3 papers
math.SP2026
Beyond Three Terms: Exponential Bounds in the Neumann Heat Trace of Polygons
Gustav MÃ¥rdby
We study the short-time asymptotic behavior of the heat trace associated with the Neumann Laplacian on polygonal domains in the plane. By establishing locality principles for the h…
math.SP2024
Three's company in six dimensions: irreducible, isospectral, non-isometric flat tori
Gustav MÃ¥rdby, 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…
math.SP2024
112 years of listening to Riemannian manifolds
Gustav MÃ¥rdby, 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…