# Books :

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

Book Chapters:

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.

# Research articles:

1. (with A. C. Sadun and A. A. Sadun) Solar Retinopathy - A Biophysical Analysis, Arch. Opthalmol. 102 (1984) 1510-1512.

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.

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 .

In Press:

74. Finitely Balanced Sequences and Plasticity of 1-Dimensional Tilings, to appear in Topology and its Applications. 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, to appear in Mathematical Proceedings of the Cambridge Philosophical Society.

76. (with Antoine Julien) Tiling deformations, cohomology, and orbit equivalence of tiling spaces, to appear in the Journal of the European Math Society.

Submitted:

77. (with Johannes Kellendonk) Conjugacies of Model Sets.

78. (with Richard Kenyon, Charles Radin and Kui Ren) Multipodal Structure and Phase Transitions in Large Constrained Graphs.

79. (with Alex Clark) Small cocycles, fine torus fibrations, and a Zd subshift with neither.

80. (with Richard Kenyon, Charles Radin and Kui Ren) Bipodal Structure in Oversaturated Random Graphs.