MENTORING: STUDENTS AND POSTDOCS
Guillermo Rey, University of Minnesota, Fall
2018-present. Guillermo is currently a postdoctoral fellow
at the University of Minnesota. His work focuses on
localization of eigenfunctions and the behavior of harmonic
measure on rough boundaries. His main research interests
include harmonic analysis, geometric measure theory, and
partial differential equations. Previously, he worked as a
software engineer at Google, after completing his Ph.D. in
mathematics at Michigan State University in 2015.
Viator, University of Minnesota and IMA, September
2016-. Robert Viator was a postdoctoral research at the
Institute for Mathematics and Applications. He has graduated
from Louisiana State University under the supervision of
Robert Lipton and, in addition to his duties at the IMA,
worked on the localization landscape approach to Weyl law in
periodic structures, under the supervision of Svitlana
Bortz, University of Minnesota, September
2016-present. Simon Bortz has graduated from the University
of Missouri, under the supervision of Steve Hofmann, in the
Spring of 2016. He joined the University of Minnesota from
the Fall of 2016, to work on the project partially
funded by the NSF INSPIRE grant (see above). Specifically,
Simon worked on Dirichlet, Neumann, and regularity problems
in higher co-dimension, as well as layer potentials for the
generalized Schr\"odinger operator. He is an acting
assistant professor at the University of Washington as of
the Fall of 2018.
Feneuil, University of Minnesota, September 2015 -
Spring 2018. Joseph Feneuil has graduated from the
University of Grenoble, under the supervision of Emmanuel
Russ. He joined the University of Minnesota as a Dunham
Jackson postdoctoral researcher in the Fall of 2015 and
worked under the supervision of Svitlana Mayboroda on
analogues of harmonic measure in higher co-dimension. He is
a research assistant professor at Temple University as of
the Fall of 2018.
- Stephen Lewis,
University of Minnesota, September 2014 - January 2015.
Stephen Lewis has obtained his PhD from the University of
Washington in 2014, under the supervision of Tatiana Toro,
and has started working under the supervision of Svitlana
Mayboroda and Douglas Arnold on localization of waves. He
has left University of Minnesota in 2015 to work in
Davey, University of Minnesota, 2013--2015. Blair has
obtained her PhD degree from the University of Chicago with
Carlos Kenig. She has started working with Vladimir
Sverak on unique continuation for elliptic and parabolic
equations and with Svitlana Mayboroda on boundary value
problems for Schr\"odinger-type elliptic operators. In this
direction, Blair (together with S. Mayboroda's graduate
student, Jonathan Hill) has established pointwise bounds and
regularity for fundamental solutions of general elliptic
PDEs of Schr\"odinger type with bounded measurable
coefficients, obtained the corresponding results for the
Green function, and is currently working on the properties
of the corresponding layer potentials. Blair is an assistant
professor at CUNY as of the Fall of 2018.
- Ariel Barton,
Purdue University and University of Minnesota, 2010--2013.
Ariel has obtained her PhD degree from the University of
Chicago under the supervision of Carlos Kenig, and was
working on the higher order elliptic problems on Lipschitz
domains and second order problems with rough coefficients
(mentored by Svitlana Mayboroda). During her postdoctoral
studies, Ariel has finished 5 research papers, 3 of them
jointly with Svitlana Mayboroda, 1 expository (see the list
of publications above), and 1 monograph, jointly with
Svitlana Mayboroda, accepted to Memoirs of the AMS. Ariel
then held a position at the University of Missouri. She
continued working on the higher order elliptic operators,
specifically, well-posedness problems for divergence form
elliptic PDEs with bounded measurable coefficients, under
the supervision of Steve Hofmann and Svitlana Mayboroda.
During this time, she has finished 1 paper on boundedness of
layer potentials for higher order PDEs (joint with S.
Mayboroda and S. Hofmann), an expository paper on recent
developments in higher order elliptic theory (joint with S.
Mayboroda) and the work on the fundamental solutions in this
context (by herself). Ariel is an assistant professor at the
University of Arkansas, Fayetteville as of the Fall of 2018.
- Zanbing Dai, University of Minnesota, is a graduate
student at University of Minnesota. He is working on
regularity problem for second order elliptic operator in
Poggi, University of Minnesota, is a doctoral student
at the University of Minnesota working under the supervision
of Svitlana Mayboroda. His current research interests lie at
the intersection of geometric measure theory, harmonic
analysis, and partial differential equations, with
particular emphasis on boundary value problems in rough
media for elliptic PDEs and generalized Schrodinger
- Jonathan Hill, University of Minnesota, graduated in
Spring 2017. Jonathan worked on the properties of the Green
function for elliptic operators with bounded measurable
coefficients. He has showed that in the case of an elliptic
operator with $t$-independent coefficients the Green
potential exhibits appropriate mapping properties in
weak-$L^p$ spaces (and this is sharp) and considered also
more general operators and systems. In particular, he worked
with Blair Davey on well-posedness of boundary problems for
generalized Schroedinger operators.
- Koushik Ramachandran, Purdue University, graduated
in May 2014. Koushik was working on asymptotics of harmonic
functions in rough paraboloid-shaped domains (supervised by
Svitlana Mayboroda jointly with Alexandre Eremenko). He has
published the results of his dissertation and has moved on
to a postdoctoral position at the Indian Statistical
Institute (ISI) at Bangalore, India.
- Eli Johnson, University of Minnesota, has worked on the
boundary regularity for fractional Laplacian under the
supervision of Svitlana Mayboroda. He is now a graduate
student at the University of Washington.
The resulting publication (in Contemporary
Mathematics) can be found
- Brandon Patterson has been working on localization of
vibrations in non-homogeneous strings
on the results of our present project
at the SIAM
Computational Science and Engineering Student Conference at
Purdue in 2011 has been awarded.
the Best Undergraduate
is now a graduate student at the University of Michigan
- Ye Wang, University of Minnesota, 2013, has
successfully completed a UROP (Undergraduate Research
Opportunities Program) project on Localization of
vibrations and conformal mappings.
- Yaowen Gu, University of Minnesota, 2012, has successfully
completed a Senior Project on the Harmonic measure and
- Levi Walls, University of Minnesota, 2016, has been
studying boundary value problems for elliptic equations,
spectral theory, and spherical harmonics.
- Joseph Pate, University of Minnesota, 2016-2017,
worked under the supervision of Svitlana Mayboroda on the
properties of the landscape function for the Neumann
problem, in concert with the localization of Neumann
eigenfunctions. He has received the UROP (Undergraduate
Research Opportunities Program) award and was supported in
part by the REU project within S. Mayboroda's CAREER grant.
- Partial Differential Equations, undergraduate, Fall 2015,
University of Minnesota.
- Real Analysis, graduate, Fall 2014, University of
- Theory of Partial Differential Equations -- II, graduate,
Spring 2014, University of Minnesota.
- Linear Algebra and Differential Equations, undergraduate,
Spring 2013, University of Minnesota.
- Introduction to Distributions, graduate, reading course,
Summer 2011, Purdue University.
- Partial Differential Equations,
Spring 2011, Purdue University.
- Ordinary Differential Equations,
Fall 2010, Purdue University.
- Ordinary Differential Equations, Fall 2009, Purdue
- Differential Equations and Partial Differential
Equations for Engineering and the Sciences, Fall 2008,
- Accelerated Calculus with Analytic Geometry II, Winter
2008, The Ohio State University.
- Real Analysis I-III, Fall 2006, Winter 2007, Spring
2007, Spring 2008, The Ohio State University
- Mathematical Analysis for Business II, Spring 2006,
The Ohio State University
- Calculus and Analytic Geometry I, Winter 2006, The Ohio
- Analytic Geometry and Calculus I, Fall 2004,
University of Missouri-Columbia
- Calculus II, Fall 2003, University of
- Elements of Calculus, Winter 2003, Winter 2004, Winter
2005, University of Missouri-Columbia
- College Algebra for Calculus Bound Students, Fall
2002, University of Missouri-Columbia