# Svitlana Mayboroda

## Svitlana Mayboroda

Director and Principal Investigator (WAVE), Department of Mathematics (UMN)#### 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

- 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

Association for Women in MathematicsAmerican Mathematical SocietySociety for Industrial and Applied Mathematics#### Biography

**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. 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 by an 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.

**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.

#### Honors and Awards

- 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

*2019*

- The landscape law for the integrated density of states (with Guy David and Marcel Filoche), submitted.

- The Dirichlet problem for elliptic operators having a BMO anti-symmetric part (with Steve Hofmann, Linhan Li, and Jill Pipher), submitted.

- Lp theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric part (with Steve Hofmann, Linhan Li, and Jill Pipher), submitted.

- Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case (with Steve Hofmann, José María Martell, Tatiana Toro, and Zihui Zhao), submitted.

- Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part I: The small constant case (with Steve Hofmann, José María Martell, Tatiana Toro, Zihui Zhao), submitted.

- Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domains (with Steve Hofmann and José María Martell), submitted.

- Universality of fold-encoded localized vibrations in enzymes (with Yann Chalopin, Francesco Piazza, Claude Weisbuch, and Marcel Filoche), Scientific Reports, Volume 9, Number 1 (2019).

- Bounds on layer potentials with rough inputs for higher order elliptic equations (with Ariel Barton and Steve Hofmann), The Proceedings of the London Mathematical Society, accepted.

- Dahlberg's theorem in higher co-dimension(with Guy David and Joseph Feneuil), Journal of Functional Analysis, accepted.

- Exponential decay estimates for fundamental solutions of Schrödinger-type operators (with Bruno Poggi), Transactions of the AMS, Volume 372, Number 6 (2019).

*2018*

- Dirichlet problem in domains with lower dimensional boundaries (with Joseph Feneuil and Zihui Zhao), Revista Matemática Iberoamericana, accepted.

- Square functions, non-tangential limits and harmonic measure in co-dimensions larger than one (with Guy David and Max Engelstein), submitted.

- Nontangential estimates on layer potentials and the Neumann problem for higher order elliptic equations (with Ariel Barton and Steve Hofmann), submitted.

- A new elliptic measure on lower dimensional sets (with Guy David and Joseph Feneuil), Acta Mathematica Sinica, English series, the special issue in honor of the 65th birthday of Professor Carlos Kenig, accepted.

- Localization of eigenfunctions via an effective potential (with Douglas Arnold, Guy David, Marcel Filoche, David Jerison), Communications in Partial Differential Equations, accepted.

- Square function estimates, BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets (with Zihui Zhao), Analysis & PDE, accepted.

- Computing spectra without solving eigenvalue problems (with Douglas Arnold, Guy David, Marcel Filoche, David Jerison), SIAM Journal on Scientific Computing, accepted.

- Elliptic theory for sets with higher co-dimensional boundaries (with Guy David and Joseph Feneuil), Memoirs of the AMS, accepted.

- Polyharmonic capacity and Wiener test of higher order (with Vladimir Maz'ya), Inventiones Mathematicae, (2018) 211: 779.

- Dirichlet and Neumann boundary values of solutions to higher order elliptic equations (with Ariel Barton and Steve Hofmann), Annales de l'Institut Fourier, accepted.

- Fundamental Matrices and Green Matrices for non-homogeneous elliptic systems (with Blair Davey and Jonathan Hill), Publicacions Matematiques, Volume 62, Number 2 (2018), 537-614.

- The Neumann problem for higher order elliptic equations with symmetric coefficients (with Ariel Barton and Steve Hofmann), Math. Ann., (2018) 371: 297.

*2017*

- Localization landscape theory of disorder in semiconductors III: Application to carrier transport and recombination in light emitting diodes(with Chi-Kang Li, Marco Piccardo, Li-Shuo Lu, Lucio Martinelli, Jacques Peretti, James S. Speck, Claude Weisbuch, Marcel Filoche, Yuh-Renn Wu), Phys. Rev. B, 95, 144206 (2017).

