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ORCIDOliver Knill
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- affiliation: Harvard University, Cambridge, MA, USA
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Journal Articles
- 1996
[j3]Oliver Knill, Evan Reed:
Complexity Growth in Almost Periodic Fluids in the Case of Lattice Gas Cellular Automata and Vlasov Systems. Complex Syst. 10(3) (1996)- 1994
- [j2]Oliver Knill:
Diagonalization of Abel's Integral Operator. SIAM J. Appl. Math. 54(5): 1250-1253 (1994) - 1987
- [j1]Oliver Knill, Roman Maeder:
The rotation group of Rubik's cube. SIGSAM Bull. 21(3): 33-43 (1987)
Informal and Other Publications
- 2024
- [i78]Oliver Knill:
Manifolds from Partitions. CoRR abs/2401.07435 (2024) - [i77]Oliver Knill:
Morse and Lusternik-Schnirelmann for graphs. CoRR abs/2405.19603 (2024) - [i76]Oliver Knill:
On Symmetries of Finite Geometries. CoRR abs/2408.13973 (2024) - 2023
- [i75]Oliver Knill:
The Sphere Formula. CoRR abs/2301.05736 (2023) - [i74]Oliver Knill:
Characteristic Topological Invariants. CoRR abs/2302.02510 (2023) - [i73]Oliver Knill:
Spectral monotonicity of the Hodge Laplacian. CoRR abs/2304.00901 (2023) - [i72]Oliver Knill:
Cohomology of open sets. CoRR abs/2305.12613 (2023) - [i71]Oliver Knill:
The Three Tree Theorem. CoRR abs/2309.01869 (2023) - [i70]Oliver Knill:
Arboricity and Acyclic Chromatic Number. CoRR abs/2311.03049 (2023) - [i69]Oliver Knill:
Discrete Algebraic sets in Discrete Manifolds. CoRR abs/2312.14671 (2023) - 2022
- [i68]Oliver Knill:
Analytic torsion for graphs. CoRR abs/2201.09412 (2022) - [i67]Oliver Knill:
Eigenvalue bounds of the Kirchhoff Laplacian. CoRR abs/2205.10968 (2022) - [i66]Oliver Knill:
The Tree-Forest Ratio. CoRR abs/2205.10999 (2022) - [i65]Oliver Knill:
The Babylonian Graph. CoRR abs/2205.13285 (2022) - 2021
- [i64]Oliver Knill:
Graph complements of circular graphs. CoRR abs/2101.06873 (2021) - [i63]Oliver Knill:
Remarks about the Arithmetic of Graphs. CoRR abs/2106.10093 (2021) - [i62]Oliver Knill:
Shannon capacity, Chess, DNA and Umbrellas. CoRR abs/2108.04994 (2021) - 2020
- [i61]Oliver Knill:
Green functions of Energized complexes. CoRR abs/2010.09152 (2020) - [i60]Oliver Knill:
Complexes, Graphs, Homotopy, Products and Shannon Capacity. CoRR abs/2012.07247 (2020) - 2019
- [i59]Oliver Knill:
A Reeb sphere theorem in graph theory. CoRR abs/1903.10105 (2019) - [i58]Oliver Knill:
The average simplex cardinality of a finite abstract simplicial complex. CoRR abs/1905.02118 (2019) - [i57]Oliver Knill:
Dehn-Sommerville from Gauss-Bonnet. CoRR abs/1905.04831 (2019) - [i56]Oliver Knill:
More on Numbers and Graphs. CoRR abs/1905.13387 (2019) - [i55]Oliver Knill:
A parametrized Poincare-Hopf Theorem and Clique Cardinalities of graphs. CoRR abs/1906.06611 (2019) - [i54]Oliver Knill:
The energy of a simplicial complex. CoRR abs/1907.03369 (2019) - [i53]Oliver Knill:
Energized simplicial complexes. CoRR abs/1908.06563 (2019) - [i52]Oliver Knill:
A simple sphere theorem for graphs. CoRR abs/1910.02708 (2019) - [i51]Oliver Knill:
Poincare Hopf for vector fields on graphs. CoRR abs/1911.04208 (2019) - [i50]Oliver Knill:
More on Poincare-Hopf and Gauss-Bonnet. CoRR abs/1912.00577 (2019) - [i49]Oliver Knill:
Constant index expectation curvature for graphs or Riemannian manifolds. CoRR abs/1912.11315 (2019) - 2018
- [i48]Oliver Knill:
An Elementary Dyadic Riemann Hypothesis. CoRR abs/1801.04639 (2018) - [i47]Oliver Knill:
Listening to the cohomology of graphs. CoRR abs/1802.01238 (2018) - [i46]Oliver Knill:
The hydrogen identity for Laplacians. CoRR abs/1803.01464 (2018) - [i45]Oliver Knill:
The Cohomology for Wu Characteristics. CoRR abs/1803.06788 (2018) - [i44]Oliver Knill:
Combinatorial manifolds are Hamiltonian. CoRR abs/1806.06436 (2018) - [i43]Oliver Knill:
Eulerian edge refinements, geodesics, billiards and sphere coloring. CoRR abs/1808.07207 (2018) - [i42]Oliver Knill:
Cartan's Magic Formula for Simplicial Complexes. CoRR abs/1811.10125 (2018) - 2017
- [i41]Oliver Knill:
Sphere geometry and invariants. CoRR abs/1702.03606 (2017) - [i40]Oliver Knill:
On Helmholtz free energy for finite abstract simplicial complexes. CoRR abs/1703.06549 (2017) - [i39]Oliver Knill:
On a Dehn-Sommerville functional for simplicial complexes. CoRR abs/1705.10439 (2017) - [i38]Oliver Knill:
On the arithmetic of graphs. CoRR abs/1706.05767 (2017) - [i37]Oliver Knill:
The strong ring of simplicial complexes. CoRR abs/1708.01778 (2017) - [i36]Oliver Knill:
On Atiyah-Singer and Atiyah-Bott for finite abstract simplicial complexes. CoRR abs/1708.06070 (2017) - [i35]Oliver Knill:
One can hear the Euler characteristic of a simplicial complex. CoRR abs/1711.09527 (2017) - 2016
- [i34]Oliver Knill:
Gauss-Bonnet for multi-linear valuations. CoRR abs/1601.04533 (2016) - [i33]Oliver Knill:
Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes. CoRR abs/1606.05958 (2016) - [i32]Oliver Knill:
Some experiments in number theory. CoRR abs/1606.05971 (2016) - [i31]Oliver Knill:
On Fredholm determinants in topology. CoRR abs/1612.08229 (2016) - 2015
- [i30]Oliver Knill:
Graphs with Eulerian unit spheres. CoRR abs/1501.03116 (2015) - [i29]Oliver Knill:
The Kuenneth formula for graphs. CoRR abs/1505.07518 (2015) - [i28]Oliver Knill:
The Jordan-Brouwer theorem for graphs. CoRR abs/1506.06440 (2015) - [i27]Oliver Knill:
The graph spectrum of barycentric refinements. CoRR abs/1508.02027 (2015) - [i26]Oliver Knill:
A Sard theorem for graph theory. CoRR abs/1508.05657 (2015) - [i25]Oliver Knill:
Universality for Barycentric subdivision. CoRR abs/1509.06092 (2015) - 2014
- [i24]Oliver Knill:
A notion of graph homeomorphism. CoRR abs/1401.2819 (2014) - [i23]Oliver Knill:
Classical mathematical structures within topological graph theory. CoRR abs/1402.2029 (2014) - [i22]Oliver Knill:
If Archimedes would have known functions. CoRR abs/1403.5821 (2014) - [i21]Oliver Knill:
Curvature from Graph Colorings. CoRR abs/1410.1217 (2014) - [i20]Oliver Knill:
Characteristic Length and Clustering. CoRR abs/1410.3173 (2014) - [i19]Oliver Knill:
Coloring graphs using topology. CoRR abs/1412.6985 (2014) - 2013
- [i18]Oliver Knill:
The McKean-Singer Formula in Graph Theory. CoRR abs/1301.1408 (2013) - [i17]Oliver Knill, Elizabeth Slavkovsky:
Thinking like Archimedes with a 3D printer. CoRR abs/1301.5027 (2013) - [i16]Oliver Knill:
The Dirac operator of a graph. CoRR abs/1306.2166 (2013) - [i15]Oliver Knill:
The Euler characteristic of an even-dimensional graph. CoRR abs/1307.3809 (2013) - [i14]Oliver Knill:
Counting rooted forests in a network. CoRR abs/1307.3810 (2013) - [i13]Oliver Knill:
On quadratic orbital networks. CoRR abs/1312.0298 (2013) - [i12]Oliver Knill:
The zeta function for circular graphs. CoRR abs/1312.4239 (2013) - 2012
- [i11]Oliver Knill:
A graph theoretical Poincare-Hopf Theorem. CoRR abs/1201.1162 (2012) - [i10]Oliver Knill:
The theorems of Green-Stokes,Gauss-Bonnet and Poincare-Hopf in Graph Theory. CoRR abs/1201.6049 (2012) - [i9]Oliver Knill:
On index expectation and curvature for networks. CoRR abs/1202.4514 (2012) - [i8]Oliver Knill:
An index formula for simple graphs. CoRR abs/1205.0306 (2012) - [i7]Oliver Knill:
A Brouwer fixed point theorem for graph endomorphisms. CoRR abs/1206.0782 (2012) - [i6]Frank Josellis, Oliver Knill:
The Lusternik-Schnirelmann theorem for graphs. CoRR abs/1211.0750 (2012) - 2011
- [i5]Oliver Knill:
A graph theoretical Gauss-Bonnet-Chern Theorem. CoRR abs/1111.5395 (2011) - [i4]Oliver Knill:
On the Dimension and Euler characteristic of random graphs. CoRR abs/1112.5749 (2011) - 2007
- [i3]Oliver Knill, Jose Ramirez-Herran:
A structure from motion inequality. CoRR abs/0708.2432 (2007) - [i2]Oliver Knill, Jose Ramirez-Herran:
On Ullman's theorem in computer vision. CoRR abs/0708.2438 (2007) - [i1]Oliver Knill, Jose Ramirez-Herran:
Space and camera path reconstruction for omni-directional vision. CoRR abs/0708.2442 (2007)
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