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Topological Invariants for Tilings (2017)
Presentation / Conference Contribution
Hunton, J. (2017, October). Topological Invariants for Tilings. Presented at Spectral Structures and Topological Methods in Mathematical Quasicrystals, Oberwolfach, Germany

The mathematical theory of aperiodic order grew out of various predecessors in discrete geometry, harmonic analysis and mathematical physics, and developed rapidly after the discovery of real world quasicrystals in 1982 by Shechtman. Many mathematica... Read More about Topological Invariants for Tilings.

Magnetic Axis Drift and Magnetic Spot Formation in Neutron Stars with Toroidal Fields (2017)
Journal Article
Gourgouliatos, K. N., & Hollerbach, R. (2018). Magnetic Axis Drift and Magnetic Spot Formation in Neutron Stars with Toroidal Fields. Astrophysical Journal, 852(1), Article 21. https://doi.org/10.3847/1538-4357/aa9d93

We explore magnetic field configurations that lead to the formation of magnetic spots on the surface of neutron stars and the displacement of the magnetic dipole axis. We find that a toroidally dominated magnetic field is essential for the generation... Read More about Magnetic Axis Drift and Magnetic Spot Formation in Neutron Stars with Toroidal Fields.

Excited cosmic strings with superconducting currents (2017)
Journal Article
Hartmann, B., Michel, F., & Peter, P. (2017). Excited cosmic strings with superconducting currents. Physical Review D, 96(12), Article 123531. https://doi.org/10.1103/physrevd.96.123531

We present a detailed analysis of excited cosmic string solutions that possess superconducting currents. These currents can be excited inside the string core, and—if the condensate is large enough—can lead to the excitations of the Higgs field. Next... Read More about Excited cosmic strings with superconducting currents.

The Breuil–Mézard conjecture when l≠p (2017)
Journal Article
Shotton, J. (2018). The Breuil–Mézard conjecture when l≠p. Duke Mathematical Journal, 167(4), 603-678. https://doi.org/10.1215/00127094-2017-0039

Let l and p be primes, let F=Qp be a finite extension with absolute Galois group GF , let F be a finite field of characteristic l, and let W GF ! GLn.F/ be a continuous representation. Let R./ be the universal framed deformation ring for . If l D p,... Read More about The Breuil–Mézard conjecture when l≠p.