PSD - Dr Amaranta Membrillo Solis

Cohomological rigidity of toric spaces

Supervisor: Dr Amaranta Membrillo Solis

Project description:

The cohomological rigidity problem asks whether a topological space is uniquely determined by its cohomology ring. The proposed project investigates this problem in the setting of toric spaces, which arise in toric topology, symplectic geometry, and mathematical physics. These spaces are highly symmetric and governed by combinatorial structures such as polytopes and simplicial complexes, making them an ideal testing ground for rigidity phenomena.

The central goal is to determine when and how cohomological data can classify manifolds arising as toric spaces, up to homotopy equivalence, homeomorphism or diffeomorphism. This involves constructing families of polytopes or simplicial complexes along with their associated toric spaces, developing computational tools to analyse their invariants, and identifying both confirming examples and counterexamples. By integrating methods from algebraic and geometric topology, the project seeks to advance our understanding of the structure and classification of manifolds equipped with an effective torus action. 

Keywords: algebraic topology, geometric topology, computational topology, combinatorics.

Area: Pure mathematics

Funding Notes

If you wish to inquire about the project, please contact the supervisor Dr Amaranta Membrillo Solis (i.a.membrillosolis@qmul.ac.uk).

How to apply 
Entry requirements 
Fees and funding