May 5 - August 22, 2014
Organizers: Herbert Koch, Daniel Tataru, Christoph Thiele
Description: Harmonic analysis and partial differential equations have been closely interlinked areas in recent decades, with ideas flowing back and forth and stimulating progress in both areas. This program brought together researchers in these two fields, some who had worked in both fields and some who had specialized in one field but were interested in learning more about the other. The aim was to strengthen existing links between the areas and open new lines of research, making use of the many possible ways in which new developments in one area impact the other.
Associated Events: Four workshops took place:
- Introductory Workshop "Topics in Harmonic Analysis and PDEs", May 12-16
- Workshop "Harmonic Analysis Methods in Dispersive PDEs", June 10-13
- Workshop on Real Analysis (with a joint session with Number Theory), July 14-18
- Closing Workshop, August 4-8
© Rogue II, Courtesy of Eric J. Heller
| No. | Author(s) | Title | Preprint | Publication |
| 2014b01 | Ivanisvili, P.; Stolyarov, D. M.; Zatitskiy, P. B. | Bellman vs Beurling: sharp estimates of uniform convexity for Lp spaces | 1405.6229 | St. Petersburg Math. J. (transl.). 27(2) (2016), 333–343. https://doi.org/10.1090/spmj/1390 |
| 2014b02 | Bernicot, F.; Coulhon, T.; Frey, D. | Gaussian heat kernel bounds through elliptic Moser iteration | 1407.3906 | J. Math. Pures Appl. 106(6) (2016), 995–1037. https://doi.org/10.1016/j.matpur.2016.03.019 |
| 2014b03 | Nguyen, C. P. | The Navier-Stokes equations in nonendpoint borderline Lorentz spaces | 1407.5129 | J. Math. Fluid Mech. 17(4) (2015), 741–760. https://doi.org/10.1007/s00021-015-0229-2 |
| 2014b04 | Volberg, A.; Yuditskii, P. | Mean type of functions of bounded characteristic and Martin functions in Denjoy domains | 1406.7737 | Adv. Math. 290 (2016), 860–887. https://doi.org/10.1016/j.aim.2015.12.012 |
| 2014b05 | Treil, S.; Volberg, A. | Entropy conditions in two weight inequalities for singular integral operators | 1408.0385 | Adv. Math. 301 (2016), 499–548. https://doi.org/10.1016/j.aim.2016.06.021 |
| 2014b06 | Ifrim, M.; Tataru, D. | The lifespan of small data solutions in two dimensional capillary water waves | 1406.5471 | Arch. Ration. Mech. Anal. 225(3) (2017), 1279–1346. https://doi.org/10.1007/s00205-017-1126-z |
| 2014b07 | Bejenaru, I.; Herr, S. | On global well-posedness and scattering for the massive Dirac-Klein-Gordon system | 1409.1778 | J. Eur. Math. Soc. (JEMS) 19(8) (2017), 2445–2467. https://doi.org/10.4171/JEMS/721 |
| 2014b08 | Müller, P. F.X.; Müller, S. | Interpolatory estimates, Riesz transforms and wavelet projections | 1409.2143 | Rev. Mat. Iberoam. 32(4) (2016), 1137–1162. https://doi.org/10.4171/RMI/910 |
| 2014b09 | Lechner, R.; Müller, P. F.X. | Localization and projections on bi-parameter BMO | 1410.8786 | Q. J. Math. 66(4) (2015), 1069–1101. https://doi.org/10.1093/qmath/hav028 |
| 2014b10 | Ivanisvili, P.; Volberg, A. | Hessian of Bellman functions and uniqueness of Brascamp-Lieb inequality | 1411.5349 | J. Lond. Math. Soc. 92(3) (2015), 657–674. https://doi.org/10.1112/jlms/jdv040 |
