Svitlana Mayboroda
Director and Principal Investigator (WAVE), Department of Mathematics (UMN)
Svitlana Mayboroda
Director and Principal Investigator (WAVE), Department of Mathematics (UMN)
- Partial differential equations: second and higher order elliptic differential equations and systems in non-smooth media, boundary value problems, regularity, potential theory, spectral theory, wave propagation and localization of the eigenmodes in rough domains, free boundary problems, harmonic/elliptic measure
- Analysis: harmonic analysis, singular integral operators, maximal functions, function spaces, wavelet and atomic decompositions, interpolation, functional calculus of differential operators, operator theory.
- Geometric measure theory: geometry of rough domains, non-linear capacity, rectifiability, Analysis and PDEs on uniformly rectifiable sets, harmonic measure, regularity of free boundaries.
- Physics: influence of rough geometry and/or material on properties of a physical system, localization of waves in acoustics, plate vibration, Anderson localization, quantum physics, systems of cold atoms.
- Engineering: analysis and design of GaN light emitting devices, the impact of disorder in nitride alloy materials on localization of carriers in quantum wells, radiative efficiency, Auger recombination, quantum droop, on performance of LEDs and lasers.
Svitlana Mayboroda is a Professor of Mathematics at ETH Zürich, and a McKnight Presidential 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. Her primary achievements include the solution of the Chang-Krantz-Stein conjecture, the boundary regularity theory and the first analogue of the Wiener criterion for higher order PDEs, a complete description of the structure of the harmonic measure, and the foundation of the theory of the localization landscape, together with Marcel Filoche.
Mayboroda's fundamental contributions to harmonic analysis and PDE have been widely recognized, including recently from the 2024 Elias Stein Prize and in 2023 she was awarded the prestigious Blavatnik Award. She is also a member of the European Academy of Sciences. Her previous achievements include the Alfred P. Sloan Research Fellowship in 2010, a National Science Foundation CAREER award in 2011, and a Fellowship of the Fondation Jacques Hadamard in 2015. In 2014 she received the inaugural award of the AWM-Sadosky Research Prize in Analysis, and, at the young age of 35, in 2015 she was named a Fellow of the American Mathematical Society. Professor Mayboroda currently holds a Simons Fellowship in the Mathematical Sciences and a von Neumann Fellowship at the Institute for Advanced Study. She is also the sole PI of an $800,000 INSPIRE award, being the only mathematician to receive an award under INSPIRE, a program of the NSF to support bold interdisciplinary projects that are larger than a single program. This summer Professor Mayboroda will give an invited talk at the International Congress of Mathematicians.
Read more on Dr. Mayboroda's University of Minnesota homepage.
Education
- PhD degree in Mathematics, University of Missouri at Columbia, USA
- Full Higher Education in the specialty Applied Mathematics (equivalent to MS), Kharkiv National University
- Full Higher Education in the specialty Finance (equivalent to MBA), KISP, Ukraine, September 2001.
Professional Background
- 2020 — McKnight Presidential Professor, University of Minnesota, USA
- 2016 — Northrop Professor, University of Minnesota, USA
- 2015 — Full Professor, University of Minnesota, USA
- 2011–2015 — Associate Professor, University of Minnesota, USA
- 2008–2011 — Assistant Professor (promoted to Associate Professor from August 2011), Purdue University, USA
- 2007 — Visiting Assistant Professor, Brown University, USA
- 2006–2008 — Zassenhaus Visiting Assistant Professor, The Ohio State University, USA
- 2005 — Visiting Assistant Professor, Australian National University, Australia
Scientific & Professional Societies
Honors and Awards
- 2024 – Member of the European Academy of Sciences
- 2024 – The Elias Stein Prize
- 2023 – The Blavatnik Award
- 2020 — McKnight Presidential Professor, University of Minnesota
- 2019 — Kirk Distinguished Fellowship at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK
- 2016 — Northrop Professor, University of Minnesota
- 2016 — Chercheur Invité (3 months) Ecole Polytechnique
- 2015 — Fellow of the American Mathematical Society
- 2015 — Foundation Jacques Hadamard Fellowship
- 2014 — AWM-Sadosky Prize in Analysis
- 2014 — Integrated NSF Support Promoting Interdisciplinary Research and Education (INSPIRE) Award
- 2013 — Chercheur Invité (2 months), Ecole Polytechnique
- 2011 — NSF Faculty Early Career Development (CAREER) Award
- 2012 — Chercheur Invité (3 months) CNRS
- 1997 — Honors Fellowship, Kharkiv National University, Ukraine
Selected Publications
2024
Non-local distance functions and geometric regularity (with Max Engelstein and Cole Jeznach), Advances in Mathematics, accepted, arXiv:2208.07342
Critical Perturbations for Second Order Elliptic Operators. Part II: Non-tangential maximal function estimates (with Simon Bortz, Steve Hofmann, José Luis Luna Garcia, Bruno Poggi), Archive for Rational Mechanics and Analysis, accepted, https://arxiv.org/abs/2302.02746.
The Anderson mobility edge as a percolation transition, (Marcel Filoche, Pierre Pelletier, Dominique Delande, Svitlana Mayboroda), Physical Review B, accepted, http://arxiv.org/abs/2309.03813.
The landscape function on Rd (with G. David and A. Gloria), Les Annales de la Faculté des Sciences de Toulouse, accepted, https://arxiv.org/abs/2307.11182.
2023
Green functions and smooth distances (with Joseph Feneuil and Linhan Li), Math. Ann., published, DOI: 10.1007/s00208-023-02715-6, arXiv:2211.05318.
Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domains (with Steve Hofmann, José María Martell), Analysis & PDE, published, DOI: 10.1090/tran/9004, https://arxiv.org/abs/1904.13116.
Small A∞ results for Dahlberg-Kenig-Pipher operators in sets with uniformly rectifiable boundaries (with Guy David, Linhan Li), Transactions of the AMS, accepted, arXiv:2207.13602.
On an Effective Equation of the Reduced Hartree-Fock Theory (with Ilias Chenn, Wei Wang, Shi- wen Zhang), Advanced Nonlinear Studies, Special Issue in honor of David Jerison, 23, 1, DOI 10.1515/ans-2022-0070, https://arxiv.org/abs/2106.13887.
The Regularity problem in domains with lower dimensional boundaries (with Zanbing Dai and Joseph Feneuil), Journal of Functional Analysis, 284, 11, DOI:10.1016/j.jfa.2023.109903, arXiv:2208.00628.
2022
Elliptic theory in domains with boundaries of mixed dimension, (with Guy David and Joseph Feneuil), Astérisque, published, 442, DOI:10.24033/ast.1202, https://arxiv.org/abs/2003.09037.
Carleson Perturbations for the Regularity Problem (with Zanbing Dai, Joseph Feneuil), Revista Matemática Iberoamericana, DOI 10.4171/RMI/1401, arXiv:2203.07992.
Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions (with Guy David), Adv. Math, 410 (A), 108717. DOI:10.1016/j.aim.2022.108717, https://arxiv.org/pdf/2010.09793.pdf.
The landscape law for tight binding Hamiltonians, (with Douglas N. Arnold, Marcel Filoche, Wei Wang, Shiwen Zhang), Communications in Mathematical Physics, 396, 1339-1391, DOI:10.1007/s00220- 022-04494-8, https://arxiv.org/pdf/2101.03282.pdf.
Carleson estimates for the Green function on domains with lower dimensional boundaries (with Guy David and Linhan Li), Journal of functional analysis, 283, 5, 109553, DOI:10.1016/j.jfa.2022.109553, http://arxiv.org/abs/2107.08101.
Harmonic measure is absolutely continuous with respect to the Hausdorff measure on all low-dimensional uniformly rectifiable sets, (with Guy David), International Mathematics Research Notices, 2023, 11, 9319-9426, DOI:10.1093/imrn/rnac109.
Wigner-Weyl description of light absorption in disordered semiconductor alloys using the localization landscape theory, (with Jean-Philippe Banon, Pierre Pelletier, Claude Weisbuch, Marcel Filoche), Phys. Rev. B, 105, 125422, DOI: 10.1103/PhysRevB.105.125422.
Green function estimates on complements of low-dimensional uniformly rectifiable sets, (with Guy David and Joseph Feneuil), Math. Ann., 385, 1797-1821, DOI: 10.1007/s00208-022-02379-8.
Spectral functions and localization landscape theory in speckle potentials (with P. Pelletier, D. De-lande, V. Josse, A. Aspect, D. Arnold, M. Filoche), Phys Rev A, 105, 023314, DOI:10.1103/PhysRevA.105.023314, arXiv:2111.13155.
2021
Lp theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric part (with Steve Hofmann, Linhan Li, Jill Pipher), Math. Z. 301, 935–976, DOI:10.1007/s00209-021- 02938-w, https://arxiv.org/pdf/1908.01030.pdf.
Elliptic Theory for Sets with Higher Co-Dimensional Boundaries (with G. David and J. Feneuil), Memoirs of the American Mathematical Society 274, 1346. DOI: 10.1090/memo/1346.
Carleson measure estimates for the Green function (with Guy David and Linhan Li), Archive for Rational Mechanics and Analysis, 243, 1525–1563, DOI: 10.1007/s00205-021-01746-0, https://arxiv.org/pdf/2102.09592.pdf, https://link.springer.com/article/10.1007/s00205-021-01746-0.
The landscape law for the integrated density of states (with Guy David and Marcel Filoche), Advances in Mathematics, 390, 2021, 107946, DOI: 10.1016/j.aim.2021.107946.,arXiv:1909.10558.
Sharp estimates for the integrated density of states in Anderson tight-binding models, (with P. Desforges, S. Zhang, G. David, D. Arnold, W. Wang, M. Filoche), Phys. Rev. A, 104, 012207, DOI: 10.1103/Phys- RevA.104.012207.
The Dirichlet problem for elliptic operators having a BMO anti-symmetric part, (with Steve Hofmann, Linhan Li, Svitlana Mayboroda, Jill Pipher), Math.Ann., 382, 103-168, DOI: 10.1007/s00208-021- 02219-1, https://arxiv.org/abs/1908.08587.
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition (with Steve Hof- mann, José María Martell, Svitlana Mayboroda, Tatiana Toro, Zihui Zhao), Geom. Funct. Anal. 31, 325–401, DOI: 10.1007/s00039-021-00566-4, https://arxiv.org/pdf/2008.04834.pdf.
Good elliptic operators on Cantor sets, (with Guy David), Advances in Mathematics, 383, 2021, 107687, DOI: 10.1016/j.aim.2021.107687.
The effective potential of an M -matrix, (with Marcel Filoche and Terence Tao), Journal of Mathematical Physics, 62, 041902 DOI: 10.1063/5.0042629.
Carleson perturbations of elliptic operators on domains with low dimensional boundaries (with Bruno Poggi), Journal of Functional Analysis, 280, 8, 2021, 108930, DOI: 10.1016/j.jfa.2021.108930.
Dirichlet problem in domains with lower dimensional boundaries (with Joseph Feneuil and Zihui Zhao), Revista Matemática Iberoamericana, 37, 3, 2021, 821–910. DOI: 10.4171/rmi/1208, https://arxiv.org/pdf/1810.06805.pdf.
Critical Perturbations for Second Order Elliptic Operators. Part I: Square function bounds for layer potentials (with S. Bortz, S. Hofmann, J. L. Luna Garcia, and B. Poggi), Analysis & PDE, 15, 5, 1215- 1286, DOI: 10.2140/apde.2022.15.1215, https://arxiv.org/abs/2003.02703.
Square functions, non-tangential limits and harmonic measure in co-dimensions larger than one (with Guy David and Max Engelstein), Duke Math. J. 170 3, 455–501, DOI: 10.1215/00127094-2020-0048, https://arxiv.org/pdf/1808.08882.pdf.
Elliptic theory for sets with higher co-dimensional boundaries (with Guy David and Joseph Feneuil), Memoirs of the AMS, 274, 1346. DOI: 10.1090/memo/1346.
2020
Reply to comment by Comtet and Texier, (with Douglas Arnold, Guy David, Marcel Filoche, David Jerison), Physical Review Letters, 124, 219702, Published 28 May 2020.
Nontangential estimates on layer potentials and the Neumann problem for higher order elliptic equa- tions (with Ariel Barton and Steve Hofmann), International Mathematics Research Notices, 2021, 23, 18300-18366, DOI: 10.1093/imrn/rnaa051, https://arxiv.org/pdf/1808.07137.pdf.