Office: 347 Illini Hall
- Math 542 Complex Variables I, Section B1, Fall 2017
- Math 447 Real Variables, Fall 2017
- Previous teaching
- 2014 - Professor at UIUC
- 2009 - 2014 Associate Professor at UIUC
- 2004 - 2009 Assistant Professor at UIUC
- 2002 - 2004 Visiting Asst. Prof. at UC Berkeley
- 2001 - 2002 Postdoctoral member at IAS, Princeton
- 2001 Ph. D. in Mathematics, Caltech (Adviser: Thomas Wolff)
- 1996 M.S. in Mathematics, Bilkent University, Ankara (Adviser: I.V. Ostrovskii)
- 1994 B.S. in Electrical Engineering, Bilkent University, Ankara
- Harmonic Analysis
- Dispersive PDE
- William R. Green, PhD 2010. Asst Prof in Rose-Hulman Institute of Technology.
- Faruk Temur, PhD 2013. Asst Prof in Izmir Institute of Technology.
- Seckin Demirbas, PhD 2015. Postdoc at Univ British Columbia (joint with N. Tzirakis)
- Ebru Toprak
- NSF DMS-1501041, award date: 5/15/2015
- NSF DMS-1201872, award date: 5/15/2012
- NSF DMS-0900865, award date: 6/1/2009
- NSF DMS-0600101, award date: 5/15/2006
- NSF DMS-0540084, award date: 9/1/2004
- NSF DMS-0303413, award date: 7/1/2003
- (with W. Green and E. Toprak) "Dispersive estimates for massive Dirac operators in dimension two", preprint 2017, 40 pages, submitted [pdf]
- (with B. Gurel and N. Tzirakis)
"
*The derivative nonlinear Schrodinger equation on the half line*", preprint 2017, 36 pages, submitted [pdf] - (with M. Goldberg and W. Green) "Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions", preprint 2017, 26 pages, submitted, [pdf]
- (with M. Goldberg and W. Green) "On the Lp boundedness of wave operators for two-dimensional Schrodinger operators with threshold obstructions", preprint 2017, 21 pages, submitted, [pdf]
- (with B. Gurel and N. Tzirakis)
"
*Smoothing for the fractional Schrodinger equation on the torus and the real line*", preprint 2017, 23pp., accepted by**Indiana Univ. Math. J.**[pdf] - (with W. Green and E. Toprak) "Dispersive estimates for Dirac operators in dimension three with obstructions at threshold energies", preprint 2016, 36 pages, submitted [pdf]
- (with N. Tzirakis) "
*Regularity properties of the Zakharov system on the half line*", preprint 2016, 34 pages, accepted by**Comm. Partial Differential Equations**[pdf] - (with W. Green) "The Dirac equation in two dimensions:
Dispersive estimates and classification of threshold
obstructions",
**Commun. Math. Phys.**352 (2017), no. 2, 719--757. [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, 2539--2568. [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,
145–162,
**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, 1978--1990. [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, 543--564. [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), 1936--1964. [pdf] - (with N. Tzirakis) "Talbot effect for the cubic nonlinear Schrodinger equation on
the torus",
**Math. Res. Lett. 20**(2013), 1081--1090. [pdf] - (with W. Green) "Dispersive estimates for matrix Schrodinger operators in
dimension two",
**DCDS-A**33 (2013), 4473--4495. [pdf] - (with N. Tzirakis) "Smoothing and global attractors for the Zakharov system on the torus",
**Analysis & PDE**6-3 (2013), 723--750. [pdf] - (with W. Green) "A
weighted dispersive estimate for Schrodinger operators
in dimension two",
**Commun. Math. Phys.**319 (2013), 791--811. [pdf] - (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] - (with N. Tzirakis) "Long time dynamics for forced and weakly damped KdV on the torus", Commun. Pure Appl. Anal. 12 (2013), 2669--2684. [pdf].
- (with N. Tzirakis) "Global smoothing for the periodic KdV evolution",
**Int. Math. Res. Notices (2013)**, 4589--4614. [pdf].
- (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.
- (with Dan Oberlin) "
Restricting the Fourier transform of measures to curves in R^2",
**Can. Math. Bull.**56 (2013), 326--336. [pdf] - (with N. Tzirakis and V. Zharnitsky)
"High frequency
perturbation of cnoidal waves",
**SIAM J. Math. Anal.**44 (2012), no. 6, 4147--4164. [pdf].
- (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] - (with N. Tzirakis and V. Zharnitsky) "Near-linear dynamics of
nonlinear dispersive waves",
**Physica D**240 (2011), 1325--1333. [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, 11--24, [pdf]
- (with N. Tzirakis and V. Zharnitsky) "Near-linear dynamics in
KdV with periodic boundary conditions",
**Nonlinearity**23 (2010) 1675--1694. [pdf] - (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]
- (with R. Oberlin) "
Estimates for the X-ray transform restricted to 2-manifolds",
**Rev. Mat. Ibero.****26**(2010), 91--114. [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), 687--722. [pdf]
- (with V. Zharnitsky) "Quasi-linear dynamics in nonlinear Schr\"
odinger equation with periodic boundary conditions",
**Commun. Math. Phys.**281 (2008), 655--673. [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, 507--531. [pdf] - (with M.
Christ) "
*Mixed norm estimates for certain generalized Radon transforms*", Trans. Amer. Math. Soc. 360 (2008), no. 10, 5477--5488. [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), 199--248. [pdf] - "
*A bilinear Fourier extension theorem and applications to the distance set problem*",**Int. Math. Res. Not. 2005:23,**1411--1425. [pdf] - "
*On Falconer's distance set conjecture*",**Rev. Mat. Ibero. 22**(2006), 649--662. [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), 359--379. [pdf] - "
*A note on the Fourier transform of fractal measures*",**Math. Res. Lett. 11**(2004), 299--313. [pdf] - (with R.
Killip and W. Schlag) "
*Energy growth in Schrodinger's equation with Markovian forcing*", Commun. Math. Phys.**240**(2003), 1--29. [pdf] - "
*Mapping properties of the elliptic maximal function*",**Rev. Mat. Ibero.****19**(2003), 221--234. [pdf] - (with M. Christ)"
*Mixed norm estimates for a restricted X-ray transform*", J. d'Analyse Math.**87**(2002), 187--198. [pdf] - "
*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] - "
*Analytic and asymptotic properties of non-symmetric Linnik's densities*",**J. Fourier Anal. Appl.****5**(1999), 523--544. - (with I.V. Ostrovskii) "
*On mixture representation of the Linnik density*",**J****. Austral. Math. Soc. Ser. A****64**(1998), 317--326. - (with I.V. Ostrovskii) "
*Analytic and asymptotic properties of generalized Linnik Probability densities*",**J. Math. Anal. Appl. 217**(1998), 555--579. - (with I.V. Ostrovskii) "
*Non-symmetric Linnik Distributions*",**C.R. Acad. Sci. Paris Serie I 325**(1997), 511--516.
- Turkish Journal of Mathematics
- Lecture notes of T. Wolff
- Kakeya page of I. Laba
- Harmonic Analysis page of T. Tao
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