Abstract 

Surfaces in three-dimensional space represent a fundamental topic in geometry, analysis, and physics, where they often arise as energy-minimizing shapes governed by constraints such as surface tension or surface bending. The modern study of surfaces sits at the interface of contemporary areas of mathematics, including integrable systems, loop groups, moduli spaces of connections and holomorphic bundles over Riemann surfaces, geometric PDEs, mathematical physics, computational methods, discretization, and visualization. This workshop brings together key researchers from these fields for the first time, fostering an exchange of ideas, techniques, and open problems to stimulate long-term collaboration.

Aims & Scope

This workshop focuses on global problems in surface geometry—a subject that has advanced rapidly in recent years through cross-fertilization among geometric analysis, integrable systems, Higgs bundles, mathematical physics, and discretization / experimentations. 

We seek to build bridges among three key methodological approaches:

• Geometric analysis, providing existence and regularity results;

• Integrable systems, supplying explicit examples and classification schemes;

• Computational and experimental methods, enabling exploration and conjecture-forming.

We will focus in particular on strengthening connections in the following themes：

• Möbius invariance in Willmore energy problems; 

• The use of complex curve techniques — such as Higgs bundles, algebraic geometry, and  ∂ ̅-analysis — in analytical settings;

• Stability of stationary surfaces constructed through integrable methods and computer experiments. 

Format

The workshop is designed to foster dialogue and collaboration through:

• Introductory overview lectures by leading researchers;

• Research-focused talks on recent advances, highlighting open problems;

• Ample time for discussion and informal interaction.

Held in China, this meeting aims to enhance East–West collaboration in mathematics, with special support for PhD students and early-career researchers.