Current Publications

[1] Guy David, M. Engelstein, and T. Toro. Free boundary regularity for almost-minimizers. arXiv:1702.06580, Advances in Mathematics, accepted, 2019.

[2] Guy David. A local description of 2-dimensional almost minimal sets bounded by a curve. arXiv:1901.10171, Annales Mathématiques de la Faculté des sciences de Toulouse, accepted, 2019.

[3] Yann Chalopin, Francesco Piazza, Svitlana Mayboroda, Claude Weisbuch, Marcel Filoche. Universality of fold-encoded localized vibrations in enzymes.  submitted, 2019. 

[4] Jérémie 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. APS Physics, published, 2019.

[5] Ariel Barton, Steve Hofmann and Svitlana Mayboroda. Bounds on layer potentials with rough inputs for higher order elliptic equations. arXiv:1703.06847, Proceedings of the London Mathematical Society, accepted, 2019.

[6] Svitlana Mayboroda and Bruno Poggi. Exponential decay estimates for fundamental solutions of Schrödinger-type operators. arXiv:1801.05499, Transactions of the AMS 180207, accepted, 2019.

[7] Guy David, Joseph Feneuil, and Svitlana Mayboroda. Dahlberg's theorem in higher co-dimension. arXiv:1704.00667, Journal of Functional Analysis, accepted, 2019.

[8] Guy David. Sliding almost minimal sets and the Plateau problem. arXiv:1812.02039, to be published.

[9] David Jerison and Nikola Kamburov. Free boundaries subject to topological constraints. arXiv:1902.00158, submitted for publication, 2019.

[10] Yves Meyer. Global and local estimates on trigonometric sums. AMS Subject Classification: Primary 42A32, Secondary 42B10, PDF icon submitted for publication, 2019.

[11] Yves Meyer. Trigonometric series with a given spectrum. AMS Subject Classification: Primary 2A32, Secondary 2B10, PDF icon submitted for publication, 2019.

[12] Xin Ai, Yingxin Chen, Shengzhi Dong, Emrys W. Evans, Richard H. Friend, Alexander J. Gillett, Haoqing Guo, Timothy J. H. Hele. Efficient radical-based light-emitting diodes with doublet emission. Nature 563, pages 536–540, 2018. See publication

[13] Guy David, Joseph Feneuil, and Svitlana Mayboroda. A new elliptic measure on lower dimensional sets. arXiv:1807.07035, Acta Mathematica Sinica, English Series, accepted, 2018.

[14] Guy R. David, Joseph Feneuil, Svitlana Mayboroda. Elliptic theory for sets with higher co-dimensional boundaries. arXiv:1702.05503, Memoirs of the AMS, accepted, 2018.

[15] Douglas N. Arnold, Guy David, Marcel Filoche, David Jerison, and Svitlana Mayboroda. Localization of eigenfunctions via an effective potential. arXiv:1712.02419, Communications in Partial Differential Equations, accepted, 2018.

[16] Svitlana Mayboroda and Zihui Zhao. Square function estimates, BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets. arXiv:1802.09648, Analysis & PDE, accepted, 2018.

[17] Douglas N. Arnold, Guy David, Marcel Filoche, David Jerison, and Svitlana Mayboroda. Computing spectra without solving eigenvalue problems., SIAM Journal of Scientific Computing, 41(1), B69–B92. (24 pages) 2019.

[18] Joseph Feneuil, Svitlana Mayboroda, and Zihui Zhao.  Dirichlet problem in domains with lower dimensional boundaries.  arXiv:1810.06805, submitted for publication, 2018.

[19] David Jerison. The Two Hyperplane Conjecture. arXiv:1809.10759, submitted for publication, 2018. 

[20] Guy David, Max Engelstein, and Svitlana Mayboroda.  Square functions, non-tangential limits and harmonic measure in codimensions larger than one.  arXiv:1808.08882, submitted for publication, 2018.  

[21] Ariel Barton, Steve Hofmann, and Svitlana Mayboroda.  Nontangential estimates on layer potentials and the Neumann problem for higher order elliptic equations.  arXiv:1808.07137, submitted for publication, 2018.

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] Vladimir Maz’ya. Regularity of solutions to the polyharmonic equation in general domains. Inventiones Mathematicae, 196, no. 1, 1–68., 2014.

[12] 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

[13] 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

[14]  Fred Jendrzejewski, Alain Bernard, Killian Muller, Patrick Cheinet, Vincent Josse, Marie Piraud, Luca Pezzé, Laurent Sanchez-Palencia, Alain Aspect, and Philippe Bouyer. Threedimensional localization of ultracold atoms in an optical disordered potential. Nature Physics 8, 398, 2012.
See publication

[15] 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

[16] 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

[17] 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. 

[18] 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

[19]  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

[20] 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.

[21] 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.  

[22] Luis A. Caffarelli, David Jerison, and Carlos E. Kenig, Some new monotonicity theorems with appli-cations to free boundary problems. Annals of Mathematics. (2) vol 155, no. 2, 369-404, 2002. 
See publication

[23] David Jerison and Nikolai Nadirashvili. The hot spots conjecture for domains with two axes of sym-metry. J. Amer. Math. Soc. vol 13, pp 741–772, 2000.
See publication

[24] 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.

[25] Stephen Semmes. Analysis of and on uniformly rectifiable sets. American Mathematical Society. Mathematical Surveys and Monographs 38, Providence, RI, xii+356, pp., 1993.

[26] 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. 


Svitlana Mayboroda writing on chalkboard
Collaboration Director, Principal Investigator

Svitlana Mayboroda is the Northrop Professor of Mathematics at the University of Minnesota. Her expertise lies in harmonic analysis, geometric measure theory, and partial differential equations, as well as an extended range of applications of these fields ranging from condensed matter physics to materials science to engineering.

Douglas Arnold
Principal Investigator

Douglas N. Arnold is the McKnight Presidential Professor of Mathematics at the University of Minnesota. His research interests are in computational mathematics, centered on the design and analysis of numerical algorithms for partial differential equations and their application to physical problems ranging from the deformation of elastic shells to the collision of black holes.

Alain Aspect
Principal Investigator

Alain Aspect is a professor at Institut d'Optique Graduate School (Augustin Fresnel chair), and at Ecole Polytechnique, in Palaiseau, France. He is an experimentalist in Atomic, Molecular, and Optical Physics, whose interests bear on basic quantum phenomena.

Guy David
Principal Investigator

Guy David is a Professor of Mathematics at the Université de Paris Sud, Laboratoire de Mathematiques d’Orsay. His main areas of expertise are in Harmonic analysis, Geometric measure Theory, and the Calculus of Variations. 

Marcel Filoche
Principal Investigator

Marcel Filoche is CNRS Research Director in Condensed Matter Physics at Ecole Polytechnique. His research interests are in the physics of complex and disordered geometries, with an emphasis on wave localization and absorption in complex structures, and transport in the pulmonary airway system at the biomedical interface.

Sir Richard Friend
Principal Investigator

Sir Richard Friend holds the Cavendish Professorship of Physics at the University of Cambridge. His research encompasses the physics, materials science and engineering of semiconductor devices made with carbon-based semiconductors, particularly polymers.