Speaker
Description
Hyperbolic spaces serve multiple purposes in the frontiers of physics at different regimes: on the large scales, when considering the global topology of the universe, and on small scales, when considering compactified extra dimensions in some Beyond the Standard Model scenarios. These spaces are non-trivial, and determining their eigenmodes (i.e. the solutions to the Helmholtz equation on them) provides essential knowledge for model-building and phenomenology. The Thurston manifold $Q_2$ serves as a benchmark hyperbolic manifold for which the boundary element method has been used before to compute eigenmodes of Laplacians. This work revisits the problem with physics-informed neural networks, where tunable weights are used to represent eigenvalues of interest. The low-lying eigenvalues of $Q_2$ are approximated and compared to their counterparts from the boundary element method and the Weyl asymptotic formula.
| Apply for student award at which level: | None |
|---|---|
| Consent on use of personal information: Abstract Submission | Yes, I ACCEPT |