I am an Associate Professor of Mathematics. I study the geometry of sets and measures in Euclidean space and general metric spaces using a mixture of geometric measure theory, harmonic analysis and quasiconformal analysis.
My recent work has focused on the question of how to construct good parameterizations of connected sets by Lipschitz and Hölder continuous maps.
Analysis Learning Seminar Low pressure environment for local participants (grad students, postdocs, faculty) to share ideas related to analysis. Mix of levels and topics. The learning seminar is currently on break. Please attend the A&P seminar. If you are a student and interested in resuming the learning seminar, please contact me.
PDE and Differential Geometry Seminar Another research seminar featuring latest advances in the field. Mondays at 2:30.
2023 Northeast Analysis Network: September 23-24 at University of Rochester. This is a regional conference series in collaboration with SUNY Albany, Syracuse University, and University of Rochester. (We last hosted the conference at UConn in 2019.)
Geometric and Harmonic Analysis: a Conference for Graduate Students: March 29-31, 2019.
Nonsmooth Analysis: a Workshop for Postdocs: November 9-11, 2017.
[Math Course Schedules: Current Semester]
Math 2210 Applied Linear Algebra
Math 5440 Partial Differential Equations
Course materials for students available on HuskyCT
Lisa Naples, Ph.D. August 2020
I am happy to advise Ph.D. students who would like to carry out research at the interface of analysis and geometry.
I can support a UConn graduate student as a research assistant (no teaching duties) in Summer 2024, Fall 2024, and Summer 2025.
Here is a picture related to my "Harmonic polynomials..." and "Flat points..." papers. The zero sets of homogeneous harmonic polynomials in x,y,z of odd degree may separate space into two components (cross your eyes to see a stereographic picture):
500x4y-1000x2y3+100y5 -5(x4+y4)z+10(x2+y2)z3+2z5=0 intersecting the unit sphere
[Statistics] Newest preprints/papers are listed first.
PhD Thesis: Harmonic Polynomials and Free Boundary Regularity for Harmonic Measure from Two Sides. Defended on May 5, 2011.
Selected slides from research talks and colloquiua, in reverse chronological order: