Research Interests:

My research lies in the calculus of variations and its applications to nonlinear elasticity, differential geometry, and the analysis of singular limits. I am particularly interested in how effective variational models emerge from more complex descriptions, and in the geometric structures selected by energy minimization.

A substantial part of my work concerns thin elastic structures. I study the formation of singularities, defects, ridges, and vertices in elastic sheets, often in Föppl-von Kármán or nonlinear plate models. The aim is to obtain ansatz-free energy bounds, identify scaling laws, and understand how geometry, boundary conditions, and reference metrics determine the shape of low-energy configurations.

More recent work also addresses curvature-driven surface energies and diffuse-interface models on surfaces. This includes discrete approximations of Willmore and Helfrich-type energies, phase separation on varying surfaces, and biomembrane models combining curvature energies with line tension. A related direction concerns adaptive finite-element meshes and their Gamma-limits.

Main themes

• Calculus of variations, Gamma-convergence, compactness, and lower-bound methods.
• Nonlinear elasticity of thin sheets, disclinations, conical singularities, and ridge formation.
• Curvature energies for surfaces, including Willmore and Helfrich-type models.
• Diffuse-interface approximations, phase separation on surfaces, and biomembrane models.
• Adaptive finite-element methods and variational limits for optimal meshes.
• Geometric analysis questions related to Jacobians, degree, and isometric immersion problems.

Earlier work from my PhD concerned perturbative quantum field theory, in particular the operator product expansion and quantum field theory on curved spacetimes.

Prospective PhD students

I am always interested in hearing from motivated students who would like to pursue a PhD in the calculus of variations and its applications to geometry, elasticity, and materials science. If you are interested in working with me, please feel free to contact me by email.