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Lorenzo A Sadun

Department of Mathematics, College of Natural Sciences

Marian Harris Thornberry Centennial Professorship in Mathematics or Physics (Holder)

Dynamical Systems, Mathematical Physics, and Probability


Phone: 512-471-7121

Office Location
PMA 9.114

Postal Address
AUSTIN, TX 78712

Ph.D., University of California, Berkeley (1987)

Research Interests

Mathematical Physics, Differential Geometry, and Analysis.

Topology and dynamics of aperiodic tilings, adiabatic quantum transport, and other problems of
both physical and geometric interest.


1. Applied Linear Algebra: The Decoupling Principle. Published Fall 2000 by Prentice Hall. ISBN 0-13-085645-2.

Book Chapter

2. Linear Algebra and Mathematical Physics, for the CRC Handbook of Linear Algebra, Leslie
Hogben ed. (2006)


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

4. (with Zvi Bern, M. B. Halpern and Clifford Taubes) Continuum Regularization of QCD, Phys. Lett. B 185(1985) 151-156.

5. (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.

6. (with Zvi Bern, M. B. Halpern and Clifford Taubes) Continuum Regularization of QuantumField Theory II. Gauge Theory, Nucl. Phys. B 284(1987) 35-91.

7. (with Zvi Bern and M. B. Halpern) Continuum Regularization of Quantum Field Theory III. The QCD4 β-function, Nucl. Phys. B 284(1987) 92-102.

8. (with Zvi Bern and M. B. Halpern) Continuum Regularization of Quantum Field Theory IV. Langevin Renormalization, Z. Phys. C 35(1987) 255-283.

9. Continuum Regularization of Quantum Field Theory V. Schwinger-Dyson Renormalization, Z. Phys. C 36(1987) 407-424.

10. (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.

11. (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.

12. (with Jan Segert) Chern Numbers for Fermionic Quadrupole Systems, J. Phys. A. 22(1989) L111-L115.

13. (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.

14. (with J. E. Avron) Chern Numbers and Adiabatic Transport in Networks with Leads, Phys. Rev. Letters 62(1989) 3082-3084.

15. (with J. E. Avron) Adiabatic Quantum Transport in Networks with Macroscopic Components, Ann. of Physics 206(1991) 440-493.

16. (with Jan Segert) Non-self-dual Yang-Mills Connections with Nonzero Chern Number, Bull. Amer. Math. Soc. 24(1991) 163-170.

17. (with A. C. Sadun) Relativistic Dynamics of Expanding Sources, Astrophys. & Space Sci. 185(1991), 21-36.

18. (with Jan Segert) Non-self-dual Yang-Mills connections with Quadrupole Symmetry, Comm. Math. Phys. 145(1992), 363-391.

19. (with Jan Segert) Stationary Points of the Yang-Mills Action, Comm. Pure & Appl. Math. 45(1992) 461-484.

20. (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.

21. (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.

22. (with M. Vishik) The Spectrum of the Second Variation of the Energy for an Ideal Incompressible Fluid, Phys. Lett. A 182 (1993), 394-398.

23. A Symmetric Family of Yang-Mills Fields, Commun. Math. Phys. 163 (1994), 257-291.

24. (with C. Radin) The Isoperimetric Problem for Pinwheel Tilings, Commun. Math. Phys. 177 (1996), 255-263.

25. A Simple Geometric Representative of µ of a Point, Commun. Math Phys. 178 (1996), 107-113.

26. (with J. Avron) Adiabatic Curvature and the S-Matrix, Commun. Math. Phys. 181 (1996),

27. (with D. Auckly) A Family of M¨obius 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.

28. 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.

29. Some Generalizations of the Pinwheel Tiling, Disc. Comp. Geom. 20 (1998), 79-110.

30. (with C. Radin) Subgroups of SO(3) Associated with Tilings, J. Algebra. 202 (1998), 611–633.

31. (with M. Speight) Geodesic Incompleteness in the CP1 Model on a Compact Riemann Surface, Lett. Math. Phys. 43 (1998), 329–334.

32. (with C. Radin) An Algebraic Invariant for Substitution Tiling Systems, to appear in Geom. Ded. 73 (1998) 21–37

33. (with C. Radin) On 2-generator subgroups of SO(3), Trans. Amer. Math. Soc. 351 (1999), 4469–4480

34. (with J. Conway and C. Radin) On Angles Whose Squared Trigonometric Functions are Rational, Discrete Comput. Geom. 22 (1999), 321–332.

