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

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 System*s, 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
Physics**43**
(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.

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 **R**^{d},
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.

**In Press:**

**Submitted**:

79. (with Antoine Julien)
Tiling deformations, cohomology, and orbit equivalence of tiling spaces.
Submitted to Annales de l'Institute Henri Poincare.

80. (with Richard Kenyon, Charles Radin and Kui Ren)
Multipodal Structure and Phase Transitions in Large Constrained Graphs.
Submitted to J. Stat. Phys.

81. (with Alex Clark)
Small cocycles, fine torus fibrations, and a
**Z**^{d} subshift with neither.
Submitted to Annales de l'Institute Henri Poincare.

82. (with Charles Radin and Kui Ren)
A Symmetry Breaking Transition in the Edge/Triangle Network Model.
Submitted to Annales de l'Institute Henri Poincare.

83. (with Richard Kenyon, Charles Radin and Kui Ren)
The Phases of Large Networks with Edge and Triangle Constraints.
Submitted to J. Stat. Phys.