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.
In Fall 2019, we are continuing the Analysis Learning Seminar. Meeting time is Fridays 3:30-4:30. This seminar will primarily feature introductory talks by UConn graduate students and postdocs. All graduate students and advanced math majors who are interested in analysis, geometry, and probability are welcome to attend! Organized by me and Marco Carfagnini
2019 Northeast Analysis Network: September 21-22, 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 5120: Complex Analysis
Math 2210Q (Sections 2 and 3): Applied Linear Algebra
I am happy to advise Ph.D. students who would like to carry out research at the interface of analysis and geometry.
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: