M. BURAK ERDOGAN
Professor
Department of Mathematics,
University of Illinois,
1409 W. Green Street (MC-382)
Urbana, Illinois 61801

Office: 369 Altgeld Hall
Phone: (217) 265-6761
E-mail: berdogan at math uiuc edu


Teaching:


Biographical Information:


Research Interests:

  • Harmonic Analysis
  • Dispersive PDE

Students:

  • William R. Green (PhD 2010. Asst Prof in Rose-Hulman Institute of Technology)
  • Faruk Temur (PhD 2013)
  • Seckin Demirbas (joint with N. Tzirakis)
  • Hee Yeon Kim (joint with N. Tzirakis)
  • Ebru Toprak

External grants:

  • NSF DMS-1201872, award date: 5/15/12
  • NSF DMS-0900865, award date: 6/1/09
  • NSF DMS-0600101, award date: 5/15/06
  • NSF DMS-0540084, award date: 9/1/04
  • NSF DMS-0303413, award date 7/1/03

Publications (supported in part by NSF):

  1. (with V. Chousionis and N. Tzirakis) "Fractal solutions of linear and nonlinear dispersive partial differential equations", preprint 2014, 22pp, accepted by Proc. Lond. Math. Soc[pdf]
  2. (with S. Demirbas and N. Tzirakis) "Existence and uniqueness theory for the fractional Schrodinger equation on the torus", preprint 2013, 19pp, to appear in Advanced Lectures in Mathematics (ALM), edited by S. T. Yau, K. Liu, and L. Ji. Special issue in honor of Prof. Shanzhen Lu., [pdf]
  3. (with J. Marzuola and N. Tzirakis) "The structure of global attractors for dissipative Zakharov systems with forcing on the torus", preprint 2013, 16pp, submitted, [pdf]
  4. (with M. Goldberg and W. Green) "Dispersive estimates for four dimensional Schrodinger and wave equations with obstructions at zero energy",  Comm. PDE. 39:10 (2014), 1936--1964. [pdf]
  5. (with N. Tzirakis) "Talbot effect for the cubic nonlinear Schrodinger equation on the torus", Math. Res. Lett. 20 (2013), 1081--1090. [pdf]
  6. (with W. Green) "Dispersive estimates for matrix Schrodinger operators in dimension two", DCDS-A 33 (2013), 4473--4495. [pdf]
  7. (with N. Tzirakis) "Smoothing and global attractors for the Zakharov system on the torus", Analysis & PDE 6-3 (2013), 723--750. [pdf]
  8. (with W. Green) "A weighted dispersive estimate for Schrodinger operators in dimension two", Commun. Math. Phys. 319 (2013), 791--811.   [pdf]
  9. (with W. Green) "Dispersive estimates for Schrodinger operators in dimension two with obstructions at zero energy", Trans. Amer. Math. Soc. 365 (2013), 6403--6440  [pdf]
  10. (with N. Tzirakis) "Long time dynamics for forced and weakly damped KdV on the torus", Commun. Pure Appl. Anal. 12 (2013), 2669--2684. [pdf].
  11. (with N. Tzirakis) "Global smoothing for the periodic KdV evolution", Int. Math. Res. Notices (2013), 4589--4614.  [pdf].
  12. (with D. Hart and  A. Iosevich) "Multi-parameter projection theorems with applications to sums-products and finite point configurations in the Euclidean setting", Recent Advances in Harmonic Analysis and Applications, Springer Proceedings in Mathematics & Statistics Volume 25, 2013, 93--103.
  13. (with Dan Oberlin) "Restricting the Fourier transform of measures to curves in R^2", Can. Math. Bull. 56 (2013), 326--336. [pdf]
  14. (with N. Tzirakis and V. Zharnitsky) "High frequency perturbation of cnoidal waves", SIAM J. Math. Anal. 44 (2012), no. 6, 4147--4164. [pdf]
