M. Burak Erdoğan Professor Department of Mathematics, University of Illinois, 1409 W. Green Street (MC-382) Urbana, Illinois 61801 Office: 347 Illini Hall Phone: (217) 265-6761 E-mail: berdogan at illinois edu Teaching: Math 540 B1, Real Analysis (MWF 10-10:50am, 243 Mechanical Eng. Bldg.) Previous teaching Biographical Information: 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 Research Interests: Harmonic Analysis Dispersive PDE Students: William R. Green, PhD 2010. Assoc Prof at Rose-Hulman Institute of Technology. Faruk Temur, PhD 2013. Asst Prof at Izmir Institute of Technology. Seckin Demirbas, PhD 2015. Postdoc at Univ British Columbia (joint with N. Tzirakis) Ebru Toprak, PhD 2018. Postdoctoral Researcher at MSRI (Fall 2018) & Hill Asst Prof at Rutgers (starting December 2018). She received 2019 AWM Dissertation Prize. Terence Harris Chi Huynh External grants: 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 Publications (supported in part by NSF): (with B. Gurel and N. Tzirakis) "Fifth order KP-II equation on the upper half plane ", preprint 2018, 38 pages. (with M. Goldberg and W. Green) "The Massless Dirac Equation in Two Dimensions: Zero-Energy Obstructions and Dispersive Estimates", preprint 2018, 37 pages, submitted, [pdf] (with G. Shakan) "Fractal solutions of dispersive partial differential equations on the torus", preprint 2018, 30 pages, accepted by Selecta Math., revised version [pdf] (with W. Green and E. Toprak) "Dispersive estimates for massive Dirac operators in dimension two", J. Differential Equations 264 (2018), no. 9, 5802--5837. [pdf] (with B. Gurel and N. Tzirakis) "The derivative nonlinear Schrodinger equation on the half line", preprint 2017, 36 pages, accepted by Ann. Inst. H. Poincare Anal. Non Lineaire [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, accepted by Commun. Math. Phys. , [pdf] (with M. Goldberg and W. Green) "On the Lp boundedness of wave operators for two-dimensional Schrodinger operators with threshold obstructions", J. Funct. Anal. 274 (2018), no. 7, 2139--2161. [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, accepted by Amer. J. Math., revised version [pdf] (with N. Tzirakis) "Regularity properties of the Zakharov system on the half line", Comm. Partial Differential Equations 42 (2017), no. 7, 1121--1149. [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. Links: Mathematics: Mountaineering: