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Global Extrema of the Zeta Regularized Determinant on Orthogonal Flat Tori
Fabio Francesconi, Julie Rowlett
The search for extremal geometries is a central theme in several areas of mathematics. Here, we address the following question: among all n-dimensional orthogonal tori of unit volu…
Three's company in six dimensions: irreducible, isospectral, non-isometric flat tori
Gustav Mårdby, Julie Rowlett, Felix Rydell
In 1964, John Milnor, using a construction of two lattices by Witt, produced the first example of two flat tori that are not globally isometric and whose Laplacians for exterior fo…
Spectral invariants of integrable polygons
Gustav Mårdby, Julie Rowlett
An integrable polygon is one whose interior angles are fractions of ; that is to say of the form for positive integers . We consider the Laplace spectrum on these…
112 years of listening to Riemannian manifolds
Gustav Mårdby, Julie Rowlett
In 1910, Hendrik Antoon Lorentz delved into the enigmatic Laplace eigenvalue equation, also known as the Helmholtz equation, pondering to what extent the geometry in which one solv…
On the spectral theory and dynamics of asymptotically hyperbolic manifolds
Julie Rowlett
We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to thei…