Malabika Pramanik's Research

Areas of interest


I got my Ph.D. in Mathematics from the University of California, Berkeley, under the guidance of Prof. Michael Christ. I was a Van Vleck visiting assistant professor at University of Wisconsin, Madison (2001-2004), visiting assistant professor at the University of Rochester (Fall 2004), and a Fairchild Senior Research Fellow at Caltech (January 2005 - August 2006). I joined the Mathematics Department at UBC in Fall 2006. (For more details, here is a copy of my CV (March 2016) in PDF format).


  1. On the maximal directional Hilbert transform. (Joint work with I. Laba and A. Marinelli) To appear in Analysis Mathematica
  2. On large sets avoiding patterns. (Joint work with R. Fraser) Analysis and PDE Volume 11, Number 5 (2018), 1083-1111.
  3. A discrete Carleson theorem along the primes with a restricted supremum. (Joint work with L. Cladek, K. Henriot, B. Krause, I. Laba) Math. Z. (2018) 289: 1033.
  4. A Roth-type theorem for dense subsets of R^d. (Joint work with B. Cook and A. Magyar) Bulletin of the London Mathematical Society, 49 No.4: 676-689 (2017)
  5. Necklaces inside thin sets of R^d. (Joint work with A. Greenleaf and A. Iosevich) Mathematics Research Letters, 24 No. 2: 347-362, 2017.
  6. On polynomial congurations in fractal sets (Joint work with K. Henriot and I. Laba) Analysis and PDE, 9 No. 5: 1153-1184, 2016.
  7. Kakeya-Type sets over Cantor sets of directions in R^d+1. (Joint work with Edward Kroc) J. Fourier Anal. Appl. (2016) 22: 623.
  8. Finite configurations in sparse sets. (Joint work with V. Chan and I. Laba) J. d'Analyse Math. (2016) 128: 289.
  9. Chaotic dynamics of the heat semigroup on Riemannian symmetric spaces. (Joint work with R. Sarkar) J. Funct. Anal., 266 No. 5: 2867-2909, 2014.
  10. A multidimensional resolution of singularities with applications to analysis. (Joint work with Tristan Collins and Allan Greenleaf) Amer. J. Math., 135 No.5: 1179-1252, 2013. (arXiv preprint)
  11. Diagonal estimates for the Bergman kernel in monomial-type domains. (Joint work with A. Nagel) Proceedings of the conference in honor of Eli Stein, Princeton, 2011.
  12. Maximal operators and differentiation theorems for sparse sets. (Joint work with Izabella Laba) Duke Math. J., 158 No.3: 347-411, 2011.
  13. An FIO calculus for marine seismic imaging, II: Sobolev estimates (Joint work with Raluca Felea and Allan Greenleaf) Math. Annalen DOI: 10.1007/s00208-011-0644-5.
  14. A Calder?n-Zygmund estimate with applications to generalized Radon transforms and Fourier integral operators. (Joint work with Keith Rogers and Andreas Seeger) Studia Math., 202 (2011), 1-15.
  15. Multilinear singular operators with fractional rank. (Joint work with Ciprian Demeter and Christoph Thiele) Pacific J. of Mathematics 246 (2010) no. 2, 293--324
  16. Maximal averages over linear and monomial polyhedra. (Joint work with Alexander Nagel) Duke Math. J. Volume 149 Number 2 (2009), 209-277.
  17. Arithmetic progressions in sets of fractional dimension. (Joint work with Izabella Laba) Geom. Funct. Anal. 19 (2009), 429-456.
  18. Oscillatory integral operators with homogeneous polynomial phases in several variables. (Joint work with Allan Greenleaf and Wan Tang) J. Functional Analysis (2007, volume 244, 444-487). (pdf)
  19. Double Hilbert transform along real-analytic surfaces in $\mathbb{R}^{d+2}$. (Joint work with Chan Woo Yang) J. London Math. Soc. (2008) 77(2):363-386.
  20. Averages over curves in $\mathbb{R}^3$ and associated maximal functions. (Joint work with Andreas Seeger) Amer. J. Math. (2007, volume 21, number 3, 61-103). (pdf)
  21. $L^p$ Sobolev regularity of a restricted X-ray transform. (Joint work with Andreas Seeger) Harmonic Analysis and its Applications at Osaka, Conference Proceedings (November 2004, 47-64). (pdf)
  22. Wolff's inequality for hypersurfaces. (Joint work with Izabella Laba). To appear in the Proceedings of El Escorial, 2005. (pdf)
  23. $L^p$ decay estimates for weighted oscillatory integral operator on $\mathbb{R}$. (Joint work with Chan Woo Yang) Revista Matematica Iberoamericana (2005, volume 21, number 3, 1071--1095). (pdf)
  24. Decay estimates for weighted scalar oscillatory integrals on $\mathbb{R}^2$. (Joint work with Chan Woo Yang) Indiana University Mathematical Journal (2004, volume 53, number 2, 613-645). (pdf)
  25. A weak $L^2$ estimate for a maximal dyadic sum operator on $\mathbb{R}^n$. (Joint work with Erin Terwilleger) Illinois Journal of Mathematics (2003, volume 47, number 3, 775-813). (pdf)
  26. Convergence of two-dimensional weighted integrals. Transactions of the American Mathematical Society (2002, volume 354, number 4, 1651-1665). (pdf)
  27. Weighted inequalities for real-analytic functions in $\mathbb{R}^2$. Journal of Geometric Analysis (2002, volume 12, number 2, 265-288). (pdf)

Preprints/In preparation

  1. Lacunarity, Kakeya-type sets and directional maximal operators. (Joint work with E. Kroc) (arXiv preprint)
  2. Diagonal estimates for the Bergman kernel on certain domains in $\mathbb{C}^n$. (Joint work with Alexander Nagel).
  3. Measures on monomial polyhedra. (Joint work with Alexander Nagel)
Malabika Pramanik
Last modified: Sept 4 2016