M. BURAK ERDOGAN
Associate 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, submitted, [pdf]
  2. (with S. Demirbas and N. Tzirakis) "Existence and uniqueness theory for the fractional Schrodinger equation on the torus", preprint 2013, 19pp, submitted, [pdf]
  3. (with M. Goldberg and W. Green) "Dispersive estimates for four dimensional Schrodinger and wave equations with obstructions at zero energy", preprint 2013, 32pp, accepted by Communications in PDE. [pdf]
  4. (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]
  5. (with N. Tzirakis) "Talbot effect for the cubic nonlinear Schrodinger equation on the torus", preprint 2013, 12pp, accepted by Math. Res. Lett. [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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