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Izabella Laba - Publications

Books/ Research/ Expository/ Beyond math

Please note that the copyright to most of the works listed below belongs to the publishers. The versions posted here or on the arXiv are not necessarily final.

Books, authored and edited

  1. "Lectures in Harmonic Analysis", by Tom Wolff, edited by myself and Carol Shubin, AMS University Lecture Series, vol. 29, 2003.

  2. "Multiparticle Quantum Scattering in Constant Magnetic Fields", with Christian Gerard, AMS Mathematical Surveys and Monographs, vol. 90, 2002.

Research articles

  1. "Splitting for integer tilings and the Coven-Meyerowitz tiling conditions", with Itay Londner, July 2022, 70 pages.

  2. "Vanishing sums of roots of unity and the Favard length of self-similar product sets", with Caleb Marshall, Discrete Analysis 2022:19, 31 pp.

  3. "The Coven-Meyerowitz tiling conditions for 3 odd prime factors", with Itay Londner, Inventiones Math. 232 (2023), 365-470. The journal version (open access) is available here.

  4. "Combinatorial and harmonic-analytic methods for integer tilings" with Itay Londner, Forum of Mathematics - Pi (2022), Vol. 10:e8, 46 pp. Journal version (open access) available here.

  5. "Maximal operators and decoupling for $\Lambda(p)$ Cantor measures", Ann. Fenn. Math. 46 (2021), 163--186. Final version available here.

  6. "On the maximal directional Hilbert transform," with Alessandro Marinelli and Malabika Pramanik, Analysis Math. 45 (3) (2019), 535-568. Final version available here.

  7. "Decoupling and near-optimal restriction estimates for Cantor sets," with Hong Wang, Int. Math. Res. Notices 2018, no. 9, 2944-2966. final version available here)

  8. "A discrete Carleson theorem along the primes with a restricted supremum," with Laura Cladek, Kevin Henriot, Ben Krause and Malabika Pramanik, Math. Zeitschrift 289 (2018), 1033-1057, final version available here

  9. "On polynomial configurations in fractal sets," with Kevin Henriot and Malabika Pramanik, Analysis & PDE 9-5 (2016), 1153--1184

  10. "Sharpness of the Mockenhaupt-Mitsis-Bak-Seeger restriction theorem in higher dimensions," with Kyle Hambrook, Bull. London Math. Soc. 48(5) (2016), 757-770. final version available here.

  11. "Finite configurations in sparse sets", with Vincent Chan and Malabika Pramanik, J. Anal. Math. 128 (2016), 289-335.

  12. "Quantitative visibility estimates for unrectifiable sets in the plane", with Matthew Bond and Joshua Zahl, Trans. Amer. Math. Soc. 368 (2016), 5475-5513.

  13. "Buffon's needle estimates for rational product Cantor sets", with Matthew Bond and Alexander Volberg, Amer. J. Math. 136 (2014), 357-391.

  14. "On the sharpness of Mockenhaupt's restriction theorem", with Kyle Hambrook, Geom. Funct. Anal. 23 (2013), 1262-1277. The final publication is available here.

  15. "Arithmetic progressions in sumsets and Lp-almost-periodicity", with Ernie Croot and Olof Sisask, Combinatorics, Probability and Computing 22 (2013), 351-365.

  16. "Maximal operators and differentiation theorems for sparse sets", with Malabika Pramanik, Duke Math. J. 158 (2011), 347-411. Here's an extended version including an appendix with additional material.

  17. "The Favard length of product Cantor sets", with Kelan Zhai, Bull. London Math. Soc. 42 (2010), 997-1009. The final publication is available here.

  18. "Arithmetic progressions in sets of fractional dimension", with Malabika Pramanik, Geom. Funct. Anal. 19 (2009), 429-456. The final publication is available here.

  19. "Geometric incidence theorems via Fourier analysis", with Alex Iosevich and Hadi Jorati, Trans. Amer. Math. Soc. 361 (2009), 6595-6611.

  20. "Arithmetic structures in random sets", with Mariah Hamel, Integers: Electronic Journal of Combinatorial Number Theory 8 (2008), #A4.

  21. "Incidence theorems for pseudoflats", with Jozsef Solymosi, Discr. Comp. Geom. 37 (2007), 163-174.

  22. "Some properties of spectral measures", with Yang Wang, Appl. Comp. Harmonic Analysis 20 (2006), 149-157.

  23. "Wolff's inequality for hypersurfaces", with Malabika Pramanik, Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Madrid, 2004 (published by Collectanea Mathematica, Vol. Extra (2006), 293-326, http://www.imub.ub.es/collect/ElEscorial.html)

  24. "Distance sets of well-distributed planar sets for polygonal norms", with Sergei Konyagin, Israel J. Math. 152 (2006), 157--179.

  25. "Falconer's distance set conjecture for polygonal norms", with Sergei Konyagin, Proceedings of the Harmonic Analysis and its Applications at Sapporo, A. Miyachi and K. Tachizawa, eds., Hokkaido University, Sapporo, 2005, pp. 43-55.

  26. "K-distance sets, Falconer conjecture, and discrete analogs", with Alex Iosevich, Integers: Electronic Journal of Combinatorial Number Theory, 5(2) (2005), #A08. A hardcopy edition of this volume is also available: Topics in Combinatorial Number Theory: Proceedings of the Integers Conference 2003 in Honor of Tom Brown, DIMATIA, ITI Series, vol. 261, dimatia@kam.mff.cuni.cz.

