Work in Preparation:

• Reduction of the Kohn Conjecture to a Nullstellensatz (new version in preparation)
• An Approximate Diederich-Fornaess Theorem (with Dmitri Zaitsev; in preparation)

Submitted Work and Preprints

• A Global Nullstellensatz for Ideals of Denjoy-Carleman Functions (with Francesca Acquistapace and Fabrizio Broglia; arXiv:1412.4461v1 [math.AG] 15 Dec 2014; 5 pages; submitted)
• Direct Proof of Termination of the Kohn Algorithm in the Real-Analytic Case (arXiv:1409.0963v1 [math.CV]  3 Sep 2014; 33 pages; submitted)
• The Kohn Algorithm on Denjoy-Carleman Classes (arXiv:0806.1917v5 [math.CV] 12 Aug 2014; 22 pages; submitted)

Work Accepted and In Press:

• On the Relationship between D'Angelo q-Type and Catlin q-Type (with Vasile Brinzanescu; arXiv:1302.2294v4 [math.CV] 8 Jan 2014; DOI: 10.1007/s12220-014-9490-5; 18 pages; in press at the Journal of Geometric Analysis)

Published Work:

• A Nullstellensatz for Lojasiewicz Ideals (with Francesca Acquistapace and Fabrizio Broglia; arXiv:1210.2504v1 [math.AG] 9 Oct 2012) Revista Matematica Iberoamericana 30 (2014), no. 4, 1479-1487;  DOI 10.4171/RMI/822
  
• Coherence and Other Properties of Sheaves in the Kohn Algorithm (arXiv:1308.5289v1 [math.AG] 24 Aug 2013) Internat. J. Math. 25(8):1450077 (13 pages), 2014; DOI: 10.1142/S0129167X14500773
• Failure of the Weierstrass Preparation Theorem in Quasi-analytic Denjoy-Carleman Rings (with Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein, and Nahum Zobin; arXiv:1212.4265v3 [math:CA] 5 Mar 2014) Advances in Mathematics 258C (2014), pp. 397-413; DOI: 10.1016/j.aim.2014.03.002 (pdf)
  
• Effective Vanishing Order of the Levi Determinant (arXiv:1102.0356v2 [math.CV] 13 Feb 2011) Mathematische Annalen 354 (2012) no.4, 1223-1245; DOI: 10.1007/s00208-011-0742-4
• Global Regularity for $\bar\partial_b$ on Weakly Pseudoconvex CR Manifolds (math.CV/0512072) Advances in Mathematics 199 (2006) 356-447 (pdf)
  
• The $\bar\partial_b$ Equation on Weakly Pseudoconvex CR Manifolds of Dimension 3 (with J.J. Kohn; math.CV/0512073) Journal of Functional Analysis 230 (2006), no.2, 251-272 (pdf)