Applied Linear Algebra: The Decoupling Principle. First edition published 2000 by Prentice Hall. (out of print) ISBN 0-13-085645-2
Applied Linear Algebra: The Decoupling Principle. Second edition published 2008 by the American Mathematical Society, ISBN-13: 978-0-08218-4441-0. ISBN-10: 0-8218-4441-5
Topology of Tiling Spaces. Published 2008 by the American Mathematical Society, ISBN-13: 978-0-08218-4727-5. ISBN-10: 0-8218-4727-9
The Six Pillars of Calculus, Business Edition, Published 2023 by the American Mathematical Society, Pure and Applied Undergraduate Texts 56. ISBN: 978-1-4704-6995-5.
The Six Pillars of Calculus, Biology Edition, Published 2023 by the American Mathematical Society, Pure and Applied Undergraduate Texts 60. ISBN: 978-1-4704-6996-2.Linear Algebra and Mathematical Physics, chapter for the CRC Handbook of Linear Algebra , 2nd edition, Leslie Hogben ed., 2013.
Cohomology of Hierarchical Tilings, chapter in Mathematics of Aperiodic Order, edited by Johannes Kellendonk, Daniel Lenz and Jean Savinien, Birkhauser 2015.
What's Wrong with the Platonic Ideal of Space and Time?, chapter in Space, Time and the Limits of Human Understanding, edited by Shyam Wuppuluri and Giancarlo Ghirardi, Springer 2016, ISBN 978-3-319-44417-8.
2. (with Zvi Bern, M. B. Halpern and Clifford Taubes)Continuum Regularization of QCD, Phys. Lett. B 185 (1985) 151-156.
3. (with Zvi Bern, M. B. Halpern and Clifford Taubes)Continuum Regularization of Quantum Field Theory I. Scalar Prototype, Nucl. Phys. B 284 (1987) 1-34.
4. (with Zvi Bern, M. B. Halpern and Clifford Taubes)Continuum Regularization of Quantum Field Theory II. Gauge Theory, Nucl. Phys. B 284 (1987) 35-91.
5. (with Zvi Bern and M. B. Halpern) Continuum Regularization of Quantum Field Theory III. The QCD4 $\beta$-function, Nucl. Phys. B 284 (1987) 92-102.
6. (with Zvi Bern and M. B. Halpern) Continuum Regularization of Quantum Field Theory IV. Langevin Renormalization, Z. Phys. C 35 (1987) 255-283.
7. Continuum Regularization of Quantum Field Theory V. Schwinger-Dyson Renormalization, Z. Phys. C 36 (1987) 407-424.
8. (with F. Gesztesy, D. Gurarie, H. Holden, M. Klaus, B. Simon and P. Vogl) Trapping and Cascading of Eigenvalues in the Large Coupling Limit, Commun. Math. Phys. 118 (1988) 597-634.
9. (with J. E. Avron, Jan Segert and Barry Simon) Topological Invariants in Fermi Systems with Time Reversal Invariance, Phys. Rev. Lett. 61 (1988), 1329-1332.
10. (with Jan Segert) Chern Numbers for Fermionic Quadrupole Systems, J. Phys. A. 22 (1989) L111-L115.
11. (with J. E. Avron, Jan Segert and Barry Simon) Chern Numbers, Quaternions and Berry's Phase in Fermi Systems, Commun. Math. Phys. 124 (1989), 595-624.
12. (with J. E. Avron) Chern Numbers and Adiabatic Transport in Networks with Leads, Phys. Rev. Letters 62 (1989) 3082-3084.
13. (with J. E. Avron) Adiabatic Quantum Transport in Networks with Macroscopic Components, Ann. of Physics 206 (1991) 440-493.
14. (with Jan Segert) Non-self-dual Yang-Mills Connections with Nonzero Chern Number, Bull. Amer. Math. Soc. 24 (1991) 163-170.
15. (with A. C. Sadun) Relativistic Dynamics of Expanding Sources, Astrophys. & Space Sci. 185 (1991), 21-36.
16. (with Jan Segert) Non-self-dual Yang-Mills connections with Quadrupole Symmetry, Comm. Math. Phys.145(1992), 363-391.
17. (with Jan Segert) Stationary Points of the Yang-Mills Action, Comm. Pure \& Appl. Math. 45 (1992) 461-484.
18. (with J. E. Avron, M. Klein and A. Pnueli) Hall conductance, Adiabatic Charge Transport and Persistent Currents of Leaky Tori, Phys. Rev. Lett. 69(1992), 128-131.
19. (with Jan Segert) Constructing Non-Self-Dual Yang-Mills Connections with Nonzero Chern Number, Proceedings of the Symposia in Pure Mathematics 54, Part 2 (1993), 529-537.
