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. K. Cordwell, A. Epstein, A. Hemmady, S. J. Miller, E. A. Palsson, A. Sharma, S. Steinerberger, Y. N. T. Vu, "On algorithms to calculate integer complexity", (2017), submitted, arXiv:1706.08424.
  2. J. DeWitt, K. Ford, E. Goldstein, S. J. Miller, G. Moreland, E. A. Palsson, S. Senger, "Dimensional lower bounds for Falconer type incidence and point configuration theorems", (2016), submitted, arXiv:1612.00539.
  3. R. F. Durst, M. Hlavacek, C. Huynh, S. J. Miller, E. A. Palsson, "Classification of crescent configurations", (2016), submitted, arXiv:1610.07836.
  4. R. F. Durst, C. Huynh, A. Lott, S. J. Miller, E. A. Palsson, W. Touw, G. Vriend, "The inverse gamma distribution and Benford's law", (2016), submitted, arXiv:1609.04106.
  5. A. Epstein, A. Lott, S. J. Miller, E. A. Palsson, "Optimal point sets determining few distinct triangles", (2016), submitted, arXiv:1609.00206.
  6. A. Greenleaf, A. Iosevich, B. Liu, E. A. Palsson, "An elementary approach to simplexes in thin subsets of Euclidean space", (2016), submitted, arXiv:1608.04777.
  7. R. Dorward, P. Ford, E. Fourakis, P. Harris, S. Miller, E. A. Palsson, H. Paugh, "Individual gap measures from Generalized Zeckendorf decompositions", Uniform Distribution Theory, 12 (2017), no. 1, 27-36. arXiv:1509.03029
  8. 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", Involve, 10 (2017), 125-150. arXiv:1508.07531
  9. Y. Do, R. Oberlin, E. A. Palsson, "Variation-norm and fluctuation estimates for ergodic bilinear averages", 66 (2017), 55-99. arXiv:1504.07134
  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", Mathematical Research Letters, 23 (2016), 1737-1759. arXiv:1110.6792
  11. D. Burt, E. Goldstein, S. Manski, S. J. Miller, E. A. Palsson, H. Suh, "Crescent configurations", Integers, 16 (2016), #A38. arXiv:1509.07220
  12. B. Murphy, E. A. Palsson, G. Petridis, "The cardinality of sumsets: different summands",
    Acta Arithmetica, 167 (2015), 375-395. arXiv:1309.2191
  13. A. Greenleaf, A. Iosevich, B. Liu, E. A. Palsson, "A group-theoretic viewpoint on Erdos-Falconer problems and the Mattila integral", Revista Matematica Iberoamericana, 31 (2015), no. 3, 799-810. arXiv:1306.3598
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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. "Falconer type theorems for simplices",
    Analysis Seminar,
    Georgia Tech,
    Atlanta, Georgia, April 12, 2017.
  2. "Falconer type theorems for simplices",
    Inverse Problems and Analysis Seminar,
    University of Delaware,
    Newark, Delaware, March 3, 2017.
  3. "Falconer type theorems for simplices",
    Harmonic Analysis And Geometry Of Fractal Sets,
    Columbus, Ohio, February 4, 2017.
  4. "Estimates for a singular integral operator motivated by Calderón's second commutator",
    Colloquium,
    TIFR Bangalore,
    Bangalore, India, January 10, 2017.
  5. "Finite point configurations",
    Seminar,
    Indian Institute of Science, Bangalore,
    Bangalore, India, January 9, 2017.
  6. "Finite point configurations",
    Department of Mathematics Colloquium,
    Virginia Tech,
    Blacksburg, Virginia, November 11, 2016.
  7. "Finite point configurations",
    Analysis and Arithmetic Combinatorics Seminar,
    University of Georgia,
    Athens, Georgia, October 24, 2016.
  8. "Finite point configurations",
    Northeast Analysis Network Conference,
    Rochester, New York, September 9, 2016.
  9. "Finite point configurations",
    Summer Analysis Workshop,
    Oberlin College,
    Oberlin, Ohio, July 9, 2016.
  10. "Finite point configurations in thin sets",
    Combinatorics Seminar,
    University of Rochester,
    Rochester, New York, February 2, 2016.
  11. "Multilinear phenomena in analysis and related areas",
    Department of Mathematics Colloquium,
    University of Illinois at Urbana-Champaign,
    Urbana-Champaign, Illinois, December 10, 2015.
  12. "A look at the distinct distance problem and crescent configurations",
    Mathematics Colloquium,
    Bard College,
    Annandale-On-Hudson, New York, December 8, 2015.
  13. "Finite point configurations and multilinear Radon transforms",
    Analysis Seminar,
    Yale University,
    New Haven, Connecticut, December 1, 2015.
  14. "Finite point configurations and multilinear Radon transforms",
    Mathematics Department Seminar,
    Colgate University,
    Hamilton, New York, October 15, 2015.
  15. "Finite point configurations",
    Special Session on Geometric Aspects of Harmonic Analysis,
    Joint Meeting of the AMS, EMS and SPM,
    Porto, Portugal, June 12, 2015.
  16. "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.
  17. "Variational bounds for a dyadic model of the bilinear Hilbert transform",
    Analysis Seminar,
    Brown University,
    Providence, Rhode Island, March 9, 2015.
  18. "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.
  19. "Finite point configurations and multilinear Radon transforms",
    Department of Mathematics Undergraduate Colloquium,
    Trinity College,
    Hartford, Connecticut, October 9, 2014.
  20. "Finite point configurations and multilinear Radon transforms",
    Trimester Seminar,
    Hausdorff Research Institute for Mathematics,
    Bonn, Germany, July 29, 2014.
  21. "Restricted convolution inequalities, multilinear operators and applications",
    Harmonic Analysis to celebrate Michael Cowling's 65th,
    Segovia, Spain, July 2, 2014.
  22. "Multilinear phenomena in analysis and related areas",
    Department of Mathematics Colloquium,
    The University of Alabama,
    Tuscaloosa, Alabama, February 18, 2014.
  23. "Finite point configurations and multilinear Radon transforms",
    Mathematics and Statistics Department Colloquium,
    Williams College,
    Williamstown, Massachusetts, January 28, 2014.
  24. "Multilinear phenomena in analysis and related areas",
    Analysis Seminar,
    University of Rochester,
    Rochester, New York, November 8, 2013.
  25. "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.
  26. "Restricted convolution inequalities, multilinear operators and applications",
    Pure Mathematics Seminar,
    University of Queensland,
    Brisbane, Australia, June 4, 2013.
  27. "k-point configurations and multilinear generalized Radon transforms",
    Maths Colloquium,
    University of Queensland,
    Brisbane, Australia, June 3, 2013.
  28. "k-point configurations and multilinear generalized Radon transforms",
    Sydney-UNSW Joint Colloquium,
    University of Sydney,
    Sydney, Australia, May 31, 2013.
  29. "k-point configurations and multilinear generalized Radon transforms",
    Colloquium,
    University of Rochester,
    Rochester, New York, May 2, 2013.
  30. "Multilinear generalized Radon transforms",
    Analysis Seminar,
    Brown University,
    Providence, Rhode Island, November 19, 2012.
  31. "Multilinear generalized Radon transforms",
    Analysis Seminar,
    Indiana University Bloomington,
    Bloomington, Indiana, October 25, 2012.
  32. "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.
  33. "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.
  34. "On multilinear generalized Radon transforms",
    Analysis Seminar,
    Cornell University,
    Ithaca, New York, March 26, 2012.
  35. "On multilinear generalized Radon transforms",
    Analysis and PDE Seminar,
    University of California Los Angeles,
    Los Angeles, California, January 13, 2012.
  36. "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.
  37. "On multilinear generalized Radon transforms and angles",
    Analysis Seminar,
    University of Rochester,
    Rochester, New York, December 9, 2011.
  38. "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.
  39. "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.
  40. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Analysis Seminar,
    Georgia Tech,
    Atlanta, Georgia, December 8, 2010.
  41. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Analysis Seminar,
    Cornell University,
    Ithaca, New York, October 25, 2010.
  42. "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Analysis Seminar,
    University of Rochester,
    Rochester, New York, October 22, 2010.
  43. "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.