3 citations · 6 across the 4 of their papers we have counts for
7 papers
Fricke's trace identity and spin groups
Matthew de Courcy-Ireland
We give a proof of Fricke's trace identity using the exceptional spin double cover of an orthogonal group in four variables. We also explain how Fricke's identity is related to the…
Families of isospectral and isoscattering quantum graphs
Pavel Kurasov, Omer Farooq, Michał Ławniczak +4
A concept of germ graphs and the M-function formalism are employed to construct large families of isospectral and isoscattering graphs. This approach represents a complete departur…
Shrinking scale equidistribution for monochromatic random waves on compact manifolds
Matthew de Courcy-Ireland
We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowl…
Experiments with the Markoff surface
Matthew de Courcy-Ireland, Seungjae Lee
We confirm, for the primes up to 3000, the conjecture of Bourgain, Gamburd, and Sarnak on strong approximation for the Markoff surface modulo primes. For prime…
Kesten-McKay law for the Markoff surface mod p
Matthew de Courcy-Ireland, Michael Magee
For each prime , we study the eigenvalues of a 3-regular graph on roughly vertices constructed from the Markoff surface. We show they asymptotically follow the Kesten-McKa…
Uncovering Multiscale Order in the Prime Numbers via Scattering
S. Torquato, G. Zhang, M. de Courcy-Ireland
The prime numbers have been a source of fascination for millenia and continue to surprise us. Motivated by the hyperuniformity concept, which has attracted recent attention in phys…