20. (with M. Vishik) The Spectrum of the Second Variation of the Energy for an Ideal Incompressible Fluid, Phys. Lett. A 182 (1993), 394-398.
21. A Symmetric Family of Yang-Mills Fields, Commun. Math. Phys. 163 (1994), 257-291.
22. (with C. Radin) The Isoperimetric Problem for Pinwheel Tilings, Commun. Math. Phys. 177 (1996), 255-263.
23. A Simple Geometric Representative of $\mu$ of a Point, Commun. Math Phys. 178 (1996), 107-113.
24. (with J. Avron) Adiabatic Curvature and the $S$-Matrix, Commun. Math. Phys. 181 (1996), 685-702.
25. (with D. Auckly) A Family of Mobius Invariant 2-Knot energies, in ``Geometric Topology: The Proceedings of the 1993 Georgia International Topology Conference'', W. Kazez, ed. AMS/IP Studies in Advanced Mathematics 2, Part 1 (1997) 235-258.
26. Simple Type is Not a Boundary Phenomenon, in ``Geometry, Topology and Physics'', B. Apanasov, S. Bradlow, W. Rodrigues and K. Uhlenbeck, ed. (1997), 233-244.
27. Some Generalizations of the Pinwheel Tiling, Disc. Comp. Geom. 20 (1998), 79-110.
28. (with C. Radin) Subgroups of $SO(3)$ Associated with Tilings, J. Algebra. 202 (1998), 611-633. Click here for pdf.
29. (with M. Speight) Geodesic Incompleteness in the $CP^1$ Model on a Compact Riemann Surface, Lett. Math. Phys. 43 (1998), 329-334.
30. (with C. Radin) An Algebraic Invariant for Substitution Tiling Systems, Geometriae Dedicata 73 (1998) 21-37. Click here for pdf.
31. (with C. Radin) On 2-generator subgroups of SO(3), Trans. Amer. Math. Soc. 351 (1999), 4469-4480. Click here for pdf.
32. (with J. Conway and C. Radin) On Angles Whose Squared Trigonometric Functions are Rational, Discrete Comput. Geom. 22 (1999), 321-332. Click here for pdf.
33. (with B. Draco and D. Van Wieren) Growth Rates in the Quaquaversal Tiling, Discrete Comput. Geom. 23 (2000), 419-435.
34. (with J. Conway and C. Radin) Relations in SO(3) Supported by Geodetic Angles, Discrete Comput. Geom. 23 (2000), 453-463. Click here for pdf.
35. (with J.E. Avron, A. Elgart and G.M. Graf) Geometry, Statistics and Asymptotics of Quantum Pumps, Physical Review B (Rapid Communications)62 (2000) R10618-R10621. Click herefor pdf.
36. (with L. Guijarro and G. Walschap) Parallel Connections over Symmetric Spaces, J. Geom. Anal. 11 (2001), 265--281.
37. (with D. Groisser) Simple Type and the Boundary of Moduli Space, J. Geom. Phys. 36 (2000), 324--384.
38. (with C. Radin) Isomorphisms of Hierarchical Structures, Ergodic Theory Dynam. Systems 21(2001), 1239-1248. Click here for pdf.
39. (with J.E. Avron) Fredholm Indices and the Phase Diagram of Quantum Hall Systems, J. Math. Phys. 42 (2001), 1--14. Click here for pdf.
40. (with J.E. Avron, A. Elgart, and G.M. Graf) Optimal Quantum Pumps, Physical Review Letters. 87 (2001), 236601. Clickhere for pdf.
41. (with Jean Marie Linhart) Fast and Slow Blowup in the S^2 Sigma Model and (4+1)-Dimensional Yang-Mills Model, Nonlinearity 15 (2002) 219-238. Click here for pdf.
42. (with N. Ormes and C. Radin) A Homeomorphism Invariant for Substitution Tiling Spaces, Geometriae Dedicata 90 (2002), 153-182. Click here for pdf.
43. (with F. Rodriguez Villegas and J. F. Voloch) Blet, a Mathematical Puzzle. American Mathematical Monthly 109 (2002) 729-740. Click here for pdf.
44. (with J.E. Avron, A. Elgart, and G.M. Graf) Time-Energy Coherent States and Adiabatic Scattering, Journal of Mathematical Physics43 (2002), 3415-3424. Click here for pdf.
45. (with R.F. Williams) Tiling Spaces are Cantor Set Fiber Bundles , Ergodic Theory and Dynamical Systems 23 (2003) 307-316. Click here for pdf.
46. (with A. Marini) Spherically Symmetric Solutions of a Boundary Value Problem for Monopoles, Journal of Mathematical Physics 44 (2003) 1071-1083. Click here for pdf.
