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BEGIN:VEVENT
SUMMARY:Andras Vasy (Stanford University)
DTSTART:20200521T160000Z
DTEND:20200521T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/1
DESCRIPTION:Title: The inverse problem for the X-ray transform\nby Andras Vasy (St
anford University) as part of International Zoom Inverse Problems Seminar\
, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shari Moskow (Drexel University)
DTSTART:20200528T160000Z
DTEND:20200528T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/2
DESCRIPTION:Title: Reduced order models for spectral domain inversion: embedding into
the continuous problem and generation of internal data\nby Shari Mosko
w (Drexel University) as part of International Zoom Inverse Problems Semin
ar\, UC Irvine\n\n\nAbstract\nWe generate data-driven reduced order models
(ROMs) for inversion of the\none and two dimensional Schrodinger equatio
n in the spectral domain given boundary data\nat a few frequencies. The RO
M is the Galerkin projection of the Schrodinger operator onto\nthe space
spanned by solutions at these sample frequencies. The ROM matrix is in gen
eral\nfull\, and not good for extracting the potential. However\, using an
orthogonal change of\nbasis via Lanczos iteration\, we can transform the
ROM to a block triadiagonal form from\nwhich it is easier to extract q. In
one dimension\, the tridiagonal matrix corresponds to\na three-point stag
gered finite difference system for the Schrodinger operator discretized\n
on a so-called spectrally matched grid which is almost independent of the
medium. In\nhigher dimensions\, the orthogonalized basis functions play th
e role of the grid steps. The\northogonalized basis functions are localize
d and also depend only very weakly on the\nmedium\, and thus by embedding
into the continuous problem\, the reduced order model\nyields highly accur
ate internal solutions. That is to say\, we can obtain\, just from boundar
y\ndata\, very good approximations of the solution of the Schrodinger equ
ation in the whole\ndomain for a spectral interval that includes the sampl
e frequencies. We present inversion\nexperiments based on the internal sol
utions in one and two dimensions.\n\n*joint with L. BORCEA\, V. DRUSKIN\,
A. MAMONOV\, M. ZASLAVSKY\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Stefanov (Purdue University)
DTSTART:20200604T160000Z
DTEND:20200604T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/3
DESCRIPTION:Title: Noise in linear inverse problems\nby Plamen Stefanov (Purdue Un
iversity) as part of International Zoom Inverse Problems Seminar\, UC Irvi
ne\n\n\nAbstract\nWe study how noise in the data affects the noise in the
reconstruction\, for linear inverse problems\, more precisely when the ope
rator we have to invert is a Fourier Integral Operator. We apply the resul
ts to the Radon transform in the plane in parallel and in fan-bean coordin
ates. In this talk\, we concentrate on additive noise\, assuming that it i
s white but the methods apply to non-white noise as well. We propose the
microlocal defect measure as a measure of the spectral power of the noise
in the phase space. We show that one can compute the spectral power of the
noise in the reconstruction\, including its standard deviation\, as a fun
ction of the known statistical characteristics of the input noise. For the
Radon transform in parallel geometry\, we show that the induced noise is
position independent\, isotropic\, and “blue”. In fan-bean coordinates
\, the noise varies with position and it is not isotropic anymore but stil
l “blue”. This dependence is weak however and the standard deviation w
hich we compute\, still gives a good characterization of the strength of t
he induced noise.\n \nThis is a joint project\, still in progress\, with S
amy Tindel\, Purdue.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Paternain (University of Cambridge)
DTSTART:20200611T160000Z
DTEND:20200611T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/4
DESCRIPTION:Title: The non-Abelian X-ray transform\nby Gabriel Paternain (Universi
ty of Cambridge) as part of International Zoom Inverse Problems Seminar\,
UC Irvine\n\n\nAbstract\nI will discuss the problem of how to reconstruct
a matrix-valued potential from the knowledge of its scattering data along
geodesics on a compact non-trapping Riemannian manifold with boundary.\n\n
\nThe problem arises in new experiments designed to measure magnetic field
s inside materials by shooting them with neutron beams from different dire
ctions\, like in a CT scan.\n\n\nTowards the end of the lecture I will foc
us on the recent solutionof the injectivity question on simple surfaces fo
r any matrix Lie group.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Habib Ammari (ETH Zürich)
DTSTART:20200702T160000Z
DTEND:20200702T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/5
DESCRIPTION:Title: Wave Interaction with Subwavelength Resonators\nby Habib Ammari
(ETH Zürich) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\n\nAbstract\nIn this lecture\, the speaker reviews recent result
s on subwavelength resonances. His main focus is on developing a mathemati
cal and computational framework for their analysis. By characterizing and
exploiting subwavelength resonances in a variety of situations\, he propos
es a mathematical explanation for super-focusing of waves\, double-negativ
e metamaterials\, Dirac singularities in honeycomb subwavelength structure
s\, and topologically protected defect modes at the subwavelength scale. H
e also describes a new resonance approach for modelling the cochlea which
predicts the existence of a travelling wave in the acoustic pressure in th
