Calculus of Variations and Geometric Measure Theory

PhD position in polynomial optimization for calculus of variations in Prague

created by kruzik on 14 Feb 2024

Deadline: 29 feb 2024

Applications are open for 2 PhD candidates to join a newly established research group led by Prof. Didier Henrion at the Czech Technical University in Prague. These positions are supported by the program OP JAK Roboprox of the Czech Ministry of Education and the European Union.

Our research group which consists of Prof. Martin Kružík and Dr. Milan Korda is dedicated to exploring polynomial optimization techniques in applied calculus of variations, in particular in continuum mechanics of solids. Variational methods represent a powerful tool for analysis and numerics of problems in elasticity, plasticity, or viscoelasticity where the notion of energy plays a key role. Their analysis often leads to the global minimization of nonconvex objective functions, a challenging task.

As a researcher in our team, you will play a pivotal role in developing a novel, mathematically rigorous approach to modeling and analysis in nonlinear mechanics of solids. Beyond these foundational research goals, there is room for tailoring your focus based on your research interests. Potential avenues of exploration include: dynamicaltime-dependent problems in the mechanics of solids, minimizing movements and spatialtemporal discretization. Numerical approaches to minimizing movements play a significant role in these topics because the existence-of-solutions proofs are usually done via semidiscretization in time. This, together with spatial discretization, leads to large-scale but highly structured polynomial optimization problems. Alternative, mesh-free numerical methods based on semidefinite optimization and the moment–sums of squares hierarchy, are also to be investigated and developed. We expect close cooperation with the Polynomial optimization group at LAAS-CNRS in Toulouse on theoretical and numerical aspects of polynomial optimization..