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. During her postdoctoral studies, Ariel has
finished 5 research papers, 3 of them jointly with Svitlana
Mayboroda, 1 expository, and 1 monograph, jointly with
Svitlana Mayboroda, submitted for publication. Ariel
currently holds a position at the University of Missouri.
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
Schroedinger-type elliptic operators. In this
direction, Blair has established pointwise bounds and
regularity for fundamental solutions of general elliptic
PDEs of Schrodinger type with bounded measurable
coefficients and is working on the properties of the
corresponding layer potentials.
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.
Joseph Feneuil, University of Minnesota, to start in
September 2015. Joseph Feneuil is currently a graduate
student at the University of Grenoble, working under the
supervision of Emmanuel Russ. He is planning to defend his
thesis in the Spring of 2015 and has accepted an offer of
the Dunham Jackson postdoctoral position at the University
of Minnesota, to work under the supervision of Svitlana
Mayboroda on harmonic analysis of elliptic boundary
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. See publications.
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.
Nadia Ott, University of Minnesota, is a graduate student
at the University of Minnesota. She is starting to work on
the localization of eigenfunctions in disordered media.
Patterson has been working on localization of
vibrations in non-homogeneous strings