e cochlea fluid and offers a basis for the tonotopic map.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroshi Isozaki (University of Tsukuba)
DTSTART:20200723T160000Z
DTEND:20200723T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/6
DESCRIPTION:Title: Inverse scattering on non-compact manifolds with general metric
\nby Hiroshi Isozaki (University of Tsukuba) as part of International Zoom
Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe consider a class o
f non-compact Riemannian manifolds\, as large as possible\, whose Laplacia
n has a continuous spectrum\, and show that the associated scattering matr
ix determines the manifold\, its topology and Riemannian metric. Knowledge
of one end is sufficient to determine the whole manifold. If the end is a
cusp\, by introducing a generalized S-matrix\, one can derive the same co
nclusion. We can also allow conic singularities for our manifolds so that
they include Riemannian orbifolds. As for the volume growth of each end\,
it can be polynomially or exponentially increasing or decreasing. So\, it
is a natural largest class of manifolds on which we can develop the spectr
al and scattering theory. This is a joint work with Matti Lassas (and Yaro
slav Kurylev).\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Guillarmou (Université Paris-Sud)
DTSTART:20200625T160000Z
DTEND:20200625T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/7
DESCRIPTION:Title: Asymptotically Euclidean metrics without conjugate points on R^n ar
e flat\nby Colin Guillarmou (Université Paris-Sud) as part of Interna
tional Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe show th
at Riemannian metrics on R^n that are asymptotic to the Euclidean metrics
to order O(1/|x|^3) and that have no conjugate points must be isometric to
the flat metric. This is joint work with M. Mazzucchelli and L. Tzou.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Vessella (University of Florence)
DTSTART:20200730T160000Z
DTEND:20200730T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/8
DESCRIPTION:by Sergio Vessella (University of Florence) as part of Interna
tional Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Schotland (University of Michigan)
DTSTART:20200813T160000Z
DTEND:20200813T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/9
DESCRIPTION:by John Schotland (University of Michigan) as part of Internat
ional Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josselin Garnier (Ecole Polytechnique)
DTSTART:20200618T160000Z
DTEND:20200618T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/10
DESCRIPTION:Title: Wave Propagation and Imaging in Random Media: From Gaussian to non
-Gaussian statistics\nby Josselin Garnier (Ecole Polytechnique) as par
t of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract
\nWe consider wave propagation and imaging in random media with the aim to
describe the wave statistics and to discuss correlation-based imaging. Wh
en scattering is strong enough the coherent (mean) wave vanishes and the s
econd-order moments of the wave field (more exactly\, the statistical Wign
er transform) satisfies a radiative transfer equation. Under such circumst
ances the wave correlations or Wigner transform should be used for correla
tion-based imaging. In this talk we discuss the statistical stability of t
he empirical Wigner transform. We discuss two regimes with different behav
iors. In the random paraxial regime the fluctuations of the smoothed Wigne
r transform are small and correlation-based imaging is possible. In random
ly perturbed open waveguides the fluctuations of the mode powers and wave
intensities grow exponentially and correlation-based imaging is challengin
g.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maarten de Hoop (Rice University)
DTSTART:20200709T160000Z
DTEND:20200709T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/11
DESCRIPTION:Title: Globally injective deep neural networks\nby Maarten de Hoop (R
ice University) as part of International Zoom Inverse Problems Seminar\, U
C Irvine\n\n\nAbstract\nWe present an analysis of injective\, ReLU\, deep
neural networks. We establish sharp conditions for injectivity of ReLU lay
ers and networks\, both fully connected and convolutional. We show through
a layer-wise analysis that an expansivity factor of two is necessary for
injectivity\; we also show sufficiency by constructing weight matrices whi
ch guarantee injectivity. Further\, we show that global injectivity with i
id Gaussian matrices\, a commonly used tractable model\, requires consider
ably larger expansivity. We then derive the inverse Lipschitz constant and
study the approximation-theoretic properties of injective neural networks
. Using arguments from differential topology we prove that\, under mild te
chnical conditions\, any Lipschitz map can be approximated by an injective
neural network. This justifies the use of injective neural networks in pr
oblems which a priori do not require injectivity.\n\nJoint work with M. Pu
thawala\, K. Kothari\, M. Lassas and I. Dokmani\\'{c}.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niky Kamran (McGill University)
DTSTART:20200716T160000Z
DTEND:20200716T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/12
DESCRIPTION:Title: Non-uniqueness results for the anisotropic Calder\\’on problem a
t fixed energy.\nby Niky Kamran (McGill University) as part of Interna
tional Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nIn its geo
metric formulation\, the anisotropic Calder\\’on problem consists in rec
overing up to some natural gauge equivalences the metric of a Riemannian m
anifold with boundary from the knowledge of the Dirichlet-to-Neumann map.
I will survey some recent non-uniqueness results obtained in collaboration
with Thierry Daud\\’e (Cergy-Pontoise) and Francois Nicoleau (Nantes) f
or the anisotropic Calder\\’on problem at fixed energy\, in the case of
disjoint or partial data. The underlying manifolds arising in these exampl
es are diffeomorphic to toric cylinders with two connected boundary compon
ents. In the case of disjoint data the metric is a suitably chosen warped
product metric which is everywhere smooth. For partial data\, the metric\,
which is adapted from Miller’s example of an elliptic operator which fa
ils to satisfy the unique continuation principle\, is smooth in the interi
or of the manifold\, but only H\\”older continuous on one connected comp
onent of the boundary.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liliana Borcea (University of Michigan)
DTSTART:20200820T160000Z
DTEND:20200820T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/13
DESCRIPTION:Title: Reduced order modeling for inverse problems\nby Liliana Borcea
(University of Michigan) as part of International Zoom Inverse Problems S
eminar\, UC Irvine\n\n\nAbstract\nI will discuss two approaches for buildi
ng reduced order models for solving inverse problems. One is for finding r
eflectors in a medium using an array of sensors that probes the medium wit
h pulses and measures the resulting waves. The other is for an inverse pro
blem for parabolic (heat) equations.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Monard (UC Santa Cruz)
DTSTART:20200806T160000Z
DTEND:20200806T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/14
DESCRIPTION:Title: Abelian and Non-Abelian X-ray transforms. Sharp mapping properties
and Bayesian inversion\nby François Monard (UC Santa Cruz) as part o
f International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nA
belian and Non-Abelian X-ray transforms are examples of integral-geometric
transforms with applications to X-ray Computerized Tomography and the ima
ging of magnetic fields inside of materials (Polarimetric Neutron Tomograp
hy).\n\n(1). We will first discuss recent results on a sharp description o
f the mapping properties of the X-ray transform (and its associated normal
operator I*I) on the Euclidean disk\, associated with a special L2 topolo
gy on its co-domain.\n\n(2). We will then focus on how to use this framewo
rk to show that attenuated X-ray transforms (with skew-hermitian attenuati
on matrix)\, more specifically their normal operators\, satisfy similar ma
pping properties. \n\n(3). Finally\, I will discuss an important applicati
on of these results to the Bayesian inversion of the problem of reconstruc
ting an attenuation matrix (or Higgs field) from its scattering data corru
pted with additive Gaussian noise. Specifically\, I will discuss a Bernste
in-VonMises theorem on the ‘local asymptotic normality’ of the posteri
or distribution as the number of measurement points tends to infinity\, us
eful for uncertainty quantification purposes. Numerical illustrations will
be given. \n\n(2) and (3) are joint work with R. Nickl and G.P.Paternain
(Cambridge).\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauri Oksanen (University College London)
DTSTART:20200903T160000Z
DTEND:20200903T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/15
DESCRIPTION:Title: Lorentzian Calderón problem under curvature bounds\nby Lauri
Oksanen (University College London) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\n\nAbstract\nWe introduce a method of solvi
ng inverse boundary value problems for wave equations on Lorentzian manifo
lds\, and show that zeroth order coefficients can be recovered under certa
in curvature bounds. The set of Lorentzian metrics satisfying the curvatur
e bounds has a non-empty interior in the sense of smooth\, compactly suppo
rted perturbations of the metric\, whereas all previous results on this pr
oblem impose conditions on the metric that force it to be real analytic wi
th respect to a suitably defined time variable. The analogous problem on R
iemannian manifolds is called the Calderón problem\, and in this case the
known results require the metric to be independent of one of the variable
s. Our approach is based on a new unique continuation result in the exteri
or of the double null cone emanating from a point. The approach shares fea
tures with the classical Boundary Control method\, and can be viewed as a
generalization of this method to cases where no real analyticity is assume
d. The talk is based on joint work with Spyros Alexakis and Ali Feizmohamm
adi.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Caro (BCAM)
DTSTART:20200910T160000Z
DTEND:20200910T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/16
