Current Publications

Published and accepted

  1. Douglas N. Arnold and Shawn W. Walker. The Hellan-Herrmann-Johnson method with curved elements. SIAM Journal on Numerical Analysis. Accepted, 2020. arXiv:1909.09687
  2. Wei Wang and Shiwen Zhang.   The exponential decay of eigenfunctions for tight binding Hamiltonians via landscape and dual landscape functions.   Annales Henri Poincaré. Accepted, 2020. arxiv:2003.07987
  3. Guy David, Max Engelstein, and Svitlana Mayboroda. Square functions, non-tangential limits and harmonic measure in co-dimensions larger than oneDuke Mathematical Journal. Accepted, 2020. arXiv:1808.08882
  4. Marcel Filoche, Douglas Arnold, Guy David, David Jerison, and Svitlana Mayboroda, Reply to comment on "Effective Confining Potential of Quantum States in Disordered Media", Phys. Rev. Lett. 124, 219702 (2020).
  5. Douglas N. Arnold, Guy David, Marcel Filoche, David Jerison, and Svitlana Mayboroda. Localization of eigenfunctions via an effective potential. Comm. PDE (2019). doi: 10.1080/03605302.2019.1626420
  6. Douglas N. Arnold, Guy David, Marcel Filoche, David Jerison, and Svitlana Mayboroda. Computing spectra without solving eigenvalue problems. SIAM J. Sci. Comput., 41(1), B69–B92 (2019). doi:10.1137/17M1156721. Featured in the Journal Club for Condensed Matter Physics, “Hidden landscape of an Anderson insulator."
  7. Guy David, Joseph Feneuil, and Svitlana Mayboroda. A new elliptic measure on lower dimensional sets. Acta Mathematica Sinica, English Series, Conference proceeding, 2018. arXiv:1807.07035
  8. Guy David, Joseph Feneuil, Svitlana Mayboroda. Elliptic theory for sets with higher co-dimensional boundaries. Memoirs of the AMS. Accepted, 2018. arXiv:1702.05503
  9. Ariel Barton, Steve Hofmann and Svitlana Mayboroda. Bounds on layer potentials with rough inputs for higher order elliptic equations. Proceedings of the London Mathematical Society. Accepted, 2019. arXiv:1703.06847
  10. Yann Chalopin, Francesco Piazza, Svitlana Mayboroda, Claude Weisbuch, Marcel Filoche. Universality of fold-encoded localized vibrations in enzymes. Sci. Rep. 9, 12835 (2019). doi: 10.1038/s41598-019-48905-8
  11. Guy David, Joseph Feneuil, and Svitlana Mayboroda. Dahlberg's theorem in higher co-dimensionJournal of Functional Analysis. Accepted, 2019. arXiv:1704.00667
  12. Guy David, Max Engelstein, and Tatiana Toro. Free boundary regularity for almost-minimizersAdvances in Mathematics. Accepted, 2019. arXiv:1702.06580
  13. Guy David. A local description of 2-dimensional almost minimal sets bounded by a curveAnnales Mathematiques de la Faculte des sciences de Toulouse. Accepted, 2019. arXiv:1901.10171
  14. Guy David. Local Regularity Properties of Almost and Quasiminimal Sets With a Sliding Boundary Condition. Asterisque 411, SMF, Accepted, 2019. arXiv:1401.1179
  15. Joseph Feneuil, Svitlana Mayboroda, and Zihui Zhao. Dirichlet problem in domains with lower dimensional boundaries.  Revista Matemática Iberoamericana. Accepted, 2019. arXiv:1810.06805
  16. W. Hahn, J.-M. Lentali, P. Polovodov, N. Young, S. Nakamura, J. S. Speck, C. Weisbuch, M. Filoche, Y.‑R. Wu, M. Piccardo, F. Maroun, L. Martinelli, Y. Lassailly, J. Peretti. Evidence of intrinsic nanoscale electron localization induced by composition disorder in InGaN/GaN quantum wells by scanning tunneling luminescence spectroscopy. Phys. Rev. B 98, 045305 (2018). doi:10.1103/PhysRevB.98.045305
  17. David Jerison and Nikola Kamburov. Free boundaries subject to topological constraints. Disc. Cont. Dyn. Systems. Accepted, 2019. arXiv:1902.00158
  18. David Jerison. The Two Hyperplane Conjecture. Acta Mathematica Sinica, English Version, vol 35 (6) June 2019, pp 728--748. arXiv:1809.10759
  19. Svitlana Mayboroda and Bruno Poggi. Exponential decay estimates for fundamental solutions of Schrodinger-type operators. Transactions of the AMS 180207. Accepted, 2019.
  20. Svitlana Mayboroda and Zihui Zhao. Square function estimates, BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets. Analysis & PDE. Accepted, 2018. arXiv:1802.09648
  21. Yves Meyer. From Salomon Bochner to Dan Shechtman. Accepted for publication in the Transactions of The Royal Norwegian Society of Sciences and Letters, 2019
  22. Yves Meyer. A letter by Eli Stein. Accepted for publication in The Journal of Geometric Analysis (JGA).
  23. Yves Meyer. Restriction algebras of Fourier-Stieltjes transforms of Radon measures. Accepted for publication in The Journal of Geometric Analysis.
  24. Yves Meyer. Trigonometric series with a given spectrum. The Tunisian Journal of Mathematics. Vol. 2 (2020), No. 4, 881906.
  25. Yves Meyer. Global and local estimates on trigonometric sums. Transactions of The Royal Norwegian Society of Sciences and Letters, 2018.
  26. Xin Ai, Yingxin Chen, Shengzhi Dong, Emrys W. Evans, Richard H. Friend, Alexander J. Gillett, Haoqing Guo, and Timothy J. H. Hele. Efficient radical-based light-emitting diodes with doublet emission. Nature 563, pages 536-540, 2018.
  27. Jeremie Richard, Lih-King Lim, Vincent Denechaud, Valentin V. Volchkov, Baptiste Lecoutre, Musawwadah Mukhtar, Fred Jendrzejewski, Alain Aspect, Adrien Signoles, Laurent Sanchez-Palencia, and Vincent Josse. Elastic Scattering Time of Matter Waves in Disordered Potentials. Physical Review Letters 122, 100403, 2019. arXiv:1810.07574

Preprints and submitted manuscripts

  1. Svitlana Mayboroda and Bruno Poggi. Carleson perturbations of elliptic operators on domains with low dimensional boundaries. Submitted. arxiv:2007.07492
  2. Guy David and Svitlana Mayboroda. Good elliptic operators on Cantor sets. Submitted. arxiv:2007.01745
  3. Douglas N. Arnold and Kaibo Hu. Complexes from Complexes. Submitted. arxiv:2005.12437
  4. Simon Bortz, Steve Hofmann, Jose Luis Luna Garcia, Svitlana Mayboroda, and Bruno Poggi. Critical Perturbations for Second Order Elliptic Operators. Part I: Square function bounds for layer potentials. Submitted, 2020. arxiv:2003.02703
  5. Guy David and Svitlana Mayboroda. Harmonic measure is absolutely continuous with respect to the Hausdorff measure on all low-dimensional uniformly rectifiable sets. Submitted, 2020. arXiv:2006.14661
  6. Guy David, Joseph Feneuil, and Svitlana Mayboroda.  Elliptic theory in domains with boundaries of mixed dimension. Submitted, 2020. arxiv:2003.09037
  7. Antonios M. Alvertis, Richard H. Friend, Akshay Rao, Alex W. Chin, and Bartomeu Monserrat. Exciton temperature dependence dictated by localization in organic semiconductors. Submitted.
  8. Ariel Barton, Steve Hofmann, and Svitlana Mayboroda. Nontangential estimates on layer potentials and the Neumann problem for higher order elliptic equations. Submitted. arXiv:1808.07137
  9. Philip C.Y. Chow, Ture F. Hinrichsen, Christopher C.S. Chan, David Palecek, Alexander Gillett, Shangshang Chen, Xinhui Zou, Chao Ma, Kam Sing Wong, Richard H. Friend, He Yan, and Akshay Rao. Endothermic charge separation in efficient non-fullerene organic solar. Submitted.
  10. Guy David, Max Engelstein, and Svitlana Mayboroda. Square functions, non-tangential limits and harmonic measure in co-dimensions larger than one. Submitted. arXiv:1808.08882
  11. Guy David, Marcel Filoche, and Svitlana Mayboroda. The landscape law for the integrated density of states. Submitted. arXiv:1909.10558
  12. Steve Hofmann, Jose Maria Martell, Svitlana Mayboroda, Tatiana Toro, and Zihui Zhao. Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case. arXiv:1908.03161
  13. Steve Hofmann, Jose Maria Martell, Svitlana Mayboroda, Tatiana Toro, and Zihui Zhao. Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part I: The small constant case. arXiv:1710.06157
  14. Steve Hofmann, Linhan Li, Svitlana Mayboroda, and Jill Pipher. Lp theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric partarXiv:1908.01030
  15. Steve Hofmann, Linhan Li, Svitlana Mayboroda, and Jill Pipher. The Dirichlet problem for elliptic operators having a BMO anti-symmetric part. Submitted. arXiv:1908.08587
  16. Steve Hofmann, Jose Maria Martell, and Svitlana Mayboroda. Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domains. arXiv:1904.13116
  17. V. Volchkov, V. Angelopoulou, Fred Jendrzejewski, Alain Aspect, Laurent Sanchez-Palencia, and Vincent Josse. Ultracold atoms in disordered potentials: elastic scattering time in the strong scattering regime. Submitted. arXiv:1910.04148
  18. Claude Weisbuch and James S. Speck. On the search for efficient solid state lighting emitters: past, present, future, invited paper in focus issue entitled "Wide bandgap III-nitride devices and SSL lighting: A tribute to Professor Akasaki", Submitted.

Background Publications

  1. Svitlana Mayboroda and Vladimir Maz’ya. Polyharmonic capacity and Wiener test of higher order. Inventiones Mathematicae, 211(2), 779-853. DOI: 10.1007/s00222-017-0756-y, 2018.
  2. Douglas N. Arnold. Finite Element Exterior Calculus. CBMS-NSF Regional Conference Series in Applied Mathematics 93. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2018.
  3. Marcel Filoche, David Jerison, and Svitlana Mayboroda. A free boundary problem for the localization of eigenfunctions. Astérisque 392, SMF 2017. See publication
  4. Marcel Filoche, Marco Piccardo, Yuh-Renn Wu, Chi-Kang Li, Claude Weisbuch, and Svitlana Mayboroda. Localization landscape theory of disorder in semiconductors I: Theory and modeling. Phys. Rev. B 95, 144204. doi:10.1103/PhysRevB.95.144204, 2017. See publication
  5. Marco Piccardo, Chi-Kang Li, Yuh-Renn Wu, James S. Speck, Bastien Bonef, Robert M. Farrell, Marcel Filoche, Lucio Martinelli, Jacques Peretti, and Claude Weisbuch. Localization landscape theory of disorder in semiconductors. II. Urbach tails of disordered quantum well layers. Phys. Rev. B, 95, 144205, 2017. See publication
  6. Chi-Kang Li, Marco Piccardo, Li-Shuo Lu, Svitlana Mayboroda, Lucio Martinelli, Jacques Peretti, James S. Speck, Claude Weisbuch, Marcel Filoche, and Yuh-Renn Wu. Localization landscape theory of disorder in semiconductors. III. Application to carrier transport and recombination in light emitting diodes. Phys. Rev. B 95, 144206, 2017. See publication
  7. Steve Hofmann and Jose Maria Martell. Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions. Duke Math. J., 165, no. 12, 2331–2389, 2016. See publication
  8. Gautier Lefebvre, Alexane Gondel, Marc Dubois, Michael Atlan, Florian Feppon, Aimé Labbé, Camille Gillot, Alix Garelli, Maxence Ernoult, Marcel Filoche, and Patrick Sebbah. One single static measurement predicts wave localization in complex structures. Physical Review Letters, Phys. Rev. Lett., 117, 074301, 2016. See publication
  9. Yves Meyer. Measures with locally finite support and spectrum. Proceedings of the National Academy of Sciences (USA). Vol 113, March 22, 2016. See publication
  10. Douglas N. Arnold, Guy David, David Jerison, Svitlana Mayboroda, and Marcel Filoche. Effective confining potential of quantum states in disordered media. Physical Review Letters, 116(5), 2016. See publication
  11. Marcelo Leite Lyra, Svitlana Mayboroda, and Marcel Filoche. Dual landscapes in Anderson localization on discrete lattices. EPL (Europhysics Letters), 109 (4), 2015. See Publication.
  12. Vladimir Maz’ya. Regularity of solutions to the polyharmonic equation in general domains. Inventiones Mathematicae, 196, no. 1, 1–68., 2014.
  13. Simon Gélinas, Akshay Rao, Abhishek Kumar, Samuel L. Smith, Alex W. Chin, Jenny Clark, Tom S. van der Poll, Guillermo C. Bazan, and Richard H. Friend. Ultrafast Long-Range Charge Separaton in Organic Semiconductor Photovoltaic Diodes. Science. 10.1126/science.1246249, 2014. See publication
  14. Justin Iveland, Lucio Martinelli, Jacques Peretti, James S. Speck, and Claude Weisbuch.  Direct measurement of Auger electrons emitted from a semiconductor light-emitting diode under electrical injection: identification of the dominant mechanism for efficiency droop. Phys. Rev. Lett., 110, 177406, 2013. See publication
  15. Fred Jendrzejewski, Alain Bernard, Killian Muller, Patrick Cheinet, Vincent Josse, Marie Piraud, Luca Pezzé, Laurent Sanchez-Palencia, Alain Aspect, and Philippe Bouyer. Three-dimensional localization of ultracold atoms in an optical disordered potential. Nature Physics 8, 398, 2012. See publication
  16. Fred Jendrzejewski, Killian Muller, Jérémie Richard, Aditya Date, Thomas Plisson, Philippe Bouyer, Alain Aspect, and Vincent Josse. Coherent Backscattering of Ultracold Atoms. Physical Review Letters 109 (19), 2012. See publication
  17. Yuh-Renn Wu, Ravi Shivaraman, Kuang-Chung Wang and James S. Speck. Analyzing the physical properties of InGaN multiple quantum well light emitting diodes from nano scale structure.  Appl. Phys. Lett. 101, 083505, 2012. See publication
  18. Marcel Filoche and Svitlana Mayboroda. Universal mechanism for Anderson and weak localization. Proc. Natl Acad. Sci.USA 109 (37):14761-14766, doi:10.1073/pnas.1120432109, 2012. 
  19. Artem A. Bakulin, Akshay Rao, Vlad G. Pavelyev, Paul H. M. van Loosdrecht, Maxim S. Pshenichnikov, Dorota Niedzialek, Jérôme Cornil, David Beljonne, and Richard H. Friend. The Role of Driving Energy and Delocalized States for Charge Separation in Organic Semiconductors. Science, 10.1126/science.1217745, 2012. See publication
  20. Juliette Billy, Vincent Josse, Zhanchun C. Zuo, Alain Bernard, Ben Hambrecht, Pierre Lugan, David Clément, Laurent Sanchez-Palencia, Philippe Bouyer, and Alain Aspect. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891, 2008. See publication
  21. B. Sapoval, S. Félix, and M. Filoche.  Localisation and damping in resonators with complex geometry. The European Physical Journal Special Topics 161, 225-232, 2008.
  22. S. Félix, M. Asch, M. Filoche, and B. Sapoval.  Localization and increased damping in irregular acoustic cavities. Journal of Science and Vibration 299, 965-976, 2007.  
  23. Luis A. Caffarelli, David Jerison, and Carlos E. Kenig, Some new monotonicity theorems with applications to free boundary problems. Annals of Mathematics. (2) vol 155, no. 2, 369-404, 2002. See publication
  24. David Jerison and Nikolai Nadirashvili. The hot spots conjecture for domains with two axes of symmetry. J. Amer. Math. Soc. vol 13, pp 741–772, 2000. See publication
  25. Yves Meyer and Ronald R. Coifman. Wavelets: Calderón–Zygmund and Multilinear Operators. Number 48 in Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1997.
  26. Stephen Semmes. Analysis of and on uniformly rectifiable sets. American Mathematical Society. Mathematical Surveys and Monographs 38, Providence, RI, xii+356, pp., 1993.
  27. Claude Weisbuch, Raymond Dingle, Arthur C.V. Gossard and William Wiegmann. Optical Characterization of Interface Disorder in GaAs-Gax Al1-x As quantum wells. Solid State Communications. 38, 709, 1981.