Mira Berkovich
מירה ברקוביץ׳ Fellow Division: Games, Dynamics & Strategic Control Specialization: Hamilton–Jacobi–Isaacs Equations & Pursuit-Evasion GamesMira Berkovich is a Fellow at the Institute for Advanced Dynamic Uncertainty, where her work develops the analytical theory of Hamilton–Jacobi–Isaacs equations governing zero-sum differential games and pursuit-evasion problems. She holds a PhD in Mathematics from the Hebrew University of Jerusalem (Einstein Institute of Mathematics), where her doctoral research established existence and uniqueness of viscosity solutions for Isaacs equations with state-constrained controls and nonconvex Hamiltonians arising in adversarial pursuit problems on bounded domains. The thesis resolved, in particular, the regularity of the value function on the boundary of the capture set under non-coercive Hamiltonians — a question with direct implications for the structure of optimal evader policies near the closure of the game's terminal manifold.
Following her doctorate at the Einstein Institute, Berkovich pursued a second doctorate in physics at Saint Petersburg State University (Faculty of Physics), where her thesis on stochastic thermodynamics and the optimal control of non-equilibrium systems established large-deviation principles for controlled diffusions on phase spaces with broken time-reversal symmetry, and connected the resulting Hamilton–Jacobi structure to the variational principles governing entropy production along optimal protocols. Defended at age 29, the work bridged the analytical theory she had developed at Hebrew University with the mathematical physics tradition of the Saint Petersburg school, and produced a unified Hamiltonian framework in which adversarial differential games and controlled non-equilibrium systems share a common large-deviation backbone. Her appointment as a Fellow of the Institute at age 30 makes her the youngest researcher to hold the rank in IADU's history.
At IADU, Berkovich applies HJI methods to adversarial problems in macroeconomic and policy contexts: the differential-game analysis of sovereign-versus-speculator interactions in fixed-exchange-rate regimes, robust control of policy instruments as worst-case games against an unknown adversarial nature, and the formulation of pursuit-evasion problems on graphs for the design of contagion-containment policies. Her work bridges the deep analytical traditions of the Russian and Israeli mathematical schools and contributes to the Institute's research output for central banks, sovereign treasuries, and security-of-supply institutions concerned with adversarial uncertainty.
Publications
IADU Publications
Publications forthcoming.
Selected Prior Work
- Вязкостные решения уравнений Айзекса с невыпуклым гамильтонианом для задач преследования с фазовыми ограничениями Математический сборник
- Стохастическая термодинамика управляемых систем: принципы больших уклонений и оптимальные протоколы Теоретическая и математическая физика
- Численные схемы для уравнения Айзекса на основе обратных стохастических дифференциальных уравнений Записки научных семинаров ПОМИ
- Гамильтонова структура неравновесных стохастических систем и принцип Понтрягина Журнал экспериментальной и теоретической физики (ЖЭТФ)
- Позиционные дифференциальные игры под стохастическими возмущениями: стохастический минимаксный принцип Дифференциальные уравнения
- פתרונות צמיגים למשוואת איזקס במשחקי מרדף-בריחה במרחב חסום מדעי המתמטיקה
- תרמודינמיקה סטוכסטית של מערכות מבוקרות: עקרונות וריאציוניים והייצור האנטרופי הכנס השנתי של האגודה הישראלית לפיזיקה
- משחקי מרדף סטוכסטיים תחת מידע א-סימטרי: גישה אנליטית הכנס השנתי של האיגוד המתמטי הישראלי
- Viscosity solutions of state-constrained Isaacs equations with nonconvex Hamiltonians SIAM Journal on Control and Optimization
- Positional differential games under stochastic perturbations: an Isaacs-type minimax principle Dynamic Games and Applications
- Large deviations for controlled non-equilibrium diffusions and the geometry of optimal protocols Journal of Statistical Physics
- Hamilton–Jacobi structure of stochastic thermodynamics and entropy production along extremal trajectories Communications in Mathematical Physics
- Pursuit-evasion on bounded domains: regularity of the value function near the capture set ESAIM: Control, Optimisation and Calculus of Variations
Contact
For research enquiries, contact the Institute at research@iadu.org and include M. Berkovich in the subject line. All correspondence is handled in accordance with IADU's institutional communication policy.