M. Burak Erdoğan
Professor
Department of
Mathematics,
University of Illinois,
1409 W. Green Street (MC382)
Urbana, Illinois 61801
Office: CAB 41
Phone: (217) 2656761
Email: berdogan at illinois edu
Teaching:
 Math 542, Complex Variables I (Fall 2023), MWF 1111:50, 119 English Building
 Math 428, Honors Topics: Intro to Fourier Analysis (Fall 2023), MWF 1212:50, 140 Henry
Biographical
Information:
Research Interests:
Students:
External grants:
 NSF DMS2154031, award date: 04/05/2022
 Simons collaboration grant 634269, award date: 9/1/2019
 NSF DMS1501041, award date: 5/15/2015
 NSF DMS1201872, award date: 5/15/2012
 NSF DMS0900865, award date: 6/1/2009
 NSF DMS0600101, award date: 5/15/2006
 NSF DMS0540084, award date: 9/1/2004
 NSF DMS0303413, award date: 7/1/2003
Publications
(supported in part by the grants above):
 (with M. Goldberg and W. Green) "Dispersive estimates for higher order Schrodinger operators with scalingcritical potentials", preprint 2023, 25pp, submittted, [pdf]
 (with C. Huynh and R. McConnell) "Talbot Effect on the Sphere and Torus for d >= 2", preprint 2023, 42pp, to appear in Math Z. [pdf]
 (with W. Green) "A note on endpoint Lpcontinuity of wave operators for classical and higher order Schrodinger operators",
J. Differential Equations 355 (2023), 144161. [pdf]
 (with M. Goldberg and W. Green) "The Lpunboundedness of wave operators for higher order Schrodinger operators", J. Funct. Anal. 285 (2023), no. 5, 110008 [pdf]
 (with W. Green) "The Lp continuity of wave operators for higher order Schrodinger operators", Adv. Math. 404 (2022), Paper No. 108450, 41 pp. [pdf]
 (with W. Green and E. Toprak) "What is the Dirac equation?",
Notices Amer. Math. Soc. 68 (2021), no. 10, 17821785. [pdf]
 (with W. Green) "On the one dimensional Dirac equation with potential ", Jour. de Mathématiques Pures et Appliquées. 151
(9) (2021), 132170. [Revised pdf]
 (with A. Barron and T. Harris) "Fourier decay of fractal measures on hyperboloids",
Trans. Amer. Math. Soc. 374 (2021), no. 2, 10411075. [pdf]
 (with W. Green and E. Toprak) "On the fourth order Schrodinger equation in three dimensions: Dispersive estimates and zero energy resonances ",
J. Differential Equations 271 (2021), 152185. [pdf]
 (with M. Goldberg and W. Green) "The Massless Dirac Equation in Two Dimensions: ZeroEnergy Obstructions and Dispersive Estimates", J. Spectral Theory 11
(2021), no. 3, 935979. [pdf]
 (with M. Goldberg and W. Green) "Strichartz estimates for the Schrodinger equation with a measurevalued potential ", Proc. Amer. Math. Soc. Ser. B 8 (2021), 336348. [pdf]
 (with B. Gurel and N. Tzirakis)
"Fifth order KPII equation on the upper half plane ", Differential and Integral Eqns 33 (2020), 555596 [pdf].
 (with W. Green and E. Toprak) "Dispersive estimates
for Dirac operators in dimension three with obstructions
at threshold energies", Amer. J. Math. 141 (2019), no. 5, 12171258 [pdf]
 (with B. Gurel and N. Tzirakis)
"Smoothing for the fractional Schrodinger equation on the torus and the real line", Indiana Univ. Math. J. 68 (2019), no. 2, 369392.
[pdf]
 (with G. Shakan) "Fractal solutions of dispersive partial differential equations on the torus", Selecta Math. (N.S.) 25 (2019), no. 1, Art. 11, 26 pp. [pdf]
 (with M. Goldberg and W. Green) "Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions", Commun. Math. Phys. 367 (2019), 241263. [pdf]
 (with W. Green and E. Toprak) "Dispersive estimates
for massive Dirac operators in dimension two", J. Differential Equations 264 (2018), no. 9, 58025837. [pdf]
 (with B. Gurel and N. Tzirakis)
"The derivative nonlinear Schrodinger equation on the half line", Ann. Inst. H. Poincare Anal. Non Lineaire 35 (2018), 19471973. [pdf]
 (with M. Goldberg and W. Green) "On the Lp boundedness of wave operators for twodimensional Schrodinger operators with threshold
obstructions", J. Funct.
Anal. 274 (2018), no. 7, 21392161. [pdf]
 (with N. Tzirakis) "Regularity properties of the
Zakharov system on the half line", Comm. Partial Differential Equations 42 (2017), no. 7, 11211149. [pdf]
 (with W. Green) "The Dirac equation in two dimensions:
Dispersive estimates and classification of threshold
obstructions", Commun. Math. Phys. 352 (2017), no. 2, 719757. [pdf]
 (with N. Tzirakis) "Dispersive partial differential
equations, wellposedness and applications", London
Mathematical Society Student Texts 86,
Cambridge University Press, 2016.
 (with N. Tzirakis) "Regularity properties of the cubic nonlinear Schrodinger equation
on the half line", J. Funct.
Anal. 271 (2016),
no. 9, 25392568. [pdf]
 (with S. Demirbas and N. Tzirakis) "Existence and uniqueness
theory for the fractional Schrodinger equation on the
torus". Some topics in harmonic analysis and applications,
145162, Advanced Lectures in
Mathematics (ALM), 34, Int. Press, Somerville, MA, 2016.
[pdf]
 (with J.
Marzuola, K. Newhall, and N. Tzirakis) "The structure of global
attractors for dissipative Zakharov systems with
forcing on the torus", SIAM J. Appl. Dyn.
Syst. 14 (2015), no. 4, 19781990.
[pdf]
 (with V. Chousionis and N. Tzirakis) "Fractal solutions of
linear and nonlinear dispersive partial differential
equations", Proc. Lond. Math. Soc. (3) 110
(2015), no. 3, 543564. [pdf]
 (with M. Goldberg and W. Green) "Dispersive estimates for four dimensional
Schrodinger and wave equations with obstructions at
zero energy", Comm. Partial Differential Equations. 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. d'Analyse 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 Math.
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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