan, Armenia, April 26-30, 2026.
  • The 13th Montreal Industrial Problem Solving Workshop, organized by the CRM and IVADO, Montreal, Canada, August 21-25, 2023.
  • BIRS Workshop on "Nonlinear Inverse Problems", Banff International Research Station, Alberta, Canada, July 16-21, 2023.
  • The Canadian Mathematical Society (CMS), Summer Meeting, University of Ottawa, Ottawa, Ontario, Canada, June 2-5, 2023.
  • Math Industry, Pacific Institute for the Mathematical Sciences, University of British Columbia, University of Calgary, University of Alberta, August 2020 (remote).
  • MATH+X Symposium on Data Science and Inverse Problems in Geophysics, Rice University, Houston, TX, USA, January 22-24, 2018.

Guest editor

  • Operator Theory and Harmonic Analysis in Armenia (OTHA-Spring 2026) in Lobachevskii Journal of Mathematics, Springer Nature URL , 2026-present.

Newspaper Interviews About My Research

  • Interview About My Research for the Newspaper Golos Armenii (Voice of Armenia), Newspaper URL , May 7, 2026.

Contact

Email: kgolubni@ttu.edu

Office: MA 249, Texas Tech University