Mean Field Equations on Torus, Pre-Modular Forms and Painlevé VI Equation

Explore the intricate connections between mean field equations on torus surfaces, pre-modular forms, and the Painlevé VI equation in this 44-minute conference talk presented at BIMSA's ICBS2025. Delve into advanced mathematical concepts as the speaker examines how these three seemingly distinct areas of mathematics intersect and influence each other. Discover the theoretical foundations of mean field equations when applied to torus geometry, understand the role of pre-modular forms in this context, and learn how these relate to the classical Painlevé VI differential equation. Gain insights into cutting-edge research that bridges differential geometry, modular forms theory, and integrable systems, making this presentation valuable for mathematicians and researchers working in these specialized fields.