Research

The central theme of my research is multilinear phenomena in analysis and related areas. Many concepts in mathematics, from boundary value problems in partial differential equations and mathematical physics to finite point configurations in geometric combinatorics, are fundamentally tied to various operator bounds. This frequently leads to the estimation of linear and multilinear integral operators using techniques from harmonic analysis, often combined with geometric and combinatorial principles. With my collaborators I studied multipoint configuration versions of the Falconer distance problem, which can be thought of as a continuous analog of the well known Erdös distinct distance problem. Such point configuration problems have direct connections to big data. A key ingredient in our proofs were estimates on multilinear analogues of linear generalized Radon transforms. Apart from having these sort of applications to geometric measure theory and combinatorics then further investigation of the multilinear generalized Radon transforms has shown applications to restriction theory, partial differential equations, Sobolev trace inequalities and multilinear analogues of Stein's spherical maximal operator theorem. In my thesis and later work with collaborators I have used time-frequency analysis to study both Lp estimates and variational estimates for singular integral operators. Such operators are frequently motivated by, and have potential applications to, both non-linear partial differential equations and ergodic theory. In addition, I have begun exploring additive number theory and have a recent paper on that topic that obtains bounds on sumsets.

Publications

  1. D. Burt, E. Goldstein, S. Manski, S. J. Miller, E. A. Palsson, H. Suh, "Crescent configurations", (2015), submitted, arXiv:1509.07220.
  2. R. Dorward, P. Ford, E. Fourakis, P. Harris, S. Miller, E. A. Palsson, H. Paugh, "Individual gap measures from Generalized Zeckendorf decompositions", (2015), submitted, arXiv:1509.03029.
  3. R. Dorward, P. Ford, E. Fourakis, P. Harris, S. Miller, E. A. Palsson, H. Paugh, "A Generalization of Zeckendorf's Theorem via Circumscribed m-gons", (2015), submitted, arXiv:1508.07531.
  4. Y. Do, R. Oberlin, E. A. Palsson, "Variation-norm and fluctuation estimates for ergodic bilinear averages", (2015), accepted for publication in Indiana University Mathematics Journal, arXiv:1504.07134.
  5. B. Murphy, E. A. Palsson, G. Petridis, "The cardinality of sumsets: different summands",
    Acta Arithmetica, 167 (2015), 375-395. arXiv:1309.2191
  6. A. Greenleaf, A. Iosevich, B. Liu, E. A. Palsson, "A group-theoretic viewpoint on Erdos-Falconer problems and the Mattila integral", (2013), accepted for publication in Revista Matematica Iberoamericana, arXiv:1306.3598.
  7. D. Geba, A. Greenleaf, A. Iosevich, E. A. Palsson, E. Sawyer, "Restricted convolution inequalities, multilinear operators and applications", Mathematical Research Letters, 20 (2013), 675-694. arXiv:1209.6574.
  8. L. Grafakos, A. Greenleaf, A. Iosevich, E. A. Palsson, "Multilinear generalized Radon transforms and point configurations", Forum Mathematicum, 27 (2015), 2323-2360. arXiv:1204.4429.
  9. Y. Do, R. Oberlin, E. A. Palsson, "Variational bounds for a dyadic model of the bilinear Hilbert transform",
    Illinois Journal of Mathematics, 57 (2013), 105-120. arXiv:1203.5135.
  10. A. Iosevich, M. Mourgoglou, E. A. Palsson, "On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators", (2011), accepted for publication in Mathematical Research Letters, arXiv:1110.6792.
  11. E. A. Palsson, "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Journal of Functional Analysis, 262 (2012), 1645-1678. arXiv:1104.5160
  12. E. A. Palsson, "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    PhD Thesis, Cornell University, May 2011.

