Research

The two main themes of my research program are multilinear operators and point configurations. 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 operators using techniques from harmonic analysis, often combined with geometric and combinatorial principles.

A particularly rich source of inspiration is a famous question of Erdös where he asked about the least number of distinct distances determined by points in the plane. Instead of distance, which is a simple pattern, I mainly study multipoint configuration versions of this problem, both in the original discrete setting, as well as in a continuous setting where geometric measure theory plays a key role. These point configuration problems have direct connections to big data.

Geometric averaging operators, such as averaging a function over a sphere, play a key role in many of my investigations and are of independent interest. A particularly important class are multilinear analogues of linear generalized Radon transforms. In addition to applications to geometric measure theory and combinatorics, further investigation of these multilinear generalized Radon transforms led to applications to restriction theory, partial differential equations, Sobolev trace inequalities and multilinear analogues of Stein's spherical maximal operator theorem.

My work on multilinear singular integral operators goes all the way back to my thesis. I used time-frequency analysis to study both Lp estimates, variational estimates and sparse estimates for such operators. These operators are frequently motivated by, and have potential applications to, both non-linear partial differential equations and ergodic theory.

Submitted

  1. A. Iosevich, P. Mattila, E. A. Palsson, M-Q. Pham, T. Pham, S. Senger, C-Y. Shen, "Packing sets in Euclidean space by affine transformations", (2024), submitted, arXiv:2405.03087.
  2. A. Iosevich, E. A. Palsson, Y. Zhai, E. Wyman, "Multi-linear forms, structure of graphs and Lebesgue spaces", (2024), submitted, arXiv:2401.17532.
  3. Z. Boone, E. A. Palsson, "A pinned Mattila-Sjölin type theorem for product sets", (2022), submitted, arXiv:2210.00675.
  4. E. A. Palsson, S. R. Sovine, "Sparse bounds for maximal triangle averaging operators", (2021), submitted, arXiv:2110.08928.
  5. E. Boldyriew, Elena Kim, S. J. Miller, E. A. Palsson, S. Sovine, F. T. Suarez, J. Zhao, "Tinkering with Lattices: A New Take on the Erdos Distance Problem", (2020), submitted, arXiv:2009.12450.
  6. A. Iosevich, E. A. Palsson, "An improved dimensional threshold for the angle problem", (2018), submitted, arXiv:1807.05465.
  7. R. F. Durst, M. Hlavacek, C. Huynh, S. J. Miller, E. A. Palsson, "Classification of crescent configurations", (2016), submitted, arXiv:1610.07836.

Accepted

  1. E. A. Palsson, F. Romero Acosta, "A Mattila-Sjölin theorem for simplices in low dimensions", (2024), accepted for publication in Mathematische Annalen, arXiv:2208.07198.
  2. J. Gaitan, A. Greenleaf, E. A. Palsson, G. Psaromiligkos, "On restricted Falconer distance sets", (2024), accepted for publication in Canadian Journal of Mathematics, arXiv:2305.18053.

