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:

Publications (supported in part by NSF):

  1. (with W. Green) "Dispersive estimates for the Schr\"odinger equation for $C^{\frac{n-3}{2}}$ potentials in odd dimensions", preprint 2009, submitted, [pdf]
  2. (with N. Tzirakis and V. Zharnitsky) "Near-linear dynamics in KdV with periodic boundary conditions", preprint 2009, submitted, [pdf]
  3. (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", preprint 2009, submitted, [pdf]
  4. (with D. Hundertmark and Y.-R. Lee) "Exponential decay of dispersion managed solitons for vanishing average dispersion", preprint 2008, submitted, [pdf]
  5. (with R. Oberlin) "Estimates for the X-ray transform restricted to 2-manifolds", accepted by Rev. Mat. Ibero.,   [pdf]
  6. (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), no.
    4, 687--722. [pdf]
  7. (with V. Zharnitsky) "Quasi-linear dynamics in nonlinear Schr\" odinger equation with periodic boundary conditions", Commun. Math. Phys., 281 (2008), no. 3, 655--673.  [pdf]
  8. (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]
  9. (with M. Christ) "Mixed norm estimates for certain generalized Radon transforms", Trans. Amer. Math. Soc., 360 (2008), no. 10, 5477--5488. [pdf]
  10. (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 , 199-248 (2006). [pdf]
  11. "A bilinear Fourier extension theorem and applications to the distance set problem", IMRN, 2005:23, 1411-1425 (2005). [pdf]
  12. "On Falconer's distance set conjecture", Rev. Mat. Ibero., 22, 649-662 (2006). [pdf]
  13. (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, No. 4, 359-379 (2004). [pdf]
  14. "A note on the Fourier transform of fractal measures", Math. Res. Lett., 11 no. 2-3, 299-313 (2004). [pdf]
  15. (with R. Killip and W. Schlag) "Energy growth in Schrodinger's equation with Markovian forcing", Commun. Math. Phys., 240, 1-29 (2003). [pdf]
  16. "Mapping properties of the elliptic maximal function", Rev. Mat. Ibero., 19, 221-234 (2003). [pdf]
  17. (with M. Christ)"Mixed norm estimates for a restricted X-ray transform", J. d'Analyse, 87, 187-198 (2002). [pdf]
  18. "Mixed norm estimates for a restricted X-ray transform in R^4 and R^5", IMRN, 2001, No.11, 575-600. [pdf]
  19. "Analytic and asymptotic properties of non-symmetric Linnik's densities", J. Fourier Anal. Appl., 5, 523-544 (1999).
  20. (with I.V. Ostrovskii) "On mixture representation of the Linnik density", J. Austral. Math. Soc. Ser. A, 64, no. 3, 317-326 (1998).
  21. (with I.V. Ostrovskii) "Analytic and asymptotic properties of generalized Linnik Probability densities", J. Math. Anal. Appl., 217, 555-579 (1998).
  22. (with I.V. Ostrovskii) "Non-symmetric Linnik Distributions", C.R. Acad. Sci. Paris, 325, Serie I, 511-516 (1997).

Links:

Mathematics:


Mountaineering:
Friends with home pages:
Turkish Newspapers and Magazines: