University of Illinois at Urbana-Champaign

Math 598 Fall 2018: Literature Seminar on projection theorems, Besicovitch and Kakeya sets in the Heisenberg group

Reference List

  1. Books and Lecture Notes
    • P. Mattila, Geometry of sets and measures in Euclidean spaces: fractals and rectifiability, Cambridge studies in advanced mathematics, 44, Cambridge Univ. Press, 1995.
    • P. Mattila, Fourier analysis and Hausdorff dimension, Cambridge studies in advanced mathematics, 150, Cambridge Univ. Press, 2015.

  2. Survey articles
    • P. Mattila, ``Recent progress on dimensions of projections'', in Geometry and analysis of fractals, Springer Proc. Math. Stat., 88, Springer (2014), 283-301.
    • P. Mattila, ``Hausdorff dimension, projections, and the Fourier transform'', Publ. Mat. 48 (2004), 3-48.
  3. Journal articles
    • Z. M. Balogh, E. Durand Cartagena, K. Faessler, P. Mattila, J. T. Tyson, ``The effect of projections on dimension in the Heisenberg group'', Rev. Mat. Iberoam., 29 (2013), 381-432.
    • Z. M. Balogh, K. Faessler, P. Mattila, J. T. Tyson, ``Projection and slicing theorems in Heisenberg groups'', Adv. Math., 231 (2012), 569-604.
    • R. Hovila, ``Transversality of isotropic projections, unrectifiability, and Heisenberg groups'', Rev. Mat. Iberoam., 30 (2014), 463-476.
    • K. Faessler and R. Hovila, ``Improved Hausdorff dimension estimate for vertical projections in the Heisenberg group'', Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 15 (2016), 459-483.
    • P. Mattila and T. Orponen, ``Hausdorff dimension, intersections of projections and exceptional plane sections'', Proc. Amer. Math. Soc., 144 (2016), 3419-3430.
    • T. Orponen, ``Quasisymmetric maps on Kakeya sets'', IMRN, 2017 (2017), 3413-3425.
    • L. Venieri, ``Heisenberg Hausdorff dimension of Besicovitch sets'', Anal. Geom. Metr. Spaces, 2 (2014), 319-327.