Published

  1. E. A. Palsson, E. Yu, "On optimal point sets determining distinct triangles", Electronic Journal of Combinatorics, 31 (2024), no. 2, Paper No. P2.24, 19 pp. arXiv:2308.13107.
  2. T. C. Anderson, A. V. Kumchev, E. A. Palsson, "A framework for discrete bilinear spherical averages and applications to ℓp-improving estimates", Colloquium Mathematicum, 175 (2024), 55-76. arXiv:2305.14346.
  3. B. Cook, K. Hughes, E. Palsson, "Discrete restriction estimates for forms in many variables", Proceedings of the Edinburgh Mathematical Society, 66 (2023), no. 4, 923-939. arXiv:2004.02301
  4. H. L. Fleischmann, S. J. Miller, E. A. Palsson, E. Pesikoff, C. Wolf, "Optimal point sets determining few distinct angles", The Australasian Journal of Combinatorics, 87 (2023), no. 1, 165-181. arXiv:2108.12034
  5. H. L. Fleischmann, H. B. Hu, F. Jackson, S. J. Miller, E. A. Palsson, E. Pesikoff, C. Wolf, "Distinct angle problems and variants", Discrete & Computational Geometry, 70 (2023), 1715-1740. arXiv:2108.12015
  6. R. Ascoli, L. Betti, J. L. Duke, X. Liu, W. Milgrim, S. J. Miller, E. A. Palsson, F. Romero Acosta, S. Velazquez Iannuzzelli, "Distinct angles and angle chains in three dimensions", Discrete Mathematics & Theoretical Computer Science, 25 (2023), no. 1, Paper No. 2, 19 pp. arXiv:2208.13284
  7. E. A. Palsson, F. Romero Acosta, "A Mattila-Sjölin theorem for triangles", Journal of Functional Analysis, 284 (2023), no. 6, Paper No. 109814, 20 pp. arXiv:2109.13429
  8. H. L. Fleischmann, S. V. Konyagin, S. J. Miller, E. A. Palsson, E. Pesikoff, C. Wolf, "Distinct angles in general position", Discrete Mathematics, 346 (2023), no. 4, Paper No. 113283, 4 pp. arXiv:2206.04367
  9. T. C. Anderson, A. V. Kumchev, E. A. Palsson, "Discrete maximal operators over surfaces of higher codimension", La Matematica, 1 (2022), no. 2, 442-479. arXiv:2006.09968
  10. A. Iosevich, E. A. Palsson, S. R. Sovine, "Simplex averaging operators: quasi-Banach and Lp-improving bounds in lower dimensions", Journal of Geometric Analysis, 32 (2022), no. 3, Paper No. 87, 16 pp. arXiv:2109.09017
  11. T. C. Anderson, E. A. Palsson, "Bounds for discrete multilinear spherical maximal functions", Collectanea Mathematica, 73 (2022), no. 1, 75-87. arXiv:1910.11409
  12. E. A. Palsson, S. Senger, C. Wolf, "Angle chains and pinned variants", Bulletin of the Hellenic Mathematical Society, 65 (2021), 35-53. arXiv:2104.09960
  13. S. Gunter, E. A. Palsson, B. Rhodes, S. Senger, "Bounds on point configurations determined by distances and dot products", Combinatorial and Additive Number Theory IV, 243-260, Springer Proceedings in Mathematics & Statistics, 297, Springer, Cham, 2021. arXiv:2011.15055
  14. E. A. Palsson, S. Senger, A. Sheffer, "On the number of discrete chains", Proceedings of the American Mathematical Society, 149 (2021), no. 12, 5347-5358. arXiv:1902.08259
  15. T. C. Anderson, E. A. Palsson, "Bounds for discrete multilinear spherical maximal functions in higher dimensions", Bulletin of the London Mathematical Society, 53 (2021), no. 3, 855-860. arXiv:1911.00464
  16. H. N. Brenner, J. S. Depret-Guillaume, E. A. Palsson, S. Senger, "Uniqueness of optimal point sets determining two distinct triangles", Integers, 21 (2021), Paper No. A43, 15 pp. arXiv:1910.00629
  17. Z. J. Hoelscher, E. A. Palsson, "Counting restricted partitions of integers into fractions: symmetry and modes of the generating function and a connection to ω(t)", PUMP Journal of Undergraduate Research, 3 (2020), 277-307. arXiv:2011.14502
  18. S. Fish, D. King, S. J. Miller, E. A. Palsson, C. Wahlenmayer, "Crescent configurations in normed spaces", Integers, 20 (2020), Paper No. A96, 38 pp. arXiv:1909.08769
  19. E. A. Palsson, S. R. Sovine, "The triangle averaging operator", Journal of Functional Analysis, 279 (2020), no. 8, #108671, 21 pp. arXiv:1910.01282
  20. 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", PUMP Journal of Undergraduate Research, 3 (2020), 95-109. arXiv:1609.04106
  21. H. N. Brenner, J. S. Depret-Guillaume, E. A. Palsson, R. W. Stuckey, "Characterizing optimal point sets determining one distinct triangle", Involve, 13 (2020), no. 1, 91-98. arXiv:1910.00633
  22. J. DeWitt, K. Ford, E. Goldstein, S. J. Miller, G. Moreland, E. A. Palsson, S. Senger, "Dimensional lower bounds for Falconer type incidence theorems", Journal d'Analyse Mathématique, 139 (2019), 143-154. arXiv:1612.00539
  23. 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", Integers, 19 (2019), Paper No. A12, 13 pp. arXiv:1706.08424
  24. A. Epstein, A. Lott, S. J. Miller, E. A. Palsson, "Optimal point sets determining few distinct triangles", Integers, 18 (2018), Paper No. A16, 17 pp. arXiv:1609.00206
  25. 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
  26. 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), no. 1, 125-150. arXiv:1508.07531
  27. Y. Do, R. Oberlin, E. A. Palsson, "Variation-norm and fluctuation estimates for ergodic bilinear averages", Indiana University Mathematics Journal, 66 (2017), no. 1, 55-99. arXiv:1504.07134
  28. A. Iosevich, M. Mourgoglou, E. A. Palsson, "On angles determined by fractal subsets of the Euclidean space", Mathematical Research Letters, 23 (2016), no. 6, 1737-1759. arXiv:1110.6792
  29. D. Burt, E. Goldstein, S. Manski, S. J. Miller, E. A. Palsson, H. Suh, "Crescent configurations", Integers, 16 (2016), #A38. arXiv:1509.07220
  30. B. Murphy, E. A. Palsson, G. Petridis, "The cardinality of sumsets: different summands",
    Acta Arithmetica, 167 (2015), no. 4, 375-395. arXiv:1309.2191
  31. 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
  32. L. Grafakos, A. Greenleaf, A. Iosevich, E. A. Palsson, "Multilinear generalized Radon transforms and point configurations", Forum Mathematicum, 27 (2015), no.4, 2323-2360. arXiv:1204.4429
  33. D. Geba, A. Greenleaf, A. Iosevich, E. A. Palsson, E. Sawyer, "Restricted convolution inequalities, multilinear operators and applications", Mathematical Research Letters, 20 (2013), no. 4, 675-694. arXiv:1209.6574
  34. Y. Do, R. Oberlin, E. A. Palsson, "Variational bounds for a dyadic model of the bilinear Hilbert transform",
    Illinois Journal of Mathematics, 57 (2013), no. 1, 105-120. arXiv:1203.5135
  35. E. A. Palsson, "Lp estimates for a singular integral operator motviated by Calderón's second commutator",
    Journal of Functional Analysis, 262 (2012), no. 4, 1645-1678. arXiv:1104.5160

Thesis

  1. E. A. Palsson, "Lp estimates for a singular integral operator motivated by Calderón's second commutator",
    PhD Thesis, Cornell University, May 2011.

Selected Talks

Have given over 99 research talks at colloquia, conferences and seminars. See the CV for more details.