Scientists from various countries discuss current issues in mathematical physics at YSU

Organized jointly by the YSU Faculty of Mathematics and Mechanics and the Institute of Mathematics of the National Academy of Sciences of the Republic of Armenia, the conference focuses on classical and quantum statistical physics, quantum dynamics, mathematical methods in quantum mechanics, and applications of point processes in statistical physics.

Artur Sahakyan, Dean of the YSU Faculty of Mathematics and Mechanics, noted that this long-standing event is being held in a jointly organized format for the first time. Previously, the Institute of Mathematics of NAS RA served as the conference's main organizer.

"The key theme of this prestigious conference is the application of stochastic, or probabilistic, methods in mathematical physics, which is a current and highly relevant area. Its importance lies in its applied orientation, as it is situated at the intersection of physics and mathematics," Artur Sahakyan said. 

Highlighting the importance of the event, the dean expressed hope that the conference would help expand existing cooperation and establish new partnerships with scientists from leading research centers around the world. 

The scientific program features more than 30 talks, most of them by leading researchers from abroad. The conference brings together specialists from the United States, the United Kingdom, Germany, France, China, Russia, the Netherlands, Italy, Poland, Belgium, Switzerland, the Czech Republic, Austria, and Armenia.

Daniel Ueltschi, a researcher at the Department of Mathematics at the University of Warwick, spoke on geometric inequalities for quantum spin systems. He discussed challenges in studying correlations between spins in quantum spin systems, noting that even models that are conceptually simple can be quite difficult to study. He also addressed the classical Ising model and its connection to the quantum XY model, presenting results obtained for the latter related to the proof of correlation inequalities.

YSU Vice-Rector for Scientific Affairs Rafayel Barkhudaryan will present a talk titled "Stochastic Models, Free Boundaries, and Numerical Methods in Financial Bubble Analysis." The research focuses on modeling speculative financial bubbles by representing the evolution of investor disagreement through Lévy jump processes. It applies optimal stopping theory and Itô-Lévy calculus, develops a theoretical framework for viscosity solutions and constructs a numerical scheme, while numerical experiments examine the impact of jumps on bubble dynamics and optimal trading strategies.

Alexander Figotin, a researcher at the University of California, will present "Floquet Theory of the Modulated LC Circuit: A Continued-Fraction and Krein-Theoretic Study." The research examines the parametric stability of a lossless LC circuit with harmonically modulated capacitance using the Ince equation and several classical mathematical methods. It presents the characteristics of instability-tongue formation for odd and even resonances, asymptotic expressions for stability boundaries, and a constructive description of the periodic Floquet factor. 

Volker Betz, a researcher at the Technical University of Darmstadt, will present research on "Complex Spin Systems." His work examines how reflection-positivity estimates for quantum spin systems can be used to establish long-range order in certain graphical models.

The conference program also includes presentations on numerical algorithms for elliptic systems, inversion of the Funk transform, mean-field games, the global regularity problem for the Navier-Stokes equations, and the statistical physics of infinite-volume systems.

The conference will continue through September 12.