M. BURAK ERDOGAN
Professor
Department of
Mathematics,
University of Illinois,
1409 W. Green Street (MC382)
Urbana, Illinois 61801
Office: 369 Altgeld Hall
Phone: (217) 2656761
Email: berdogan at math uiuc edu
Teaching:
Biographical
Information:
Research
Interests:
 Harmonic Analysis
 Dispersive PDE
Students:

William R. Green (PhD 2010. Asst Prof in
RoseHulman 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 DMS1201872, award date: 5/15/12
 NSF DMS0900865, award date: 6/1/09
 NSF DMS0600101, award date: 5/15/06
 NSF DMS0540084, award date: 9/1/04
 NSF DMS0303413, award date 7/1/03
Publications
(supported in part by NSF):
 (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]
 (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]
 (with J.
Marzuola, K. Newhall, and N. Tzirakis) "The structure of global
attractors for dissipative Zakharov systems with
forcing on the torus", preprint 2013, 16pp,
revised, [pdf]
 (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), 19361964. [pdf]
 (with N. Tzirakis) "Talbot
effect for the cubic nonlinear Schrodinger equation on
the torus", Math. Res. Lett. 20 (2013),
10811090. [pdf]
 (with W. Green) "Dispersive
estimates for matrix Schrodinger operators in
dimension two", DCDSA 33 (2013),
44734495. [pdf]
 (with N. Tzirakis) "Smoothing
and
global attractors for the Zakharov system on the torus",
Analysis & PDE 63 (2013), 723750. [pdf]
 (with W. Green) "A
weighted dispersive estimate for Schrodinger operators
in dimension two", Commun. Math.
Phys. 319
(2013), 791811. [pdf]
 (with W. Green) "Dispersive
estimates for Schrodinger operators in dimension two
with obstructions at zero energy", Trans.
Amer. Math. Soc. 365 (2013),
64036440 [pdf]
 (with N. Tzirakis) "Long
time dynamics for forced and weakly damped KdV on the
torus", Commun.
Pure Appl. Anal. 12 (2013), 26692684. [pdf].
 (with N. Tzirakis) "Global
smoothing for the periodic KdV evolution", Int.
Math. Res. Notices (2013), 45894614. [pdf].
 (with D. Hart
and A.
Iosevich) "Multiparameter
projection
theorems with applications to sumsproducts and finite
point configurations in the Euclidean setting",
Recent Advances in Harmonic Analysis and Applications,
Springer Proceedings in Mathematics & Statistics
Volume 25, 2013, 93103.
 (with Dan
Oberlin) "Restricting
the Fourier transform of measures to curves in R^2",
Can. Math. Bull. 56 (2013), 326336. [pdf]
 (with N. Tzirakis and V. Zharnitsky)
"High frequency
perturbation of cnoidal waves", SIAM J.
Math. Anal. 44
(2012), no. 6, 41474164. [pdf].
 (with J.
Chapman, D. Hart, A. Iosevich and D. Koh)
"Pinned distance sets,
ksimplices, Wolff's exponent in finite fields and
sumproduct estimates", Math Z 271 (2012), 6393,
[pdf]
 (with N. Tzirakis and V. Zharnitsky) "Nearlinear dynamics of
nonlinear dispersive waves", Physica D
240 (2011),
13251333. [pdf]
 (with D.
Hundertmark and Y.R.
Lee) "Exponential
decay of dispersion managed solitons for vanishing
average dispersion", Math. Res. Lett. 18 (2011), no. 01,
1124, [pdf]
 (with N. Tzirakis and V. Zharnitsky) "Nearlinear dynamics in
KdV with periodic boundary conditions", Nonlinearity
23 (2010)
16751694. [pdf]
 (with W. Green) "Dispersive
estimates for the Schrodinger equation for
$C^{\frac{n3}{2}}$ potentials in odd dimensions",
Int Math Res Notices
2010:13, 25322565. [pdf]
 (with R.
Oberlin) "Estimates
for the Xray transform restricted to 2manifolds",
Rev. Mat. Ibero. 26 (2010), 91114.
[pdf]
 (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), 687722.
[pdf]
 (with V. Zharnitsky) "Quasilinear dynamics in nonlinear Schr\"
odinger equation with periodic boundary conditions",
Commun. Math. Phys. 281 (2008), 655673. [pdf]
 (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, 507531. [pdf]
 (with M.
Christ) "Mixed norm estimates for certain
generalized Radon transforms", Trans. Amer. Math. Soc. 360
(2008), no. 10, 54775488. [pdf]
 (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), 199248. [pdf]
 "A bilinear Fourier extension theorem and
applications to the distance set problem", Int.
Math. Res. Not. 2005:23, 14111425. [pdf]
 "On Falconer's distance set conjecture", Rev.
Mat. Ibero. 22 (2006), 649662. [pdf]
 (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),
359379. [pdf]
 "A note on the Fourier transform of fractal
measures", Math. Res. Lett. 11 (2004),
299313. [pdf]
 (with R.
Killip and W. Schlag) "Energy growth in
Schrodinger's equation with Markovian forcing", Commun. Math.
Phys. 240 (2003), 129. [pdf]
 "Mapping properties of the elliptic maximal
function", Rev. Mat. Ibero. 19
(2003), 221234. [pdf]
 (with M. Christ)"Mixed norm estimates for a
restricted Xray transform", J. d'Analyse 87
(2002), 187198. [pdf]
 "Mixed norm estimates for a restricted Xray
transform in R^4 and R^5", Int.
Math. Res. Not. 2001, No.11, 575600. [pdf]
 "Analytic and asymptotic properties of
nonsymmetric Linnik's densities", J. Fourier
Anal. Appl. 5 (1999), 523544.
 (with I.V.
Ostrovskii) "On mixture representation of the
Linnik density", J. Austral. Math. Soc.
Ser. A 64 (1998), 317326.
 (with I.V. Ostrovskii) "Analytic and asymptotic
properties of generalized Linnik Probability densities",
J. Math. Anal. Appl. 217 (1998), 555579.
 (with I.V. Ostrovskii) "Nonsymmetric Linnik
Distributions", C.R. Acad. Sci. Paris Serie I
325 (1997), 511516.
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