47. (with A. Clark) When size matters: subshifts and their related tiling spaces, Ergodic Theory and Dynamical Systems 23 (2003) 1043-1057. Click here for pdf.
48. (with S. Keel) Oort's
Conjecture for A_g x C, Journal of the Americal Mathematical
Society 16
(2003) 887-900. Click here
for pdf.
49. Tiling
Spaces are Inverse Limits. Journal of Mathematical Physics 44 (2003) 5410-5414.
Click here
for pdf.
50. (with J.E. Avron, A. Elgart, G.M. Graf and K. Schnee) Adiabatic charge pumping in open quantum systems, Communications in Pure and Applied Math 57 (2004) 528-561. Click here for pdf.
51. (with J.E. Avron, A. Elgart and G.M. Graf) Transport
and Dissipation in Quantum Pumps. Journal of
Statistical Physics 116 (2004)
425-473. Click here
for pdf.
52. (with C. Radin) Structure of the hard sphere solid, Phys. Rev. Lett. 94 (2005), paper 015502. Click here for pdf.
53. (with C. Holton and C. Radin) Conjugacies for Tiling Dynamical Systems. Communications in Mathematical Physics 254 (2005) 343-359. Click here for pdf.
54. (with P. Buczek and J. Wolny) Periodic
Diffraction Patterns for 1D Quasicrystals. Acta Physica Polonica B 36 (2005) 919-933.
55. (with L. Bowen, C. Holton and C. Radin) Uniqueness
and Symmetry in Problems of Optimally Dense Packings. Math
Phys. Electron. J. 11 (2005)
paper 1.
56. (with H. Koch and C. Radin), The
most stable
structure for hard spheres, Physical
Review E 72 (2005), paper
016708. Click here
for pdf.
57. (with R. Kenyon and B. Solomyak)
Topological Mixing for
Substitutions on Two Letters, Ergodic Theory and Dynamical
Systems 25 (2005)
1919-1934.
58. (with A. Clark)
When Shape Matters: Deformations of Tiling Spaces, Ergodic
Theory and Dynamical Systems 26
(2006) 69-86.
59.
Tilings, tilings spaces and topology, Philosophical Magazine 86 (2006) 875-881. 60. Pattern-Equivariant
Cohomology with Integer Coefficients, Ergodic Theory and Dynamical
Systems 27 (2007), 1991-1998. 61. (with N.P. Frank)
Topology of (Some) Tiling Spaces without Finite Local Complexity,
Discrete and Continuous Dynamical Systems 23
(2009) 847-865.
62. (with M. Barge, B. Diamond, and J. Hunton)
Cohomology of Substitution
Tiling Spaces , Ergodic Theory and Dynamical Systems 30 (2010)
1607-1627.
In Press: Submitted:
63. (with B. Rand)
An Approximation Theorem for Maps Between Tiling Spaces,
Discrete and Continuous Dynamical Systems 29 (2011)
323-326.
64. (with Marcy Barge)
Quotient Cohomology for Tiling Spaces, New York Journal of Mathematics
17 (2011) 579-599.
65.
Exact Regularity and the Cohomology of Tiling Spaces,
Ergodic Theory and Dynamical Systems 31 (2011) 1819-1834.
66. (with M. Barge, H. Bruin and L. Jones)
Homological Pisot Substitutions and Exact Regularity,
Israel Journal of Mathematics 188 (2012), 281-300.
67. (with Natalie Frank)
Fusion: a general framework for hierarchical tilings
of Rd,
Geometriae Dedicata 171 (2014) 149-186.
68. (with Natalie Frank)
Fusion tilings with infinite local complexity, Topology Proceedings
43 (2014) 235-276.
69. (with Johannes Kellendonk)
Meyer sets, topological eigenvalues, and Cantor fiber bundles
Journal of the London Math Society 89 (2014), 114-130.
70. (with Charles Radin)
Phase transitions in a complex network,
J. Phys. A: Math. Theor. 46 (2013) 305002
71. (with Charles Radin and Kui Ren)
The Asymptotics of Large Constrained Graphs,
J. Phys. A. 47 (2014) 175001
72. (with Charles Radin)
Singularities in the entropy of asymptotically large simple graphs,
J. Stat. Phys. 158 (2015) 853-865
73. (with Mike Kelly)
Pattern Equivariant Cohomology and Theorems of Kesten and Oren,
Bulletin of the London Math Society 47 (2015) 13-20.
Also on arxiv .
74. Finitely Balanced Sequences and
Plasticity of 1-Dimensional Tilings,
Topology and its Applications 205 (2016) 82-87.
Available online at the
journal website
(personal or institutional subscription required).
75. (with Alan Haynes, Henna Koivusalo and James Walton)
Gaps problems and
frequencies of patches in cut and project sets,
Mathematical Proceedings of the Cambridge Philosophical Society
161 (2016) 65-85.
76. (with Richard Kenyon, Charles Radin and Kui Ren)
Bipodal Structure in Oversaturated Random Graphs,
International Mathematics Research Notices doi: 10.1093/imrn/rnw261
77. (with Faustin Adiceam, David Damanik, Franz Gaehler, Uwe Grimm,
Alan Haynes, Antoine Julien, Andres Navas, and Barak Weiss)
Open Problems and Conjectures Related to the Theory of
Mathematical Quasicrystals,
Arnold Math J. 2 (2016) 579-592.
78. (with Johannes Kellendonk)
Conjugacies of Model Sets.
Discrete and Continuous Dynamical Systems 37 (2017) 3805-3830.
79. (with Alex Clark)
Small cocycles, fine torus fibrations, and a
Z2 subshift with neither.
Annales Henri Poincare. 18 2017, 2301-2326
80. (with Richard Kenyon, Charles Radin and Kui Ren)
Multipodal Structure and Phase Transitions in Large Constrained Graphs.
J. Stat. Phys. 168 (2017) 233-258.
81. (with Richard Kenyon, Charles Radin and Kui Ren)
The Phases of Large Networks with Edge and Triangle Constraints.
J. Phys. A. 50 (2017) 435001
82. (with Charles Radin and Kui Ren)
A Symmetry Breaking Transition in the Edge/Triangle Network Model.
Annales Henri Poincare D 5 (2018) 251-286.
83. (with Antoine Julien)
Tiling deformations, cohomology, and orbit equivalence of tiling spaces.
Annales Henri Poincare 19 (2018) 3053.
84. (with Michael Kelly)
Pattern Equivariant Mass Transport in Aperiodic Tilings and Cohomology.
International Mathematics Research Notices (March 2020), doi:
10.1093/imrn/rnz310
85. (with Joe Neeman and Charles Radin)
Phase Transitions in Finite Random Networks, J. Stat. Phys. 181 (2020)
305-328, 10.1007/s10955-020-02582-4.
86.
Effects of Latency on Estimates of the COVID-19 Replication Number,
Bull. Math. Biol 2020; 82(9): 114.
Published online 2020 Aug 20. doi: 10.1007/s11538-020-00791-2. Also available
on MedRxiv.
87. (with Man Yi Yim, Ilya Fiete and Thibaud Taillefumier)
Place-cell Capacity and Volatility with Grid-Like Inputs
eLife 2021;10:e62702, doi:10.7554/eLife.62704.
88. (with Jose Aliste-Prieto and Betseygail Rand)
Rotation numbers and rotation classes on one-dimensional tiling spaces,
Annales Henri Poincaré. 22 (2021) 2161-2193.
doi:10.1007/s00023-021-01019-2.
89. (with Dirk Frettlöh and Alexey Garber)
Number of Bounded Distance Equivalence Classes
in Hulls of Repetitive Delone Sets
Discrete and Continuous Dynamical Systems 42 (2022) 1403-1414.
doi:10.3934/dcds.2021157.
90. (with Eden Miro, Dan Rust and Gwendolyn Tadeo)
Topological Mixing of Random Substitutions.
Israel J. Mathematics 255 (2023) 123-153. doi:10.1007/s11856-022-2406-3.
91. (with Joe Neeman and Charles Radin)
Moderate Deviations in Trangle Count.
Random Structures and Algorithms 63 (2023) 779-820.
doi:10.1002/rsa.21147.
92. (with Joe Neeman and Charles Radin)
Typical large graphs with given edge and triangle densities,
Probability Theory and Related Fields 186 (2023) 1167-1223.
doi:10.1007/s00440-023-01187-8.
93. (with Jack Fuller III, Pujan Ajmera, Anastassia Alexandrova, Steven
Barnes and Alfredo Sadun)
Coenzyme Q10 trapping in mitochondrial Complex I underlies Leber's
Hereditary Optic Neuropathy. Proceedings of the National Academy of Sciences
120 (2023) e2304884120. doi:10.1073/pnas.2304884120.
94. (with Thibaud Taillefumier)
Global solutions with infinitely many
bloweups in a mean-field neural network,
preprint 2022, arxiv:2205.08035
95. (with Joe Neeman and Charles Radin)
Existence of a symmetric bipodal
phase in the edge-triangle model, preprint 2022, arxiv:2211.10498
96. (with Charles Radin)
Optimal graphons in the edge-2star
model, preprint 2023 arxiv:2305.00333.
97. (with Michael Baake and Franz Gähler)
Dynamics and topology of the
Hat family of tilings, preprint 2023, arxiv:2305.05639.