Research
Research Interests
I am interested in Geometric Measure Theory and, in particular, I study rectifiability of measures in Euclidean and Hilbert spaces. During the 2020-2021 academic year, I participated in the AMS Mathematics Research Community on Analysis in Metric Space, and I have since been studying problems at the intersection of Geometric Measure Theory and Metric Space Analysis.
Publications
Badger, Matthew; Naples, Lisa; Vellis, Vyron. Hölder curves and parameterizations in the analyst's traveling salesman theorem. Adv. Math. 349 (2019), 564--647. MR3941391 (link to arXiv version)
Badger, Matthew; Naples, Lisa. Radon measures and Lipschitz graphs. Bull. Lond. Math. Soc. 53 (2021), no. 3, 921--936. MR4275101 (link to arXiv version)
Eriksson-Bique, S., Gartland, C., Donne, E.L., Naples, L. and Nicolussi-Golo, S.. Nilpotent groups and biLipschitz embeddings into L^ 1. International Mathematics Research Notices 2023 (12), 10759-1079 (link to arXiv version)
Submitted Articles
Naples, Lisa, 2020. Rectifiability of pointwise doubling measures in Hilbert Space. arXiv preprint arXiv:2002.07570 (link to arXiv version)
McCurdy, Sean; Naples, Lisa, 2022. Non-existence of cusps for degenerate Alt-Caffarelli functionals arXiv preprint arXiv:2202.00616 (link to arXiv version)
Alvarado, Enrique G. ; Catalano, Louisa; Merchan, Tomas; Naples Lisa, 2023. Asymptotics of Maximum Distance Minimizers arXiv preprint arXiv:2309.08055 (link to arXiv version)
Research with Undergraduates
During Summer 2024 I co-mentored a research project through the Polymath Jr. project. My research group is currently putting together a site to display our work which we hope to make available soon!
During Summer 2021 I worked with two undergraduate student researchers on a project funding by Macalester College's Collaborative Summer Grant.
If you are at undergraduate student at Fairfield University interesting in exploring research in Analysis, feel free to reach out to discuss opportunities!
Recent and Upcoming Research Talks
- Asymptotics of Maximum Distance Minimizers, Geometry of Measures and Free Boundaries: A conference in honor of Tatiana Toro, July 2024
- JMM 2025, AMS Special Session on Non-smooth Analysis and Geometry , January 2023
Recent and Upcoming Research Conference Organization
Co-organizer (with Ryan Alvarado and Matthew Badger), Fall 2025 Sectional Meeting, AMS Special Session on Nonsmooth Analysis and Geometry
Co-organizer (with Evan Randles), JMM 2024, AMS Special Session on Analysis and Differential Equations at Undergraduate Institutions