I am a James H. Simons Instructor and NSF Postdoctoral Fellow at Stony Brook University. I study the geometry of sets and measures using a mixture of geometric measure theory, harmonic analysis and quasiconformal analysis.
In Fall 2014, I will join the faculty at the University of Connecticut.
Complex Analysis, Probability and Metric Geometry: AMS Special Session at the Southeastern Spring Sectional Meeting in Knoxville, March 22 and 23, 2014.
Harmonic Analysis, Partial Differential Equations and Geometric Measure Theory: AMS Special Session at the Joint Mathematics Meeting in San Diego, January 10, 2013.
MAT 550: Real Analysis II
MAT 638: Brownian Motion and Harmonic Measure
MAT 211: Introduction to Linear Algebra
MAT 322: Analysis in Several Dimensions
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: