Guillermo Rey, University of Minnesota, Fall 2018-Spring 2019. Guillermo was 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.
Robert
Viator, University of Minnesota and IMA,
2016-2017. 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 Mayboroda.
Simon
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.
Joseph
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
industry.
Blair
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.
Cole Jeznach, University of Minnesota, is a graduate student at University of Minnesota. Supervised jointly with Max Engelstein.
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 higher co-dimension.
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.
Undergraduate
Research:
Brandon
Patterson has been working on localization of
vibrations in non-homogeneous strings
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
Brownian motion.
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.