In recent times the hydrodynamic behaviour of electrons in graphene has attracted much interest from both the theoretical and experimental viewpoints. The usual approach to graphene hydrodynamics is &...
We prove that a smooth, complex plane curve of odd degree can be defined by a polynomial with real coefficients if and only if it is isomorphic to its complex conjugate; there are counterexamples in e...
Abstract: A spanning tree of a graph G is a connected subset of G without cycles. The Uniform Spanning Tree (UST) is obtained by choosing one of the possible spanning trees of G at random. The Minimum...
Abstract: Earthquakes and tectonic fault slip are among the most hazardous and unpredictable natural phenomena. Fluids play a key role in tectonic faulting and recent research suggests that fluids are...
Quantum simulators were originally proposed to be helpful for simulating one partial differential equation (PDE) in particular – Schrodinger’s equation. If quantum simulators can be useful for simulat...
We derive the heat equation for the thermal energy under diffusive space-time scaling from a purely deterministic microscopic dynamics satisfying Newton equations perturbed by an external chaotic forc...
Vertex algebras formalise the properties of what physicists would call operator product expansions (OPEs) in chiral conformal field theories (CFTs). One way to motivate the axioms of vertex algebras i...
Abstract: In 2014, Vaughan Jones introduced methods to construct unitary representations of Thomp- son groups F, T, V (from planar algebras or Cuntz algebras) and another to produce knots from th...
The Hodge conjecture is a central problem in modern algebraic geometry. It is notoriously difficult to attack, and we still lack general evidence towards its validity. In my talk I will present a proo...
