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.
Stability of Oscillatory Integral Asymptotics in Two Dimensions, submitted. PDF
A resolution of singularities algorithm for local fields of characteristic zero and some applications, submitted. PS PDF
L^p boundedness of maximal averages over hypersurfaces in R^3, to appear, Trans. AMS PS PDF
Maximal averages over hypersurfaces and the Newton polyhedron, J. Funct. Anal. vol 262 #5 (2012) 2314--2348. PS PDF
Resolution of singularities in two dimensions and the stability of integrals, Adv. Math., 226 #2 (2011) 1772--1802, PS PDF
Resolution of singularities, asymptotic expansions of integrals, and applications, J. Analyse Math. vol 111 #1 (2010) 221-245. PS PDF
Oscillatory integral decay, sublevel set growth, and the Newton polyhedron, Math. Annalen vol. 346 #4 (2010), 857-890. PS PDF
The asymptotic behavior of degenerate oscillatory integrals in two dimensions, J. Funct. Anal. vol 257 #6 (2009), 1759--1798. PS PDF
A coordinate-dependent local resolution of singularities with applications, J. Funct. Anal. vol. 255, #8 (2008) 1957--1994.PS PDF
Simply nondegenerate multilinear oscillatory integral operators with smooth phase, Math. Res. Lett. vol. 15 #4 (2008) 653-660. PS PDF
A T(1) theorem for singular Radon transforms, Math Annalen vol 339 no. 3, (2007) 599-626. PDF
An analog to a theorem of Fefferman and Phong for averaging operators along curves with fractional integral kernel, GAFA, vol 17, no. 4 (2007), 1106--1138. 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
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
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
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