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 timefrequency analysis to study both L^{p} estimates, variational estimates and sparse estimates for such operators. These operators are frequently motivated by, and have potential applications to, both nonlinear partial differential equations and ergodic theory.
Submitted
 E. A. Palsson, E. Yu, "On optimal point sets determining distinct triangles", (2023), submitted, arXiv:2308.13107.
 T. C. Anderson, A. V. Kumchev, E. A. Palsson, "A framework for discrete bilinear spherical averages and applications to ℓ^{p}improving estimates", (2023), submitted, arXiv:2305.14346.
 J. Gaitan, A. Greenleaf, E. A. Palsson, G. Psaromiligkos, "On restricted Falconer distance sets", (2023), submitted, arXiv:2305.18053.
 Z. Boone, E. A. Palsson, "A pinned MattilaSjölin type theorem for product sets", (2022), submitted, arXiv:2210.00675.
 E. A. Palsson, F. Romero Acosta, "A MattilaSjölin theorem for simplices in low dimensions", (2021), submitted, arXiv:2208.07198.
 E. A. Palsson, S. R. Sovine, "Sparse bounds for maximal triangle averaging operators", (2021), submitted, arXiv:2110.08928.
 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.
 A. Iosevich, E. A. Palsson, "An improved dimensional threshold for the angle problem", (2018), submitted, arXiv:1807.05465.
 R. F. Durst, M. Hlavacek, C. Huynh, S. J. Miller, E. A. Palsson, "Classification of crescent configurations", (2016), submitted, arXiv:1610.07836.
 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.
Accepted
 B. Cook, K. Hughes, E. Palsson, "Supercritical discrete restriction estimates for forms in many variables", (2020), accepted for publication in Proceedings of the Edinburgh Mathematical Society, arXiv:2004.02301.
Published
 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, 165181. arXiv:2108.12034
 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, (2023) https://doi.org/10.1007/s0045402200466w. arXiv:2108.12015
 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
 E. A. Palsson, F. Romero Acosta, "A MattilaSjölin theorem for triangles", Journal of Functional Analysis, 284 (2023), no. 6, Paper No. 109814, 20 pp. arXiv:2109.13429
 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
 T. C. Anderson, A. V. Kumchev, E. A. Palsson, "Discrete maximal operators over surfaces of higher codimension", La Matematica, 1 (2022), no. 2, 442479. arXiv:2006.09968
 A. Iosevich, E. A. Palsson, S. R. Sovine, "Simplex averaging operators: quasiBanach and L^{p}improving bounds in lower dimensions", Journal of Geometric Analysis, 32 (2022), no. 3, Paper No. 87, 16 pp. arXiv:2109.09017
 T. C. Anderson, E. A. Palsson, "Bounds for discrete multilinear spherical maximal functions", Collectanea Mathematica, 73 (2022), no. 1, 7587. arXiv:1910.11409
 E. A. Palsson, S. Senger, C. Wolf, "Angle chains and pinned variants", Bulletin of the Hellenic Mathematical Society, 65 (2021), 3553. arXiv:2104.09960
 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, 243260, Springer Proceedings in Mathematics & Statistics, 297, Springer, Cham, 2021. arXiv:2011.15055
 E. A. Palsson, S. Senger, A. Sheffer, "On the number of discrete chains", Proceedings of the American Mathematical Society, 149 (2021), no. 12, 53475358. arXiv:1902.08259
 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, 855860. arXiv:1911.00464
 H. N. Brenner, J. S. DepretGuillaume, 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
 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), 277307. arXiv:2011.14502
 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
 E. A. Palsson, S. R. Sovine, "The triangle averaging operator", Journal of Functional Analysis, 279 (2020), no. 8, #108671, 21 pp. arXiv:1910.01282
 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), 95109. arXiv:1609.04106
 H. N. Brenner, J. S. DepretGuillaume, E. A. Palsson, R. W. Stuckey, "Characterizing optimal point sets determining one distinct triangle", Involve, 13 (2020), no. 1, 9198. arXiv:1910.00633
 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), 143154. arXiv:1612.00539
 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
 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
 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, 2736. arXiv:1509.03029
 R. Dorward, P. Ford, E. Fourakis, P. Harris, S. Miller, E. A. Palsson, H. Paugh, "A Generalization of Zeckendorf's Theorem via Circumscribed mgons", Involve, 10 (2017), no. 1, 125150. arXiv:1508.07531
 Y. Do, R. Oberlin, E. A. Palsson, "Variationnorm and fluctuation estimates for ergodic bilinear averages", Indiana University Mathematics Journal, 66 (2017), no. 1, 5599. arXiv:1504.07134
 A. Iosevich, M. Mourgoglou, E. A. Palsson, "On angles determined by fractal subsets of the Euclidean space", Mathematical Research Letters, 23 (2016), no. 6, 17371759. arXiv:1110.6792
 D. Burt, E. Goldstein, S. Manski, S. J. Miller, E. A. Palsson, H. Suh, "Crescent configurations", Integers, 16 (2016), #A38. arXiv:1509.07220

B. Murphy, E. A. Palsson, G. Petridis, "The cardinality of sumsets: different summands",
Acta Arithmetica, 167 (2015), no. 4, 375395. arXiv:1309.2191  A. Greenleaf, A. Iosevich, B. Liu, E. A. Palsson, "A grouptheoretic viewpoint on ErdosFalconer problems and the Mattila integral", Revista Matematica Iberoamericana, 31 (2015), no. 3, 799810. arXiv:1306.3598
 L. Grafakos, A. Greenleaf, A. Iosevich, E. A. Palsson, "Multilinear generalized Radon transforms and point configurations", Forum Mathematicum, 27 (2015), no.4, 23232360. arXiv:1204.4429
 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, 675694. arXiv:1209.6574

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, 105120. arXiv:1203.5135 
E. A. Palsson, "L^{p} estimates for a singular integral operator motviated by Calderón's second commutator",
Journal of Functional Analysis, 262 (2012), no. 4, 16451678. arXiv:1104.5160 
E. A. Palsson, "L^{p} estimates for a singular integral operator motivated by Calderón's second commutator",
PhD Thesis, Cornell University, May 2011.