DESCRIPTION:Title: The Calderón problem with corrupted data\nby Pedro Caro (BCAM
) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\n
Abstract\nThe inverse Calderón problem consists in determining the conduc
tivity inside a medium by electrical measurements on its surface. Ideally\
, these measurements determine the Dirichlet-to-Neumann map and\, therefor
e\, one usually assumes the data to be given by such map. This situation c
orresponds to having access to infinite-precision measurements\, which is
totally unrealistic. In this talk\, I will consider the Calderón problem
assuming data to contain measurement errors and provide formulas to recons
truct the conductivity and its normal derivative on the surface (joint wor
k with Andoni García). I will also present similar results for Maxwell’
s equations (joint work with Ru-Yu Lai\, Yi-Hsuan Lin\, Ting Zhou ). When
modelling errors in these two different frameworks\, one realizes the exis
tence of certain freedom that yields different reconstruction formulas. To
understand the whole picture of what is going on\, we rewrite the problem
in a different setting\, which will bring us to analyse the observational
limit of wave packets with noisy measurements (joint work with Cristóbal
J. Meroño).\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Kuchment (Texas A&M University)
DTSTART:20200917T160000Z
DTEND:20200917T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/17
DESCRIPTION:Title: Detecting presence of low-emission radiation sources\nby Peter
Kuchment (Texas A&M University) as part of International Zoom Inverse Pro
blems Seminar\, UC Irvine\n\n\nAbstract\nThe talk will describe the proble
m of detecting presence of a low emission nuclear source shielded by stron
g background and/or cargo.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Sjostrand (Université de Bourgogne)
DTSTART:20200924T160000Z
DTEND:20200924T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/18
DESCRIPTION:Title: On a d\, d-bar system with a large parameter\nby Johannes Sjos
trand (Université de Bourgogne) as part of International Zoom Inverse Pro
blems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Petkov (University of Bordeaux)
DTSTART:20201008T160000Z
DTEND:20201008T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/19
DESCRIPTION:Title: Location and Weyl asymptotics for the eigenvalues of some non self
-adjoint operators\nby Vesselin Petkov (University of Bordeaux) as par
t of International Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rakesh (University of Delaware)
DTSTART:20201022T160000Z
DTEND:20201022T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/20
DESCRIPTION:Title: The fixed angle scattering problem\nby Rakesh (University of D
elaware) as part of International Zoom Inverse Problems Seminar\, UC Irvin
e\n\n\nAbstract\nWe first discuss our (with Mikko Salo) uniqueness result
for the fixed angle scattering problem that the acoustic property (zeroth
order coefficient) of a medium is uniquely determined by the far-field dat
a\, measured in all directions for all frequencies\, associated with two i
ncoming plane waves from opposite directions. Next we discuss our (with Ve
nky Krishnan and Soumen Senapati) uniqueness result for a similar problem
where the coefficient depends on space and time variables. \n\nBoth proble
ms are formally determined and the results are proved by showing Lipschitz
stability for two inverse problems for hyperbolic PDEs with boundary data
\, using a variation of the Bukhgeim-Klibanov method.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allan Greenleaf (University of Rochester)
DTSTART:20201029T160000Z
DTEND:20201029T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/21
DESCRIPTION:Title: Microlocal analysis of Doppler synthetic aperture radar\nby Al
lan Greenleaf (University of Rochester) as part of International Zoom Inve
rse Problems Seminar\, UC Irvine\n\n\nAbstract\nConventional monostatic sy
nthetic aperture radar (SAR) uses range data obtained from measurements of
scattered radar waves to produce images of the Earth’s surface. The wav
eforms\, which are transmitted from an air- or space-borne platformand mea
sured by a co-located receiver\, are pulses with small temporal duration b
ut wide bandwidth.The short duration of the pulses can give rise to high s
patial resolution in the images\,and there is a considerable mathematical
literature concerning SAR.I will discuss an alternative approach\, called
Doppler SAR\, which uses a single frequency waveform. We use techniques
of microlocal analysis to describe the artifacts that might arise in DSAR
imaging\,and characterize some artifact-free regions. This is joint work w
ith Raluca Felea\, Romina Gaburro and Cliff Nolan.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Perry (University of Kentucky)
DTSTART:20201203T170000Z
DTEND:20201203T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/22
DESCRIPTION:by Peter Perry (University of Kentucky) as part of Internation
al Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chrysoula Tsogka (UC Merced)
DTSTART:20201001T160000Z
DTEND:20201001T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/23
DESCRIPTION:Title: The Noise Collector for sparse recovery in high dimensions\nby
Chrysoula Tsogka (UC Merced) as part of International Zoom Inverse Proble
ms Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kui Ren (Columbia University)
DTSTART:20201105T170000Z
DTEND:20201105T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/24
DESCRIPTION:Title: Inverse problems in photoacoustic imaging of nonlinear physics
\nby Kui Ren (Columbia University) as part of International Zoom Inverse P
roblems Seminar\, UC Irvine\n\n\nAbstract\nThis talk will discuss inverse
problems in the photoacoustic imaging of two-photon absorption of heteroge
neous media where we intend to reconstruct coefficients in systems of semi
linear diffusion and transport equations from single or multiple given dat
a sets. The main goal of the talk is (a) to give an overview of recent dev
elopments on the modeling\, computational and mathematical aspects of the
problem\, and (b) to point out some important questions that need to be ad
dressed.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Eskin (UCLA)
DTSTART:20201112T170000Z
DTEND:20201112T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/25
DESCRIPTION:by Gregory Eskin (UCLA) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yavar Kian (Aix Marseille University)
DTSTART:20201015T160000Z
DTEND:20201015T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/26
DESCRIPTION:Title: Simultaneous determination of internal source and coefficients of
a diffusion equation from a single boundary measurement\nby Yavar Kia
n (Aix Marseille University) as part of International Zoom Inverse Problem
s Seminar\, UC Irvine\n\n\nAbstract\nIn this talk\, we will consider the
inverse problem of determining simultaneously several class of coefficient
s and an internal source (a source term or an initial condition) appearin
g in a diffusion equation from a single boundary measurement. Our problem
can be formulated as the simultaneous determination of information about
a diffusion process (velocity field\, density of the medium) and of the so
urce of diffusion. We consider this problems in the context of a classical
diffusion process described by a convection-diffusion equation as well as
an anomalous diffusion phenomena described by a time fractional diffusio
n equation. Some parts of this talk are based on a joint work with Zhiyuan
Li\, Yikan Liu and Masahiro Yamamoto.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ozan Öktem (KTH)
DTSTART:20201210T170000Z
DTEND:20201210T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/27
DESCRIPTION:by Ozan Öktem (KTH) as part of International Zoom Inverse Pro
blems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Hezari (UC Irvine)
DTSTART:20201119T170000Z
DTEND:20201119T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/28
DESCRIPTION:by Hamid Hezari (UC Irvine) as part of International Zoom Inve
rse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Feizmohammadi (University College London)
DTSTART:20210121T170000Z
DTEND:20210121T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/29
DESCRIPTION:Title: The Jacobi weighted ray transform\nby Ali Feizmohammadi (Unive
rsity College London) as part of International Zoom Inverse Problems Semin
ar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiran Wang (Emory University)
DTSTART:20210211T170000Z
DTEND:20210211T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/30
DESCRIPTION:by Yiran Wang (Emory University) as part of International Zoom
Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Hezari (UC Irvine)
DTSTART:20210114T170000Z
DTEND:20210114T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/31
DESCRIPTION:Title: The inverse spectral problem for centrally symmetric real analytic
domains\nby Hamid Hezari (UC Irvine) as part of International Zoom In
verse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lexing Ying (Stanford University)
DTSTART:20210128T170000Z
DTEND:20210128T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/32
DESCRIPTION:Title: Solving Inverse Problems with Deep Learning\nby Lexing Ying (S
tanford University) as part of International Zoom Inverse Problems Seminar