| 2014b11 | Ivanisvili, P.; Osipov, N. N.; Stolyarov, D. M.; Vasyunin, V. I.; Zatitskiy, P. B. | Sharp estimates of integral functionals on classes of functions with small mean oscillation | 1412.4749 | C. R. Math. Acad. Sci. Paris. 353(12) (2015), 1081–1085. https://doi.org/10.1016/j.crma.2015.07.016 |
| 2014b12 | Kim, J. | A characterization of maximal operators associated with radial Fourier multipliers | 1501.07669 | Proc. Amer. Math. Soc. 145(3) (2017), 1077–1085. https://doi.org/10.1090/proc/13445 |
| 2014b13 | Killip, R.; Oh, T.; Pocovnicu, O.; Visan, M. | Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on ℝ3 | 1409.6734 | Arch. Ration. Mech. Anal. 225(1) (2017), 469–548. https://doi.org/10.1007/s00205-017-1109-0 |
| 2014b14 | Oh, T. | Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data | 1502.02258 | Commun. Pure Appl. Anal. 14(4) (2015), 1563–1580. https://doi.org/10.3934/cpaa.2015.14.1563 |
| 2014b15 | Bényi, Á.; Oh, T. | Linear and bilinear T(b) theorems à la Stein | 1502.02260 | Proc. Amer. Math. Soc. Ser. 2 (2015), 1–16. https://doi.org/10.1090/bproc/18 |
| 2014b16 | Bejenaru, I.; Guo, Z.; Herr, S.; Nakanishi, K. | Well-posedness and scattering for the Zakharov system in four dimensions | 1504.01073 | Anal. PDE. 8(8) (2015), 2029–2055. https://doi.org/10.2140/apde.2015.8.2029 |
| 2014b17 | Krause, B.; Zorin-Kranich, P. | Weighted and vector-valued variational estimates for ergodic averages | 1409.7120 | Ergodic Theory Dynam. Systems. 38(1) (2018), 244–256. https://doi.org/10.1017/etds.2016.27 |
| 2014b18 | Mirek, M.; Trojan, B.; Zorin-Kranich, P. | Variational estimates for averages and truncated singular integrals along the prime numbers | 1410.3255 | Trans. Amer. Math. Soc. 369(8) (2017), 5403–5423. https://doi.org/10.1090/tran/6822 |
| 2014b19 | Müller, D.; Seeger, A. | Sharp Lp-bounds for the wave equation on groups of Heisenberg type | 1408.3051 | Anal. PDE. 8(5) (2015), 1051–1100. https://doi.org/10.2140/apde.2015.8.1051 |
| 2014b20 | Seeger, A.; Ullrich, T. | Haar projection numbers and failure of unconditional convergence in Sobolev spaces | 1507.01211 | Math. Z. 285(1-2) (2017), 91–119. https://doi.org/10.1007/s00209-016-1697-7 |
| 2014b21 | Killip, R.; Visan, M. | Scale invariant Strichartz estimates on tori and applications | 1409.3603 | Math. Res. Lett. 23(2) (2016), 445–472. https://doi.org/10.4310/MRL.2016.v23.n2.a8 |
| 2014b22 | Killip, R.; Murphy, J.; Visan, M. | The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions | 1506.06151 | Anal. PDE. 9(7) (2016), 1523–1574. https://doi.org/10.2140/apde.2016.9.1523 |
| 2014b23 | Ivanisvili, P.; Volberg, A. | Bellman partial differential equation and the hill property for classical isoperimetric problems | 1506.03409 | |
| 2014b24 | Hong, Y.; Taliaferro, K.; Xie, Z. | Uniqueness of solutions to the 3D quintic Gross-Pitaevskii hierarchy | 1410.6961 | J. Funct. Anal. 270(1) (2016), 34–67. https://doi.org/10.1016/j.jfa.2015.10.003 |
| 2014b25 | Lacey, M. T. | An elementary proof of the A2 bound | 1501.05818 | Israel J. Math. 217(1) (2017), 181–195. https://doi.org/10.1007/s11856-017-1442-x |
| 2014b26 | Lacey, M. T.; Spencer, S. | On entropy bumps for Calderón-Zygmund operators | 1504.02888 | Concr. Oper. 2(1) (2015), 47–52. https://doi.org/10.1515/conop-2015-0003 |
| 2014b27 | Eisner, T.; Krause, B. | (Uniform) convergence of twisted ergodic averages | 1407.4736 | Ergodic Theory Dynam. Systems. 36(7) (2016), 2172–2202. https://doi.org/10.1017/etds.2015.6 |
| 2014b28 | Donninger, R.; Schörkhuber, B. | On blowup in supercritical wave equations | 1411.7905 | Comm. Math. Phys. 346(3) (2016), 907–943. https://doi.org/10.1007/s00220-016-2610-2 |
| 2014b29 | Donninger, R.; Schörkhuber, B. | Stable blowup for wave equations in odd space dimensions | 1504.00808 | Ann. Inst. H. Poincaré C Anal. Non Linéaire. 34(5) (2017), 1181–1213. https://doi.org/10.1016/j.anihpc.2016.09.005 |
| 2014b30 | Stolyarov, D. M.; Zatitskiy, P. B. | Theory of locally concave functions and its applications to sharp estimates of integral functionals | 1412.5350 | Adv. Math. 291 (2016), 228–273. https://doi.org/10.1016/j.aim.2015.11.048 |
| 2014b31 | Dat, C. T.; Verbitsky, I. | Nonlinear elliptic equations and intrinsic potentials of Wolff type | 1409.4076 | J. Funct. Anal. 272(1) (2017), 112–165. https://doi.org/10.1016/j.jfa.2016.10.010 |
| 2014b32 | Gonçalves, F. | Interpolation formulas with derivatives in de Branges spaces | 1503.05178 | Trans. Amer. Math. Soc. 369(2) (2017), 805–832. https://doi.org/10.1090/tran6672 |
| 2014b33 | Frey, D.; McIntosh, A.; Portal, P. | Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in Lp | 1407.4774 | JAMA. 134 (2018), 399–453. https://doi.org/10.1007/s11854-018-0013-3 |
| 2014b34 | Portal, P.; van Neerven, J. | Finite speed of propagation and off-diagonal bounds for Ornstein-Uhlenbeck operators in infinite dimensions | 1507.02082 | Ann. Mat. Pura Appl. 195(6) (2016), 1889–1915. https://doi.org/10.1007/s10231-015-0541-8 |
| 2014b35 | Borthwick, D.; Marzuola, J. L. | Dispersive estimates for scalar and matrix Schrödinger operators on ℍn+1 | 1410.8829 | Math. Phys. Anal. Geom. 18(1) 22 (2015), 26. https://doi.org/10.1007/s11040-015-9191-8 |
| 2014b36 | Buschenhenke, S.; Müller, D.; Vargas, A. | A Fourier restriction theorem for a two-dimensional surface of finite type | 1508.00791 | Anal. PDE. 10(4) (2017), 817–891. https://doi.org/10.2140/apde.2017.10.817 |
| 2014b37 | Harrop-Griffiths, B.; Ifrim, M.; Tataru, D. | The lifespan of small data solutions to the KP-I | 1409.4487 | Int. Math. Res. Not. IMRN 1 (2017), 1–28. https://doi.org/10.1093/imrn/rnw017 |
| 2014b38 | Laustsen, N. J.; Lechner, R.; Müller, P. F.X. | Factorization of the identity through operators with large diagonal | 1509.03141 | J. Funct. Anal. 275(11) (2018), 3169–3207. https://doi.org/10.1016/j.jfa.2018.02.010 |
| 2014b39 | D'Ancona, P.; Cassano, B. | Scattering in the energy space for the NLS with variable coefficients | 1502.00937 | Math. Ann. 366(1-2) (2016), 479–543. https://doi.org/10.1007/s00208-015-1335-4 |
| 2014b40 | Harrop-Griffiths, B. | Long time behavior of solutions to the mKdV | 1407.1406 | Comm. Partial Differential Equations. 41(2) (2016), 282–317. https://doi.org/10.1080/03605302.2015.1114495 |
| 2014b41 | Koch, H.; Tataru, D. | Conserved energies for the cubic NLS in 1-d | 1607.02534 | |
| 2014b42 | Mirek, M.; Stein, E. M.; Trojan, B. | Lp(Zd)-estimates for discrete operators of Radon type: maximal functions and vector-valued estimates | 1512.07518 | J. Funct. Anal. 277(8) (2019), 2471-2521. https://doi.org/10.1016/j.jfa.2018.10.020 |
| 2014b43 | Seeger, A.; Ullrich, T. | Lower bounds for Haar projections: deterministic examples | 1511.01470 | Constr. Approx. 46(2) (2017), 227–242. https://doi.org/10.1007/s00365-016-9353-3 |
| 2014b44 | Chen, X. | Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds III: global-in-time Strichartz estimates without loss | 1504.02375 | Ann. Inst. H. Poincaré C Anal. Non Linéaire. 35(3) (2018), 803–829. https://doi.org/10.1016/j.anihpc.2017.08.003 |
| 2014b45 | Hughes, K.; Krause, B.; Trojan, B. | The maximal function and conditional square function control the variation: an elementary proof | 1408.1213 | Proc. Amer. Math. Soc. 144(8) (2016), 3583–3588. https://doi.org/10.1090/proc/12866 |
| 2014b46 | Feehan, P. M.N. | Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow | 1409.1525 | |
| 2014b47 | Krause, B.; Zorin-Kranich, P. | A random pointwise ergodic theorem with Hardy field weights | 1410.0806 | Illinois J. Math. 59(3) (2015), 663–674. https://doi.org/10.1215/ijm/1475266402 |
| 2014b48 | Wang, X. | Global infinite energy solutions for the 2d gravity water waves system | 1502.00687 | Comm. Pure Appl. Math. 71(1) (2018), 90–162. https://doi.org/10.1002/cpa.21711 |
| 2014b49 | Ivanisvili, P.; Volberg, A. | Isoperimetric functional inequalities via the maximum principle: the exterior differential systems approach | 1511.06895 | 50 Years with Hardy Spaces. Op. Th.: Adv. and App. 261. https://doi.org/10.1007/978-3-319-59078-3_14 |
| 2014b50 | Ivanisvili, P.; Volberg, A. | Poincaré inequality 3/2 on the Hamming cube | 1608.04021 | Rev. Mat. Iberoam. 36(1) (2020), 79–97. https://doi.org/10.4171/rmi/1122 |
| 2014b51 | Thiele, C.; Treil, S.; Volberg, A. | Weighted martingale multipliers in the non-homogeneous setting and outer measure spaces | 1411.5345 | Adv. Math. 285 (2015), 1155–1188. https://doi.org/10.1016/j.aim.2015.08.019 |
| 2014b52 | Dodson, B. | Global well-posedness and scattering for the focusing, energy-critical nonlinear Schrödinger problem in dimension d=4 for initial data below a ground state threshold | 1409.1950 | |
| 2014b53 | Oliveira e Silva, D.; Thiele, C. | Estimates for certain integrals of products of six Bessel functions | 1509.06309 | Rev. Mat. Iberoam. 33(4) (2017), 1423–1462. https://doi.org/10.4171/RMI/977 |
| 2014b54 | Carneiro, E.; Oliveira e Silva, D.; Sousa, M. | Extremizers for Fourier restriction on hyperboloids | 1708.03826 | Ann. Inst. H. Poincaré C Anal. Non Linéaire. 36(2) (2019), 389–415. https://doi.org/10.1016/j.anihpc.2018.06.001 |
| Name | Affiliation |
| Alex Amenta | Université Paris-Sud |
| Theresa Anderson | Brown University |
| Ioannis Angelopoulos | University of Toronto |
| Pascal Auscher | Université Paris-Sud |
| Ioan Bejenaru | University of California, San Diego |
| Arpad Benyi | Western Washington University |
| Frederic Bernicot | CNRS - Laboratoire Jean Leray |
| Dmitriy Bilyk | University of Minnesota |
| Tristan Buckmaster | Universität Leipzig |
| Aynur Bulut | University of Michigan |
| Aynur Bulut | University of Michigan |
| Stefan Buschenhenke | ICMAT |
| Federico Cacciafesta | Universita' di Roma |
