Polona Durcik

Polona Durcik

   Harry Bateman Instructor
   Department of Mathematics, Caltech

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

Math Genealogy

Caltech/UCLA joint Analysis seminar

Teaching

Spring 2020: Ma110c
Winter 2020: Ma108b, Ma191b
Spring 2019: Ma110c
Winter 2019: Ma6b, Ma108b
Spring 2018: Ma191c
Winter 2018: Ma6b, Ma108b

Research

Research interests: Harmonic analysis and its connections with ergodic theory, arithmetic combinatorics and PDE.

Preprints:
  • (with V. Kovač) A Szemerédi-type theorem for subsets of the unit cube, submitted, arXiv:2003.01189.
  • (with L. Cladek, B. Krause, J. Madrid) Directional maximal function along the primes, submitted, arXiv:1909.13319.
  • (with C. Thiele) Singular Brascamp-Lieb: a survey,  To appear in the Springer INdAM Series, Proceedings of Geometric Aspects of Harmonic Analysis, Cortona 2018, arXiv:1904.08844.
  • (with J. Roos) Averages of simplex Hilbert transforms, submitted, arXiv:1812.11701.
  • (with V. Kovač) Boxes, extended boxes, and sets of positive upper density in the Euclidean space, submitted, arXiv:1809.08692.
  • (with C. Thiele) Singular Brascamp-Lieb inequalities with cubical structure, To appear in Bull. Lond. Math. Soc., arXiv:1809.08688.
  • (with S. Guo, J. Roos) A polynomial Roth theorem on the real line, Trans. Amer. Math. Soc. 371 (2019), no. 10, 6973-6993., arXiv:1704.01546.
  • (with V. Kovač, L. Rimanić) On side lengths of corners in positive density subsets of the Euclidean space, Int. Math. Res. Not. 2018, no. 22, 6844-6869., arXiv:1609.09056.
  • (with V. Kovač, C. Thiele) Power-type cancellation for the simplex Hilbert transform, J. Anal. Math. (2019). https://doi.org/10.1007/s11854-019-0052-4 arXiv:1608.00156.
  • (with V. Kovač, K. A. Škreb, C. Thiele) Norm-variation of ergodic averages with respect to two commuting transformations,  Ergodic Theory Dynam. Systems 39 (2019), no. 3, 658-688., 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.