MENTORING: STUDENTS AND POSTDOCS
Postdoctoral
Researchers:
- 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). She has accepted a tenure-track
position at the University of Arkansas, Fayetteville.
- Blair
Davey, University of Minnesota, 2013--2017. 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 has secured a
tenure-track position at the CUNY, starting in the Fall of
2015.
- 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.
- Joseph
Feneuil, University of Minnesota, September 2015 -
present. Joseph Feneuil has graduated from the
University of Grenoble, under the supervision of Emmanuel
Russ. He has joined the University of Minnesota as a Dunham
Jackson postdoctoral researcher in the Fall of 2015 and is
working under the supervision of Svitlana Mayboroda on
analogues of harmonic measure in higher co-dimension.
- Simon
Bortz, University of Minnesota, September
2016-present. Simon Bortz has graduatied from the University
of Missouri, under the supervision of Steve Hofmann, in the
Spring of 2016. He has 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 is working on Dirichlet, Neumann, and
regularity problems in higher co-dimension, as well as layer
potentials for the generalized Schr\"odinger operator.
- Robert
Viator, University of Minnesota and IMA, September
2016-present. Robert Viator is 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, is working on the localization landscape
approach to Weyl law in periodic structures, under the
supervision of Svitlana Mayboroda.
Graduate
Students:
- 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.
- Jonathan Hill,
University of Minnesota, is working 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 is moving
towards considering more general operators and systems. In
particular, he is working with Blair Davey on well-posedness
of boundary problems for generalized Schroedinger operator.
Jonathan and Blair have already proved the basic estimates
of fundamental solutions, Green function, and Neumann Green
function.
- Eli Johnson, University of Minnesota, has worked on the
boundary regularity for fractional Laplacian under the
supervision of Svitlana Mayboroda. He is currently moving to
graduate school at the University of Washington.
- Bruno
Poggi, University of Minnesota, is a graduate student
at the University of Minnesota. He is working on sharp
exponential decay estimates for the heat kernel and
fundamental solution for the generalized Schrodinger
operator under the supervision of Svitlana Mayboroda.
Undergraduate
Research:
- Brandon
Patterson has been working on localization of
vibrations in non-homogeneous strings
The resulting publication (in Contemporary
Mathematics) can be found
here
Brandon's
talk
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
Speaker Award
Brandon
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
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, is
working 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 is supported in
part by the REU project within S. Mayboroda's CAREER grant.
TEACHING:
- Real Analysis, graduate, Fall 2014, University of
Minnesota.
- 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
University.
- Differential Equations and Partial Differential
Equations for Engineering and the Sciences, Fall 2008,
Purdue University.
- 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
State University
- Analytic Geometry and Calculus I, Fall 2004,
University of Missouri-Columbia
- Calculus II, Fall 2003, University of
Missouri-Columbia
- 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