  27. "Distance sets of well-distributed planar point sets", with Alex Iosevich, Discr. Comp. Geom. 31 (2004), 243--250.

  28. "Tiling and spectral properties of near-cubic domains", with Mihalis Kolountzakis, Studia Math. 160 (2004), 287-299.

  29. "Spectra of certain types of polynomials and tiling of integers with translates of finite sets", with Sergei Konyagin, J. Number Theory 103 (2003), 267-280.

  30. "A local smoothing estimate in higher dimensions", with Tom Wolff, J. d'Analyse Math. 88 (2002), 149-171.

  31. "On spectral Cantor measures", with Yang Wang, J. Funct. Anal. 193 (2002), 409-420.

  32. "A characterization of finite sets that tile the integers", with Andrew Granville and Yang Wang, September 2001.

  33. "The spectral set conjecture and multiplicative properties of roots of polynomials", J. London Math. Soc. 65 (2002), 661-671

  34. "An improved bound on the Minkowski dimension of Besicovitch sets in medium dimension", with Terence Tao, Geom. Funct. Anal. 11 (2001), 773-806

  35. "Fuglede's conjecture for a union of two intervals", Proc. AMS 129 (2001), 2965-2972.

  36. "An x-ray transform estimate in R^n", with Terence Tao, Revista Mat. Iberoamericana 17 (2001), 375-407

  37. "An improved bound on the Minkowski dimension of Besicovitch sets in R^3", with Nets Hawk Katz and Terence Tao, Annals of Math. 152 (2000), 383-446. The version posted here is the original version from February 1999.

  38. "Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds", with Avy Soffer, Helv. Phys. Acta 72 (1999), 274-294.

  39. "Scattering theory for 3-particle systems in constant magnetic fields: dispersive case", with Christian Gerard, Ann. Inst. Fourier (Grenoble) 46 (1996), 801-876.

  40. "Scattering theory for N-particle systems in constant magnetic fields, II: Long-range interactions", with Christian Gerard, Commun. Part. Diff. Eq. 20 (1995), 1791-1830.

  41. "Scattering theory for N-particle systems in constant magnetic fields", with Christian Gerard, Duke Math. J. 76 (1994), 433-466.

  42. "Scattering for hydrogen-like systems in a constant magnetic field", Comm. Part. Diff. Eq. 20 (1995), 741-762.

  43. "Long-range one-particle scattering in a homogeneous magnetic field", Duke Math. J. 70 (1993), 283-303.

Expository articles and lecture slides

  1. "Tiling the integers with translates of one tile: the Coven-Meyerowitz tiling conditions for three prime factors": Expository slides on my work with Itay Londner on integer tilings. The slides are from September 2021 and were written by Itay Londner and myself.

  2. Slides from my Etta Z. Falconer lecture, Mathfest, 2016

  3. "Polynomial configurations in fractal sets": I don't have a proper expository paper on my work on configurations in fractals (joint with Vincent Chan, Kevin Henriot and Malabika Pramanik), but here is my set of slides from ICERM, February 2016.

  4. "Harmonic analysis and the geometry of fractals", Proceedings of the 2014 International Congress of Mathematicians, Seoul, 2014. Update, August 2014: the slides of my talk are available here.

  5. "Recent progress on Favard length estimates for planar Cantor sets", in: Operator-Related Function Theory and Time-Frequency Analysis, Proceedings of the 2012 Abel Symposium, K. Grochenig, Y. Lyubarskii, K. Seip, eds., Springer 2015, pp. 117-145.

  6. "Buffon's needle estimates and vanishing sums of roots of unity", CMS Notes, 44 (2012), no. 6, 16-17.

  7. "From harmonic analysis to arithmetic combinatorics", July 2007 (revised version), Bull. Amer. Math. Soc. 45 (2008), 77-115. (A shorter version was published in the 2007 AMS Current Events Bulletin booklet, see also errata).

  8. "From harmonic analysis to arithmetic combinatorics: a brief survey", July 2006, to appear in the proceedings of the MSRI workshop "Women in Mathematics: the legacy of Ladyzhenskaya and Oleinik".

  9. "On sets of integers not containing long arithmetic progressions", with Michael Lacey, October 2001. After completing this paper, we learned that the result was not new; the journal submission has been withdrawn, but I thought it useful to leave the paper here as an expository note.

  10. "Multiparticle quantum systems in constant magnetic fields", in: Multiparticle Quantum Scattering With Applications to Nuclear, Atomic and Molecular Physics, D. Truhlar and B. Simon, eds., IMA Volumes in Mathematics and its Applications, Vol. 89, Springer-Verlag 1997, 147-215.

Beyond mathematics

  1. Slides from my presentation at "A conversation on professional norms in mathematics", JHU, September 2019

  2. "As You Do Unto Us", AWM Newsletter, 48 (6), November-December 2018, 22-25.. Based on an earlier blog post.

  3. "Photography", in "Art in the Life of Mathematicians," Anna Kepes Szemeredi, ed., AMS, 2015, pp. 138-163. This is the final version of the text of my chapter, without the photographs. (For a selection of my photography, see my Google+ page.)

All of my papers since 1999 are also posted on the ArXiv. If you have any problems with downloading or printing out the files, or if you would like to have a hard copy mailed to you, please let me know.