| Federico Cacciafesta | Universita' di Roma |
| Timothy Candy | Imperial College London |
| Emanuel Carneiro | IMPA |
| Pedro Pérez Caro | University of Helsinki |
| Juan Cavero de Carondelet | Consejo Superior de Investigaciones Cientificas |
| Xi Chen | Australian National University |
| Antoine Choffrut | School of Mathematics, University of Edinburgh |
| Antoine Choffrut | School of Mathematics, University of Edinburgh |
| Antoine Choffrut | School of Mathematics, University of Edinburgh |
| Michael Christ | University of California |
| David Cruz-Uribe | Trinity College |
| Piero D'Ancona | University of Roma I - Sapienza |
| Galia Dafni | Concordia University |
| Guy David | Université de Paris Sud |
| Jean-Marc Delort | Université Paris 13 |
| Ciprian Demeter | Indiana University |
| Francesco di Plinio | Università di Roma |
| Martin Dindos | University of Edinburgh |
| Benjamin Dodson | University of California - Berkeley |
| Roland Donninger | EPF Lausanne |
| Oliver Dragicevic | University of Ljubljana |
| Polona Durcik | Universität Bonn |
| Thomas Duyckaerts | Paris 13 University |
| Tatjana Eisner | University of Leipzig |
| Boris Ettinger | Princeton University |
| Paul Feehan | Rutgers University |
| Renan Finder | IMPA |
| Dorothee Frey | Australian National University |
| Cristian Dan Gavrus | UC Berkeley |
| Patrick Gerard | Université Paris-Sud |
| Pierre Germain | New York University |
| Felipe Ferreira Gonçalves | IMPA |
| Jordan Greenblatt | UCLA |
| Shaoming Guo | Universität Bonn |
| Zihua Guo | School of Mathematical Sciences |
| Benjamin Harrop-Griffiths | University of California, Berkeley |
| Haakan Hedenmalm | KTH Royal Institute of Technology |
| Sebastian Herr | Universität Bielefeld |
| Jonathan Hickman | The University of Edinburgh |
| Steven Hofmann | University of Missouri |
| Kevin Hughes | University of Edinburgh |
| Dirk Hundertmark | Karlsruhe Institute of Technology |
| Tuomas Hytönen | University of Helsinki |
| Mihaela Ifrim | University of California, Berkeley |
| Alexandru Ionescu | Princeton University |
| Paata Ivanishvili | Michigan State University |
| Ben Jaye | Kent State University |
| Rowan Killip | UCLA |
| Jongchon Kim | University of Wisconsin-Madison |
| Herbert Koch | Universität Bonn |
| Vjekoslav Kovac | University of Zagreb |
| Benjamin Krause | UCLA |
| Joachim Krieger | EPFL |
| Christoph Kröner | UC Berkeley |
| Soonsik Kwon | Korea Advanced Institute of Science and Technology |
| Michael T. Lacey | Georgia Institute of Technology |
| Nicolas Laillet | Université Paris-Diderot |
| Tobias Lamm | Karlsruhe Institute of Technology |
| Phi Long Le | University of Missouri-Columbia |
| Richard Lechner | Johannes Kepler Universität |
| Junfeng Li | Beijing Normal Univeristy, University of Bonn |
| Baoping Liu | University of Chicago |
| Guozhen Lu | Wayne State University |
| Teresa Luque | Universidad de Sevilla |
| Jonas Lührmann | ETH Zurich |
| Jose Ramon Madrid Padilla | IMPA |
| Yvan Martel | Ecole Polytechnique |
| Jose Maria Martell | Consejo Superior de Investigaciones Cientificas |
| Jeremy Marzuola | University of North Carolina, Chapel Hill |
| Svitlana Mayboroda | University of Minnesota |
| Dana Mendelson | Massachusetts Institute of Technology |
| Frank Merle | Université de Cergy-Pontoise |
| Mariusz Mirek | Universität Bonn |
| Andrew Morris | University of Oxford |
| Jason Murphy | University of California Los Angeles |
| Camil Muscalu | Cornell University |
| Paul F. X. Müller | J. Kepler Universität |
| Detlef Müller | C.A.-Universität zu Kiel |
| Kenji Nakanishi | Kyoto University |
| Cong Phuc Nguyen | Louisiana State University |
| Sung-Jin Oh | University of California, Berkeley |
| Tadahiro (Choonghong) Oh | The University of Edinburgh |
| Diogo Oliveira e Silva | Universität Bonn |
| Eyvindur Palsson | University of Rochester |
| Benoit Pausader | Princeton |
| Lillian Pierce | Universität Bonn |
| Oana Pocovnicu | Institute for Advanced Study |
| Pierre Portal | Australian National University |
| Malabika Pramanik | University of British Columbia |
| María Cruz Prisuelos Arribas | ICMAT |
| Maria del Carmen Reguera Rodriguez | University of Birmingham |
| Joris Roos | Universität Bonn |
| Angkana Rueland | University of Oxford |
| Birgit Schörkhuber | Vienna University of Technology |
| Andreas Seeger | University of Wisconsin - Madison |
| Wenhui Shi | University of Bonn |
| Christopher Sogge | Johns Hopkins University |
| Vedran Sohinger | University of Pennsylvania |
| Mateus Costa de Sousa | IMPA |
| Gigliola Staffilani | MIT |
| Elias M. Stein | Princeton University |
| Stefan Steinerberger | Yale University |
| Andrei Stoica | University of Lund |
| Dmitriy Stolyarov | Steklov Mathematical Institute of the Russian Academy of Sciences |
| Brian Street | University of Wisconsin-Madison |
| Michael Struwe | ETH Zurich |
| Kenneth Taliaferro | University of Texas at Austin |
| Daniel Tataru | University of California at Berkeley |
| Christoph Thiele | Universität Bonn |
| Kyle Thompson | Univeristy of Toronto |
| Sergey Tikhonov | ICREA and Centre de Recerca Matemàtica |
| Xavier Tolsa | Universitat Autònoma de Barcelona |
| Bartosz Trojan | University of Wroclaw |
| Gennady Uraltsev | Universität Bonn |
| Ignacio Uriarte-Tuero | Michigan State University |
| Armen Vagharshakyan | Kent State University |
| Ana Vargas | Universidad Autónoma de Madrid |
| Luis Vega | BCAM - Basque Center for Applied Mathematics |
| Igor Verbitsky | University of Missouri |
| Francisco Villarroya Alvarez | Lunds Universitet |
| Monica Visan | UCLA |
| Marco Vitturi | University of Edinburgh |
| Alexander Volberg | Michigan Sate University |
| Xuecheng Wang | Princeton University |
| Yuzhao Wang | North China Electric Power University (Memorial University of Newfoundland for now) |
| Klaus Widmayer | New York University |
| James Wright | University of Edinburgh |
| Blazej Wróbel | University of Wroclaw |
| Zhihui Xie | The University of Texas at Austin |
| Po Lam Yung | University of Oxford |
| Lifeng Zhao | University of Science and Technology of China |
| Jiqiang Zheng | The Graduate School of China Academy of Engineering PhysicsMathematics |
| Christian Zillinger | Universität Bonn |
| Pavel Zorin-Kranich | Hebrew University |
| Kristina Ana Škreb | University of Zagreb |
This list does not include people who only participated in the workshops.
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