35. (with B. Draco and D. Van Wieren) Growth Rates in the Quaquaversal Tiling, Discrete Comput. Geom. 23 (2000), 419–435.

36. (with J. Conway and C. Radin) Relations in SO(3) Supported by Geodetic Angles, Discrete Comput. Geom. 23 (2000), 453–463.

37. (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.

38. (with L. Guijarro and G. Walschap) Parallel Connections over Symmetric Spaces, J. Geom. Anal. 11 (2001), 265–281.

39. (with D. Groisser) Simple Type and the Boundary of Moduli Space, J. Geom. Phys. 36 (2000), 324–384.

40. (with C. Radin) Isomorphisms of Hierarchical Structures, Ergodic Theory Dynam. Systems 21(2001), 1239-1248.

41. (with J.E. Avron) Fredholm Indices and the Phase Diagram of Quantum Hall Systems, J. Math. Phys. 42 (2001), 1–14.

42. (with J.E. Avron, A. Elgart, and G.M. Graf) Optimal Quantum Pumps, Physical Review Letters 87 (2001), 236601.

43. (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.

44. (with N. Ormes and C. Radin) A Homeomorphism Invariant for Substitution Tiling Spaces, Geometriae Dedicata 90 (2002), 153–182.

45. (with F. Rodriguez Villegas and J. F. Voloch) Blet, a Mathematical Puzzle, American Mathematical Monthly 109 (2002) 729–740.

46. (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.

47. (with R.F. Williams) Tiling Spaces are Cantor Set Fiber Bundles, Ergodic Theory and Dynamical Systems 23 (2003) 307–316.

48. (with A. Marini) Spherically Symmetric Solutions of a Boundary Value Problem for Monopoles, Journal of Mathematical Physics 44 (2003) 1071–1083.

49. (with A. Clark) When size matters: subshifts and their related tiling spaces, Ergodic Theory and Dynamical Systems 23 (2003) 1043–1057.

50. (with S. Keel) Oort’s Conjecture for Ag ⊗ C, Journal of the Americal Mathematical Society 16 (2003) 887–900.

51. Tiling Spaces are Inverse Limits, Journal of Mathematical Physics 44 (2003) 5410–5414.

52. (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.

53. (with J.E. Avron, A. Elgart and G.M. Graf) Transport and Dissipation in Quantum Pumps. Journal of Statistical Physics 116 (2004) 425–473.

54. (with C. Radin) Structure of the hard sphere solid, Phys. Rev. Lett. 94 (2005), paper 015502.

55. (with C. Holton and C. Radin) Conjugacies for Tiling Dynamical Systems. Communications in Mathematical Physics 254 (2005) 343–359.

56. (with P. Buczek and J. Wolny) Periodic Diffraction Patterns for 1D Quasicrystals. Acta Physica Polonica B 36 (2005) 919-933.

57. (with L. Bowen, C. Holton and C. Radin) Uniqueness and Symmetry in Problems of OptimallyDense Packings. Math Phys. Electron. J. 11 (2005) paper 1.

58. (with H. Koch and C. Radin), The most stable structure for hard spheres, Physical Review E 72 (2005), paper 016708.

59. (with R. Kenyon and B. Solomyak) Topological Mixing for Substitutions on Two Letters, Ergodic Theory and Dynamical Systems 25 (2005) 1919-1934.

60. (with A. Clark) When Shape Matters: Deformations of Tiling Spaces, Ergodic Theory and Dynamical Systems 26 (2006) 69-86.

61. Tilings, tilings spaces and topology, Philosophical Magazine 86 (2006) 875-881.


62. Pattern-Equivariant Cohomology with Integer Coefficients.

63. (with N.P. Frank) Topology of (Some) Tiling Spaces without Finite Local Complexity.

  • 2000-2002 The President’s Associates Centennial Teaching Fellowship in Mathematics
  • 2001 College of Natural Sciences Distinguished Teaching Award
  • 1999 Invited lecture at AMS Sectional Meeting, Las Vegas, NV.
  • 1990 Commendation for “superior performance” as an Instructor at New York University
  • 1983 Distinguished Teaching Award, given by U.C.-Berkeley Physics Department
  • 1979 Putnam Exam - Placed 12th