Reference:
0017-26
We are seeking a Postdoctoral Research Associate to collaborate with the Principal Investigator, Dr. Bernd Schulze, on the 36-month project “Extending Rigidity and Graphic Statics: Moments and Shears.”
Project Summary:
This project advances the mathematical theories of rigidity and graphic statics, which study when structures made of stiff bars and rotational joints are rigid or flexible. While classical rigidity theory and graphic statics focus on axial forces along bars, real-world structures such as bridges, buildings, robotic systems, and mechanical metamaterials also experience shear forces and moments. This project will extend existing theories to include these effects, using geometric, combinatorial, and symmetry-based methods, alongside homological methods from algebraic topology.
The project aims to:
1. Develop a comprehensive theory of graphic statics that incorporates moments, shear forces, and graphic kinematics, and extends to multivariate spline formulations.
2. Extend combinatorial and geometric rigidity theory to structures with bending and shearing resistance, moving beyond traditional bar-and-joint models.
3. Investigate symmetry-refined and periodic rigidity results using equivariant cosheaf homology, providing deeper insights into structural behaviour and enabling computationally efficient models.
Main Responsibilities:
4. Conduct independent and collaborative research in discrete mathematics and geometry, with a focus on rigidity theory, graphic statics, and the incorporation of moments and shear forces, under the supervision of Dr. Bernd Schulze.
5. Develop and apply mathematical tools from rigidity theory, discrete geometry, combinatorics, and algebraic topology, and formulate new rigidity matrices, counting rules, and symmetry-adapted results.
6. Collaborate closely with project partners at the University of Cambridge and SOM, and other national and international collaborators.
7. Prepare high-quality research outputs, including journal and conference proceedings articles.
8. Present research findings at conferences, workshops, and seminars.
Candidate Requirements:
9. A PhD (or near completion) in Discrete Mathematics or a closely related field.
10. Expertise in at least one of the methodological areas of the project, namely rigidity theory, graphic statics, discrete geometry, combinatorics, or algebraic topology.
Lancaster University hosts an internationally recognised research group in rigidity theory and its applications, and has strong research activity in algebra, analysis, probability, statistics, and mathematically-oriented applications. This position offers the opportunity to work at the cutting edge of discrete mathematics, combining theoretical innovation with potential applications in engineering and beyond.
This is a fixed-term contract for 36 months.