This is a 4-year research position supervised by Fatemeh Mohammadi and myself.
Project description:
The project is about the underlying connections between Rigidity Theory and Tropical Geometry. Rigidity theory is traditionally grounded in the use of abstract mathematics to better understand the kinematic properties of rigid bodies connected by flexible hinges. In a more broad interpretation, rigidity theory is seen as the study of the behaviour of particle systems that are subject to polynomial constraints between particles. An important reason for this latter interpretation is that it opens the door to a plethora of techniques from algebraic geometry. One particularly important tool here is tropical geometry. This is the study of tropicalisation, a technique that involves "flattening" equations into simpler linear equations and inequalities in a specific way that preserves key information about the original polynomials.
In recent years, tropical geometry has been applied successful to rigidity theory. Even more recently, key concepts of tropical geometry have been better understood using techniques from rigidity theory. The focus of this project will be to extend relationship between the two topics, and to develop applications from this interplay that will impact the wider fields of mathematics.
The successful candidates will work in the area of tropical geometry and rigidity theory. A master's degree in Mathematics or Computer Science is required. It is helpful (but not essential) to have background in the following areas for the project: Tropical Geometry, Algebraic Geometry, Rigidity Theory or Matroid Theory.
Application deadline: 30th June 2025.
For more information and application details, visit: https://www.fatemehmohammadi.com/joining-my-group