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The Complexity of Translationally Invariant Spin Chains with Low Local Dimension
(Annales Henri Poincaré, 2017-11)
We prove that estimating the ground state energy of a
translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is
QMAEXP-complete, even for systems of low local dimension (roughly 40). This is
an improvement ...
Symmetries and geometrical properties of dynamical fluctuations in molecular dynamics
(Entropy, 2017-10-01)
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external ...
Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model
(Journal of Physics: Conference Series, 2017-10-22)
© Published under licence by IOP Publishing Ltd. We consider Alternating Direction Implicit (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. in ...
A new class of de Sitter vacua in type IIB large volume compactifications
(JOURNAL OF HIGH ENERGY PHYSICS, 2017-10-26)
Mathematical modelling of asymmetrical metal rolling processes
(University of CambridgeDAMTPJesus College, 2017-12-05)
This thesis explores opportunities in the mathematical modelling of metal rolling processes, specifically asymmetrical sheet rolling. With the application of control systems in mind, desired mathematical models must make ...
High-Energy Aspects of Inflationary Cosmology
(University of CambridgeDepartment of Applied Mathematics and Theoretical PhysicsCorpus Christi College, 2017-07-21)
Since the discovery of the cosmic microwave background (CMB), our understanding of the cosmos has been rapidly evolving. Detailed measurements of the CMB temperature fluctuations have led to a standard cosmological model, ...
Exceptional collections, and the Néron–Severi lattice for surfaces
(ElsevierAdvances in Mathematics, 2017-01-10)
We work out properties of smooth projective varieties X over a (not necessarily algebraically closed) field $\textit{k}$ that admit collections of objects in the bounded derived category of coherent sheaves D$^{b}$(X) that ...
$\textit{K}$-Theory of Fermat Curves
(Department of Pure Mathematics and Mathematical Statistics, University of CambridgeUniversity of CambridgeChurchill College, 2017-01-10)
I investigate the $K_2$ groups of the quotients of Fermat curves given in projective coordinates by the equation $F_n:X^n+Y^n=Z^n$. On any quotient where the number of known elements is equal to the rank predicted by ...
L-space intervals for graph manifolds and cables
(Cambridge University PressCompositio Mathematica, 2017-05)
We present a graph manifold analog of the Jankins–Neumann classification of Seifert fibered spaces over $S^2$ admitting taut foliations, providing a finite recursive formula to compute the L-space Dehn-filling interval for ...
Freiman homomorphisms on sparse random sets
(Oxford University PressQuarterly Journal of Mathematics, 2017-02-03)
A result of Fiz Pontiveros shows that if $A$ is a random subset of $\mathbb{Z}_N$ where each element is chosen independently with probability $N^{-1/2+o(1)}$, then with high probability every Freiman homomorphism defined ...