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Oliver Knill

Affiliations:
  • Harvard University, Cambridge, MA, USA


According to our database1, Oliver Knill authored at least 80 papers between 1987 and 2024.

Collaborative distances:
  • Dijkstra number2 of six.
  • Erdős number3 of six.

Timeline

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PhD thesis 
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Links

Online presence:

On csauthors.net:

Bibliography

2024
Morse and Lusternik-Schnirelmann for graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2024

Manifolds from Partitions.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2024

2023
Discrete Algebraic sets in Discrete Manifolds.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2023

Arboricity and Acyclic Chromatic Number.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2023

The Three Tree Theorem.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2023

Cohomology of open sets.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2023

Spectral monotonicity of the Hodge Laplacian.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2023

Characteristic Topological Invariants.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2023

The Sphere Formula.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2023

2022
The Babylonian Graph.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2022

The Tree-Forest Ratio.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2022

Eigenvalue bounds of the Kirchhoff Laplacian.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2022

Analytic torsion for graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2022

2021
Shannon capacity, Chess, DNA and Umbrellas.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2021

Remarks about the Arithmetic of Graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2021

Graph complements of circular graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2021

2020
Complexes, Graphs, Homotopy, Products and Shannon Capacity.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2020

Green functions of Energized complexes.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2020

2019
Constant index expectation curvature for graphs or Riemannian manifolds.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

More on Poincare-Hopf and Gauss-Bonnet.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

Poincare Hopf for vector fields on graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

A simple sphere theorem for graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

Energized simplicial complexes.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

The energy of a simplicial complex.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

A parametrized Poincare-Hopf Theorem and Clique Cardinalities of graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

More on Numbers and Graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

Dehn-Sommerville from Gauss-Bonnet.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

The average simplex cardinality of a finite abstract simplicial complex.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

A Reeb sphere theorem in graph theory.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2019

2018
Cartan's Magic Formula for Simplicial Complexes.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2018

Eulerian edge refinements, geodesics, billiards and sphere coloring.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2018

Combinatorial manifolds are Hamiltonian.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2018

The Cohomology for Wu Characteristics.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2018

The hydrogen identity for Laplacians.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2018

Listening to the cohomology of graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2018

An Elementary Dyadic Riemann Hypothesis.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2018

2017
One can hear the Euler characteristic of a simplicial complex.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2017

On Atiyah-Singer and Atiyah-Bott for finite abstract simplicial complexes.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2017

The strong ring of simplicial complexes.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2017

On the arithmetic of graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2017

On a Dehn-Sommerville functional for simplicial complexes.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2017

On Helmholtz free energy for finite abstract simplicial complexes.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2017

Sphere geometry and invariants.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2017

2016
On Fredholm determinants in topology.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2016

Some experiments in number theory.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2016

Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2016

Gauss-Bonnet for multi-linear valuations.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2016

2015
Universality for Barycentric subdivision.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2015

A Sard theorem for graph theory.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2015

The graph spectrum of barycentric refinements.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2015

The Jordan-Brouwer theorem for graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2015

The Kuenneth formula for graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2015

Graphs with Eulerian unit spheres.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2015

2014
Coloring graphs using topology.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2014

Curvature from Graph Colorings.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2014

Characteristic Length and Clustering.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2014

If Archimedes would have known functions.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2014

Classical mathematical structures within topological graph theory.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2014

A notion of graph homeomorphism.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2014

2013
Thinking like Archimedes with a 3D printer
[BibTeX]
[DOI]
Oliver Knill
,
Elizabeth Slavkovsky
CoRR, 2013

The McKean-Singer Formula in Graph Theory
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2013

The zeta function for circular graphs.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2013

On quadratic orbital networks.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2013

Counting rooted forests in a network.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2013

The Euler characteristic of an even-dimensional graph.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2013

The Dirac operator of a graph.
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2013

2012
The Lusternik-Schnirelmann theorem for graphs
[BibTeX]
[DOI]
Frank Josellis
,
Oliver Knill
CoRR, 2012

A Brouwer fixed point theorem for graph endomorphisms
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2012

An index formula for simple graphs
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2012

On index expectation and curvature for networks
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2012

The theorems of Green-Stokes,Gauss-Bonnet and Poincare-Hopf in Graph Theory
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2012

A graph theoretical Poincare-Hopf Theorem
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2012

2011
On the Dimension and Euler characteristic of random graphs
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2011

A graph theoretical Gauss-Bonnet-Chern Theorem
[BibTeX]
[DOI]
Oliver Knill
CoRR, 2011

2007
Space and camera path reconstruction for omni-directional vision
[BibTeX]
[DOI]
Oliver Knill
,
Jose Ramirez-Herran
CoRR, 2007

On Ullman's theorem in computer vision
[BibTeX]
[DOI]
Oliver Knill
,
Jose Ramirez-Herran
CoRR, 2007

A structure from motion inequality
[BibTeX]
[DOI]
Oliver Knill
,
Jose Ramirez-Herran
CoRR, 2007

1996
Complexity Growth in Almost Periodic Fluids in the Case of Lattice Gas Cellular Automata and Vlasov Systems.
[BibTeX]
[DOI]
Oliver Knill
,
Evan Reed
Complex Syst., 1996

1994
Diagonalization of Abel's Integral Operator.
[BibTeX]
[DOI]
Oliver Knill
SIAM J. Appl. Math., 1994

1987
The rotation group of Rubik's cube.
[BibTeX]
[DOI]
Oliver Knill
,
Roman Maeder
SIGSAM Bull., 1987


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