arXiv subjects

Gard Olav Helle

Publications and source records attributed to Gard Olav Helle.

4 recordsLinked to original sources

arXiv2026

A quantum advection-diffusion solver using the quantum singular value transform

We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy. The theoretical results are supported by numerical simulations of one- and two-dimensional benchmarks.

quant-ph↗

arXiv2022

Singular Quiver Varieties over Extended Dynkin Quivers

We classify the singularities in the unframed Nakajima quiver varieties associated with extended Dynkin quivers and the corresponding minimal imaginary root with a small restriction on the parameter and use this to construct a number of hyper-Kähler cobordisms between binary polyhedral spaces.

math.RT↗

arXiv2022

Equivariant instanton Floer homology and calculations for the binary polyhedral spaces

We calculate the equivariant instanton Floer homology, in the sense of Miller Eismeier, for the trivial $SO(3)$-bundle over the binary polyhedral spaces with coefficients in a PID $R$ for which $2\in R$ is invertible. Along the way we modify a part of the algebraic construction needed to define the equivariant instanton Floer groups.

math.GT↗

arXiv2018

Boardman's whole-plane obstruction group for Cartan-Eilenberg systems

Each extended Cartan--Eilenberg system $(H, \partial)$ gives rise to two exact couples and one spectral sequence. We show that the canonical colim-lim interchange morphism associated to $H$ is a surjection, and that its kernel is isomorphic to Boardman's whole-plane obstruction group $W$, for each of the two exact couples.

math.AT↗