My research is in classical analysis. I am interested in understanding how to resolve singularities of polynomials or more generally real-analytic functions, for applications in analysis. In addition, I am generally interested in oscillatory integrals and Radon transforms.
More detailed information about the following papers may be found here.
"Oscillatory integral decay, sublevel set growth, and the Newton polyhedron," submitted. PS PDF
"Resolution of singularities, asymptotic expansions of sublevel sets, and applications," preprint, to be submitted. PS PDF
"Simply nondegenerate multilinear oscillatory integral operators with smooth phase," to appear, Math. Res. Lett. PS PDF
"A coordinate-dependent local resolution of singularities with applications," submitted. PS PDF
"A T(1) theorem for singular Radon transforms", Math Annalen vol 339 no. 3, (2007) 599-626. PS PDF
"Stability of sublevel set estimates and sharp L^2 regularity of Radon transforms in the Plane", Math Res Letters, v.12 (2005) #1, 1-17. PS PDF
"An analog to a theorem of Fefferman and Phong for averaging operators along curves with fractional integral kernel", to appear, GAFA, 2007. PS PDF
"Sharp estimates for oscillatory integral operators with C-infinity phase", American J of Math. vol 127 (2005) #3 659-695. PS PDF
"A direct resolution of singularities for functions of two variables with applications to analysis", J. Anal. Math. 92 (2004), 233--257. PS PDF
"Newton polygons and local integrability of negative powers of smooth functions in the plane", Trans. Amer. Math. Soc. vol 358 (2006), #2, 657-670. PS PDF
"Scalings, metrics, and smoothing of translation-invariant Radon transforms along curves", J. Funct. Anal. 206 (2004), no. 2, 307--321. PS
"Boundedness of singular Radon transforms on L^p spaces under a finite-type condition", Amer. J. of Math., (2001). PS
"A method for proving L^p boundedness of singular Radon transforms in codimension one for 1 < p < infinity", Duke Math Journal 108 (2001), 363-393. PS