- Localization landscape theory of disorder in semiconductors I: Theory and modeling (with Marcel Filoche, Marco Piccardo, Yuh-Renn Wu, Chi-Kang Li, Claude Weisbuch), Phys. Rev. B, 95, 144204 (2017).

- A free boundary problem for the localization of eigenfunctions (with Guy David, Marcel Filoche, David Jerison), a monograph, Astérisque, 392 (2017), 203 pages.

- Square function estimates on layer potentials for higher-order elliptic equations (with Ariel Barton and Steve Hofmann), Mathematische Nachrichten, 290: 2459-2511.

- Local Hardy spaces associated with inhomogeneous higher order elliptic operators (with Dachun Yang and Jun Cao), Anal. Appl. (Singap.) 15 (2017), no. 2, 137-224.

*2016*

- Absolute continuity between the surface measure and harmonic measure implies rectifiability, (with Steve Hofmann, José María Martell, Xavier Tolsa and Alexander Volberg), submitted.

- Localization of eigenfunctions, Notices of the AMS, accepted.

- One single static measurement predicts wave localization in complex structures , (with Gautier Lefebvre, Alexane Gondel, Marc Dubois, Michael Atlan, Florian Feppon, Aimé Labbé, Camille Gillot, Alix Garelli, Maxence Ernoult, Marcel Filoche, Patrick Sebbah), Physical Review Letters, 117, 074301 (2016).

- Higher-order elliptic equations in non-smooth domains: some old and new results(with Ariel Barton), Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory. Celebrating Cora Sadosky's life. Volume 1.

- Rectifiability of harmonic measure(with Jonas Azzam, Steve Hofmann, José María Martell, Mihalis Mourgoglou, Xavier Tolsa, and Alexander Volberg), Geom. Funct. Anal. 26 (2016), no. 3, 703- 728. DOI: 10.1007/s00039-016-0371-x

- Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure(with Jonas Azzam, Steve Hofmann, José María Martell, Mihalis Mourgoglou, Xavier Tolsa, and Alexander Volberg), C. R. Math. Acad. Sci. Paris 354 (2016), no. 4, 351--355.

- The effective confining potential of quantum states in disordered media(with Doug Arnold, Guy David, Marcel Filoche, and David Jerison), Physical Review Letters , 116 (2016), 056602.

- Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces(with Ariel Barton), Mem. Amer. Math. Soc. 243 (2016), no. 1149, v+110 pp.

- Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions,(with Steve Hofmann and José María Martell), Duke Math. J. 165 (2016), no. 12, 2331--2389.

- Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators (with Dachun Yang and Jun Cao), Forum Math. 28 (2016), no. 5, 823--856.

*2015*

- Layer potentials and boundary value problems for elliptic equations with complex bounded coefficients satisfying the small Carleson measure norm condition(with Steve Hofmann and Mihalis Mourgoglou), Advances in Mathematics,480--564.

- Dual hidden landscapes for Anderson localization in discrete lattices (with Marcel Filoche, Marcelo Lyra), Europhys. Lett. EPL, Volume 109, Number 4, Editor's choice.

- The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients(with Steve Hofmann, Carlos Kenig, and Jill Pipher), Mathematische Annalen, 361 (2015), no. 3-4, 863--907.

- Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators(with Steve Hofmann, Carlos Kenig, and Jill Pipher), Journal of the American Mathematical Society , 28 (2015), no. 2, 483-529.http://www.ams.org/journals/jams/0000-000-00/S0894-0347-2014-00805-5/S0894-0347-2014-00805- 5.pdf

*2014*

- Regularity of solutions to the polyharmonic equation in general domains(with Vladimir Maz'ya), Inventiones Mathematicae , 196 (2014), no. 1, 1-68.

- Uniform Rectifiability and Harmonic Measure III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains(with Steve Hofmann and José María Martell), International Mathematics Research Notices , 2014, no. 10, 2702-2729. http://dx.doi.org/10.1093/imrn/rnt002.

- Boundary-value problems for higher-order elliptic equations in non-smooth domains(with Ariel Barton), Concrete operators, spectral theory, operators in harmonic analysis and approximation, 53-93, Oper. Theory Adv. Appl. , 236, Birkhäuser Springer, Basel, 2014.

*2013 and Earlier*

- The Dirichlet problem for higher order equations in composition form (with Ariel Barton), Journal of Functional Analysis, Volume 265, Issue 1, (2013), 49-107, http://dx.doi.org/10.1016/j.jfa.2013.03.013.

- The landscape of Anderson localization in a disordered medium (with Marcel Filoche), Contemporary Mathematics, 601 (2013), 113-121, http://dx.doi.org/10.1090/conm/601/11916.

- Universal mechanism for Anderson and weak localization (with Marcel Filoche), Proceedings of the National Academy of Sciences, (2012), 109 (37) 14761-14766, doi:10.1073/pnas.1120432109

- Localization of eigenfunctions of a one-dimensional elliptic operator (with Marcel Filoche and Brandon Patterson), Contemporary Mathematics, 581 (2012), 99-116, http://dx.doi.org/10.1090/conm/581.

- Second order elliptic operators with complex bounded measurable coefficients in $L^p$, Sobolev and Hardy spaces (with Steve Hofmann and Alan McIntosh), Les Annales Scientifiques de l'Ecole Normale Supérieure, Volume 44, fascicule 5 (2011), 723--800.

- The connections between Dirichlet, Regularity and Neumann problems for second order elliptic operators with complex bounded measurable coefficients, Advances in Mathematics, 225 (2010), 1786--1819.

- Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation (with Vladimir Maz'ya), Inventiones Mathematicae, 175 (2009), no. 2, 287--334.

- Strong localization induced by one clamped point in thin plate vibrations (with Marcel Filoche), Physical Review Letters, Volume: 103, Issue: 25, Article Number: 254301, (2009).

- Finite square function implies integer dimension (with Alexander Volberg), C. R. Math. Acad. Sci. Paris, 347 (2009), pp. 1271--1276.

- Hardy and BMO spaces associated to divergence form elliptic operators (with Steve Hofmann), Mathematische Annalen, 344 (2009), no. 1, 37--116.

- Boundedness of the square function and rectifiability (with Alexander Volberg), C. R. Math. Acad. Sci. Paris, 347 (2009), pp. 1051--1056.

- Pointwise estimates for the polyharmonic Green function in general domains (with Vladimir Maz'ya), Cialdea, Alberto (ed.) et al., Analysis, partial differential equations and applications. The Vladimir Maz'ya anniversary volume. Selected papers of the international workshop, Rome, Italy, June 30--July 3, 2008. Basel: Birkhäuser. Operator Theory: Advances and Applications 193, 143-158 (2009).

- Boundedness of the Hessian of a biharmonic function in a convex domain (with Vladimir Maz'ya), Comm. Partial Differential Equations 33 (2008), no. 7-9, 1439--1454.

- Interpolation of Hardy-Sobolev-Besov-Triebel-Lizorkin Spaces and applications to problems in partial differential equations (with Nigel Kalton and Marius Mitrea), Proceedings of the Conference in honor of M.Cwikel, Contemp. Math., 2007.

- The solution of the Chang-Krantz-Stein conjecture(with Marius Mitrea), to appear in Proceedings of the Workshop in Harmonic Analysis , Tokyo, Japan.

- The Poisson problem for the Lamé system on low-dimensional Lipschitz domains(with Marius Mitrea), Integral methods in science and engineering , 137--160, Birkhauser Boston, Boston, MA, 2006.

- Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces (with Marius Mitrea), Annali di Matematica Pura ed Applicata (4) 185 (2006), no. 2, 155--187.

- Sharp estimates for Green potentials on non-smooth domains (with Marius Mitrea), Mathematical Research Letters, 11 (2004), 481--492.

- Square-function estimates for singular integrals and applications to partial differential equations (with Marius Mitrea),

Differential Integral Equations, 17 (2004), no. 7-8, 873--892.

- On one approach to the solution of problems of numerical analysis of the electrostatic field, Collection of the scientific works of KISP , V. 6 (2001), 223-227.