Applied Mathematics and Quantitative Modeling

Background

The rapid advancement of complex systems research has positioned applied mathematics as a central tool for analyzing dynamic, nonlinear, and high-dimensional phenomena across disciplines. In particular, modern financial systems provide a rich and challenging application domain, characterized by uncertainty, interdependence, and continuous evolution. Traditional analytical frameworks often struggle to capture the intricate behaviors of such systems, especially under conditions of volatility and structural change. Recent developments in applied mathematics—including numerical analysis, stochastic processes, dynamical systems, and computational simulation—offer powerful methodologies for modeling and understanding these complexities.

By treating financial systems as illustrative case studies, these mathematical approaches enable deeper insights into system dynamics, enhance predictive capabilities, and contribute to more rigorous analytical frameworks. This integration not only advances theoretical research in mathematics but also demonstrates its practical relevance in addressing real-world problems.

The symposium, which serves as a specialized session of the 4th International Conference on Applied Physics and Mathematical Modeling (CONF-APMM 2026), will focus on mathematics and modeling.

Goal/Rationale

Despite significant progress in applied mathematics, there remains a gap between theoretical model development and its application to complex real-world systems. Financial markets, as highly dynamic and data-rich environments, provide an ideal testing ground for advancing quantitative modeling techniques. However, existing approaches often lack generalizability, robustness, or the ability to fully capture nonlinear interactions and emergent behaviors.

This symposium aims to bridge this gap by promoting the development and application of advanced mathematical methods within complex system contexts. The primary objectives are as follows:

• Establish a platform for the exchange of ideas on applied mathematics and quantitative modeling
• Encourage the application of mathematical theories to real-world complex systems, with finance as a key example
• Explore recent advances in computational methods, stochastic modeling, and nonlinear analysis
• Foster dialogue between mathematicians, computational scientists, and applied researchers
• Address challenges in model scalability, accuracy, and interpretability
• Promote interdisciplinary approaches that integrate theory, computation, and application
• Support the development of innovative mathematical frameworks for complex system analysis

Through these efforts, the symposium seeks to strengthen the connection between mathematical theory and practical problem-solving, advancing both methodological innovation and applied impact.

Scope

This symposium focuses on theoretical and computational advances in applied mathematics, with an emphasis on quantitative modeling of complex systems. Financial systems will be considered as representative application scenarios, though contributions from other domains are also welcome.

Relevant topics include, but are not limited to:

• Nonlinear dynamical systems and complexity analysis
• Stochastic processes and probabilistic modeling
• Numerical methods and iterative algorithms
• Computational simulation and high-performance computing
• Data-driven and machine learning–assisted modeling
• Mathematical modeling of interconnected systems
• Stability, bifurcation, and chaos in applied systems
• Optimization techniques in large-scale systems
• Multiscale and high-dimensional modeling approaches
• Applications of mathematical methods in finance and other complex domains

Submissions should emphasize methodological rigor, theoretical contribution, or innovative applications, contributing to a deeper understanding of complex systems through quantitative and mathematical perspectives.