21 citations · 132 across the 37 of their papers we have counts for
38 papers
Quantum cellular automata are a coarse homology theory
Matthias Ludewig
We show that quantum cellular automata naturally form the degree-zero part of a coarse homology theory. The recent result of Ji and Yang that the space of QCA forms an Omega-spectr…
Classification of adjustments on central crossed modules
Matthias Ludewig, Konrad Waldorf
Adjustments are additional structures on crossed modules of Lie groups, serving as a tool in higher gauge theory to circumvent the fake flatness of connections on 2-bundles. In thi…
Transgressing the algebraic coarse character map
Alexander Engel, Matthias Ludewig
We pursue an old conjecture of John Roe about the algebraic K-theory of the algebra of finite propagation, locally trace-class operators, namely that transgressing the algebraic co…
Large-scale quantization of trace I: Finite propagation operators
Matthias Ludewig, Guo Chuan Thiang
Inspired by parallel developments in coarse geometry in mathematics and exact macroscopic quantization in physics, we present a family of general trace formulae which are universal…
Coronas and Callias type operators in coarse geometry
Ulrich Bunke, Matthias Ludewig
We interpret the coarse symbol and index class of a Callias type Dirac operator on a manifold as a pairing between the coarse symbol and index classes associated to a…
Coarse geometric approach to topological phases: Invariants from real-space representations
Christoph S. Setescak, Caio Lewenkopf, Matthias Ludewig
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, ground…
Coarse geometry and its applications in solid state physics
Matthias Ludewig
In this article, we give an overview over recent developments in the mathematical treatment of topological insulators using coarse geometry.
A representation of the string 2-group
Peter Kristel, Matthias Ludewig, Konrad Waldorf
We construct a representation of the string 2-group on a 2-vector space, aiming to establish it as the categorification of the spinor representation. Our model for 2-vector spaces…
Quantization of conductance and the coarse cohomology of partitions
Matthias Ludewig, Guo Chuan Thiang
We demonstrate how integer quantization of Hall conductance arises from the large-scale geometry of the sample. Specifically, the Hall conductance is a higher-trace pairing of the…
The spinor bundle on loop space
Matthias Ludewig
We give a construction of the spinor bundle of the loop space of a string manifold together with its fusion product, inspired by ideas from Stolz and Teichner. The spinor bundle is…
Lie 2-groups from loop group extensions
Matthias Ludewig, Konrad Waldorf
We give a very simple construction of the string 2-group as a strict Fréchet Lie 2-group. The corresponding crossed module is defined using the conjugation action of the loop group…
Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory
Matthias Ludewig
In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is the question when the composition of two Lagrangian correspondences is again Lagrangian.…
The stringor bundle
Peter Kristel, Matthias Ludewig, Konrad Waldorf
We set up a framework of 2-Hilbert bundles, which allows to rigorously define the "stringor bundle", a higher differential geometric object anticipated by Stolz and Teichner in an…
Large-scale geometry obstructs localization
Matthias Ludewig, Guo Chuan Thiang
We explain the coarse geometric origin of the fact that certain spectral subspaces of topological insulator Hamiltonians are delocalized, in the sense that they cannot admit an ort…
The insidious bicategory of algebra bundles
Peter Kristel, Matthias Ludewig, Konrad Waldorf
In this paper we construct a bicategory of (super) algebra bundles over a smooth manifold, where the 1-morphisms are bundles of bimodules. The main point is that naive definitions…
The Clifford Algebra Bundle on Loop Space
Matthias Ludewig
We construct a Clifford algebra bundle formed from the tangent bundle of the smooth loop space of a Riemannian manifold, which is a bundle of super von Neumann algebras on the loop…
Delocalized spectra of Landau operators on helical surfaces
Yosuke Kubota, Matthias Ludewig, Guo Chuan Thiang
On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely degenerate Landau levels. We consider surfaces with asymptotically co…
Breaking symmetries for equivariant coarse homology theories
Ulrich Bunke, Matthias Ludewig
We describe a symmetry breaking construction in coarse geometry which allows to obtain information about equivariant coarse homology classes by restriction to smaller groups and sp…
2-vector bundles
Peter Kristel, Matthias Ludewig, Konrad Waldorf
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as…
A Short Proof of the Localization Formula for the Loop Space Chern Character of Spin Manifolds
Matthias Ludewig, Zelin Yi
In this note, we give a short proof of the localization formula for the loop space Chern character of a compact Riemannian spin manifold M, using the rescaled spinor bundle on the…
Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
Matthias Ludewig, Guo Chuan Thiang
We use coarse index methods to prove that the Landau Hamiltonian on the hyperbolic half-plane, and even on much more general imperfect half-spaces, has no spectral gaps. Thus the e…
Cobordism invariance of topological edge-following states
Matthias Ludewig, Guo Chuan Thiang
We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore…
A Framework for Geometric Field Theories and their Classification in Dimension One
Matthias Ludewig, Augusto Stoffel
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particula…
Construction of the Supersymmetric Path Integral: A Survey
Matthias Ludewig
This is a survey based on joint work with Florian Hanisch and Batu Güneysu reporting on a rigorous construction of the supersymmetric path integral associated to compact spin manif…