Polona Durcik

Polona Durcik

   I am a postdoc at the Department of Mathematics at Caltech.

   Office: 304
   Phone: 626 395 3744
   E-mail: durcik (at) caltech (dot) edu

Caltech/UCLA joint Analysis seminar


Spring 2019: Math 110c


Research interests: Harmonic analysis, applications of real analysis techniques to ergodic theory and arithmetic combinatorics.

  • (with C. Thiele) Singular Brascamp-Lieb: a survey, Proceedings of 'Geometric Aspects of Harmonic Analysis', on the occasion of Fulvio Ricci's 70th birthday, arXiv:1904.08844.
  • (with J. Roos) Averages of simplex Hilbert transformsarXiv:1812.11701.
  • (with V. Kovač) Boxes, extended boxes, and sets of positive upper density in the Euclidean spacearXiv:1809.08692.
  • (with C. Thiele) Singular Brascamp-Lieb inequalitiesarXiv:1809.08688.
  • (with S. Guo, J. Roos) A polynomial Roth theorem on the real line, To appear in Trans. Amer. Math. Soc., arXiv:1704.01546.
  • (with V. Kovač, L. Rimanić) On side lengths of corners in positive density subsets of the Euclidean space, To appear in Int. Math. Res. Not., arXiv:1609.09056.
  • (with V. Kovač, C. Thiele) Power-type cancellation for the simplex Hilbert transform, To appear in J. Anal. Math., arXiv:1608.00156.
  • (with V. Kovač, K. A. Škreb, C. Thiele) Norm-variation of ergodic averages with respect to two commuting transformations,  To appear in Ergodic Theory Dynam. Systems., arXiv:1603.00631.
  • Lp estimates for a singular entangled quadrilinear form, Trans. Amer. Math. Soc. 369 (2017), no. 10, 6935-6951., arXiv:1506.08150.
  • An L4 estimate for a singular entangled quadrilinear form, Math. Res. Lett. 22 (2015), no. 5, 1317-1332., arXiv:1412.2384.
  • Lp estimates for entangled multilinear forms, Master's thesis (2014), pdf.


Math Genealogy