Selected Talks

  1. "Finite point configurations",
    Special Session on Geometric Aspects of Harmonic Analysis,
    Joint Meeting of the AMS, EMS and SPM,
    Porto, Portugal, June 12, 2015.
  2. "Finite point configurations",
    International Conference on Harmonic Analysis and Applications,
    The Graduate Center of City University of New York,
    New York, New York, June 1, 2015.
  3. "Variational bounds for a dyadic model of the bilinear Hilbert transform",
    Analysis Seminar,
    Brown University,
    Providence, Rhode Island, March 9, 2015.
  4. "Variational bounds for a dyadic model of the bilinear Hilbert transform",
    Analysis Seminar,
    State University of New York Albany,
    Albany, New York, November 12, 2014.
  5. "Finite point configurations and multilinear Radon transforms",
    Department of Mathematics Undergraduate Colloquium,
    Trinity College,
    Hartford, Connecticut, October 9, 2014.
  6. "Finite point configurations and multilinear Radon transforms",
    Trimester Seminar,
    Hausdorff Research Institute for Mathematics,
    Bonn, Germany, July 29, 2014.
  7. "Restricted convolution inequalities, multilinear operators and applications",
    Harmonic Analysis to celebrate Michael Cowling's 65th,
    Segovia, Spain, July 2, 2014.
  8. "Multilinear phenomena in analysis and related areas",
    Department of Mathematics Colloquium,
    The University of Alabama,
    Tuscaloosa, Alabama, February 18, 2014.
  9. "Finite point configurations and multilinear Radon transforms",
    Mathematics and Statistics Department Colloquium,
    Williams College,
    Williamstown, Massachusetts, January 28, 2014.
  10. "Multilinear phenomena in analysis and related areas",
    Analysis Seminar,
    University of Rochester,
    Rochester, New York, November 8, 2013.
  11. "Falconer type theorems for simplices",
    Special Session on Harmonic Analysis and Applications,
    Joint Meeting of the AMS and the RMS,
    Alba Iulia, Romania, June 29, 2013.
  12. "Restricted convolution inequalities, multilinear operators and applications",
    Pure Mathematics Seminar,
    University of Queensland,
    Brisbane, Australia, June 4, 2013.
  13. "k-point configurations and multilinear generalized Radon transforms",
    Maths Colloquium,
    University of Queensland,
    Brisbane, Australia, June 3, 2013.
  14. "k-point configurations and multilinear generalized Radon transforms",
    Sydney-UNSW Joint Colloquium,
    University of Sydney,
    Sydney, Australia, May 31, 2013.
  15. "k-point configurations and multilinear generalized Radon transforms",
    Colloquium,
    University of Rochester,
    Rochester, New York, May 2, 2013.
  16. "Multilinear generalized Radon transforms",
    Analysis Seminar,
    Brown University,
    Providence, Rhode Island, November 19, 2012.
  17. "Multilinear generalized Radon transforms",
    Analysis Seminar,
    Indiana University Bloomington,
    Bloomington, Indiana, October 25, 2012.
  18. "Variational bounds for a dyadic model of the bilinear Hilbert transform",
    AMS Special Session on Harmonic Analysis and Convexity,
    Fall Central Sectional Meeting,
    Akron, Ohio, October 21, 2012.
  19. "Variational bounds for a dyadic model of the bilinear Hilbert transform",
    AMS Special Session on Wavelet and Frame Theoretic Methods in Harmonic Analysis and Partial Differential Equations in Memory of Daryl Geller,
    Fall Eastern Sectional Meeting,
    Rochester, New York, September 29, 2012.
  20. "On multilinear generalized Radon transforms",
    Analysis Seminar,
    Cornell University,
    Ithaca, New York, March 26, 2012.
  21. "On multilinear generalized Radon transforms",
    Analysis and PDE Seminar,
    University of California Los Angeles,
    Los Angeles, California, January 13, 2012.
  22. "On multilinear generalized Radon transforms",
    AMS Special Session on Radon Transforms and Geometric Analysis (in honor of Sigurdur Helgason's 85th birthday),
    Joint Mathematics Meetings,
    Boston, Massachusetts, January 7, 2012.
  23. "On multilinear generalized Radon transforms and angles",
    Analysis Seminar,
    University of Rochester,
    Rochester, New York, December 9, 2011.
  24. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Incompressible Fluids, Turbulence and Mixing. In honor of Peter Constantin's 60th birthday.,
    Carnegie Mellon University,
    Pittsburgh, Pennsylvania, October 15, 2011.
  25. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    AMS Session on Topics in Analysis,
    Joint Mathematics Meetings,
    New Orleans, Louisiana, January 9, 2011.
  26. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Analysis Seminar,
    Georgia Tech,
    Atlanta, Georgia, December 8, 2010.
  27. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Analysis Seminar,
    Cornell University,
    Ithaca, New York, October 25, 2010.
  28. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Analysis Seminar,
    University of Rochester,
    Rochester, New York, October 22, 2010.
  29. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Calderón-Zygmund Analysis Seminar,
    University of Chicago,
    Chicago, Illinois, May 3, 2010.