  15. (with J. Chapman, D. Hart, A. Iosevich and D. Koh) "Pinned distance sets, k-simplices, Wolff's exponent in finite fields and sum-product estimates", Math Z 271 (2012), 63--93, [pdf]
  16. (with N. Tzirakis and V. Zharnitsky) "Near-linear dynamics of nonlinear dispersive waves", Physica D 240 (2011), 1325--1333. [pdf]
  17. (with D. Hundertmark and Y.-R. Lee) "Exponential decay of dispersion managed solitons for vanishing average dispersion", Math. Res. Lett. 18 (2011), no. 01, 11--24,   [pdf]
  18. (with N. Tzirakis and V. Zharnitsky) "Near-linear dynamics in KdV with periodic boundary conditions", Nonlinearity 23 (2010) 1675--1694.  [pdf]
  19. (with W. Green) "Dispersive estimates for the Schrodinger equation for $C^{\frac{n-3}{2}}$ potentials in odd dimensions", Int Math Res Notices 2010:13, 2532--2565. [pdf]
  20. (with R. Oberlin) "Estimates for the X-ray transform restricted to 2-manifolds", Rev. Mat. Ibero. 26 (2010), 91--114.   [pdf]
  21. (with M. Goldberg and W. Schlag) "Strichartz and smoothing estimates for Schrodinger operators with almost critical magnetic potentials in three and higher dimensions", Forum Math. 21 (2009), 687--722. [pdf]
  22. (with V. Zharnitsky) "Quasi-linear dynamics in nonlinear Schr\" odinger equation with periodic boundary conditions", Commun. Math. Phys. 281 (2008), 655--673.  [pdf]
  23. (with M. Goldberg and W. Schlag) "Strichartz and smoothing estimates for Schrodinger operators with large magnetic potentials in R^3", J. Eur. Math. Soc. (JEMS) 10 (2008), no. 2, 507--531. [pdf]
  24. (with M. Christ) "Mixed norm estimates for certain generalized Radon transforms", Trans. Amer. Math. Soc. 360 (2008), no. 10, 5477--5488. [pdf]
  25. (with W. Schlag) "Dispersive estimates for Schrodinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II",  J. Anal. Math. 99 (2006), 199--248. [pdf]
  26. "A bilinear Fourier extension theorem and applications to the distance set problem", Int. Math. Res. Not. 2005:23, 1411--1425. [pdf]
  27. "On Falconer's distance set conjecture", Rev. Mat. Ibero. 22 (2006), 649--662. [pdf]
  28. (with W. Schlag) "Dispersive estimates for Schrodinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: I", Dynamics of PDE 1 (2004), 359--379. [pdf]
  29. "A note on the Fourier transform of fractal measures", Math. Res. Lett. 11 (2004), 299--313. [pdf]
  30. (with R. Killip and W. Schlag) "Energy growth in Schrodinger's equation with Markovian forcing", Commun. Math. Phys. 240 (2003), 1--29. [pdf]
  31. "Mapping properties of the elliptic maximal function", Rev. Mat. Ibero. 19 (2003), 221--234. [pdf]
  32. (with M. Christ)"Mixed norm estimates for a restricted X-ray transform", J. d'Analyse 87 (2002), 187--198. [pdf]
  33. "Mixed norm estimates for a restricted X-ray transform in R^4 and R^5", Int. Math. Res. Not. 2001, No.11, 575--600. [pdf]
  34. "Analytic and asymptotic properties of non-symmetric Linnik's densities", J. Fourier Anal. Appl. 5 (1999), 523--544.
  35. (with I.V. Ostrovskii) "On mixture representation of the Linnik density", J. Austral. Math. Soc. Ser. A 64 (1998), 317--326.
  36. (with I.V. Ostrovskii) "Analytic and asymptotic properties of generalized Linnik Probability densities", J. Math. Anal. Appl. 217 (1998), 555--579.
  37. (with I.V. Ostrovskii) "Non-symmetric Linnik Distributions", C.R. Acad. Sci. Paris Serie I 325 (1997), 511--516.

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