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. A particularly rich source of inspiration for me 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. In this setting, geometric averaging operators, such as averaging a function over a sphere, arise naturally and play a key role in answering the point configuration questions as well as being of independent interest.
- E. A. Palsson, F. Romero Acosta, A Mattila-Sjölin theorem for triangles, Journal of Functional Analysis, 284 (2023), no. 6, #109814.
- 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.
- 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.
- 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.
- E. A. Palsson, S. R. Sovine, The triangle averaging operator, Journal of Functional Analysis, 279 (2020), no. 8, #108671.
- 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.
- 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.
- 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.