\, UC Irvine\n\n\nAbstract\nThis talk is about some recent progress on sol
ving inverse problems using deep learning. Compared to traditional machine
learning problems\, inverse problems are often limited by the size of the
training data set. We show how to overcome this issue by incorporating ma
thematical analysis and physics into the design of neural network architec
tures. We first describe neural network representations of pseudodifferent
ial operators and Fourier integral operators. We then continue to discuss
applications including electric impedance tomography\, optical tomography\
, inverse acoustic/EM scattering\, seismic imaging\, and travel-time tomog
raphy.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Tamasan (University of Central Florida)
DTSTART:20210204T170000Z
DTEND:20210204T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/33
DESCRIPTION:Title: On a source reconstruction in an absorbing and scattering domain i
n the plane from measurements of fluxes at the boundary\nby Alexandru
Tamasan (University of Central Florida) as part of International Zoom Inve
rse Problems Seminar\, UC Irvine\n\n\nAbstract\nThis talk concerns the sou
rce reconstruction problem in a transport problem through an absorbing and
scattering medium from measurements of boundary fluxes at the boundary.
I will focus on the full boundary data in the scattering case\, and the pa
rtial data (measurements on an arc) in the non-scattering case\, and expla
in how a combination of these two cases solves the reconstruction problem
in the partial data case. The method\, specific to two dimensional domains
\, relies on Bukgheim’s theory of A-analytic maps and it is joint work w
ith H. Fujiwara (Kyoto U) and K. Sadiq (RICAM).\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carola-Bibiane Schönlieb (University of Cambridge)
DTSTART:20210218T170000Z
DTEND:20210218T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/34
DESCRIPTION:Title: Machine Learned Regularization for Solving Inverse Problems\nb
y Carola-Bibiane Schönlieb (University of Cambridge) as part of Internati
onal Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nInverse prob
lems are about the reconstruction of an unknown physical quantity from ind
irect measurements. Most inverse problems of interest are ill-posed and re
quire appropriate mathematical treatment for recovering meaningful solutio
ns. Regularization is one of the main mechanisms to turn inverse problems
into well-posed ones by adding prior information about the unknown quantit
y to the problem\, often in the form of assumed regularity of solutions. C
lassically\, such regularization approaches are handcrafted. Examples incl
ude Tikhonov regularization\, the total variation and several sparsity-pro
moting regularizers such as the L1 norm of Wavelet coefficients of the sol
ution. While such handcrafted approaches deliver mathematically and comput
ationally robust solutions to inverse problems\, providing a universal app
roach to their solution\, they are also limited by our ability to model so
lution properties and to realise these regularization approaches computati
onally. Recently\, a new paradigm has been introduced to the regularizatio
n of inverse problems\, which derives regularization approaches for invers
e problems in a data driven way. Here\, regularization is not mathematical
ly modelled in the classical sense\, but modelled by highly over-parametri
sed models\, typically deep neural networks\, that are adapted to the inve
rse problems at hand by appropriately selected (and usually plenty of) tra
ining data. In this talk\, I will review some machine learning based regul
arization techniques\, present some work on unsupervised and deeply learne
d convex regularisers and their application to image reconstruction from t
omographic and blurred measurements\, and finish by discussing some open m
athematical problems.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Houssem Haddar (Ecole Polytechnique)
DTSTART:20210225T170000Z
DTEND:20210225T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/35
DESCRIPTION:by Houssem Haddar (Ecole Polytechnique) as part of Internation
al Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuli Siltanen (University of Helsinki)
DTSTART:20210304T170000Z
DTEND:20210304T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/36
DESCRIPTION:Title: Learning from electric X-ray images: the new EIT\nby Samuli Si
ltanen (University of Helsinki) as part of International Zoom Inverse Prob
lems Seminar\, UC Irvine\n\n\nAbstract\nA fundamental connection between E
lectrical Impedance Tomography (EIT) and classical X-ray tomography was fo
und in [Greenleaf et al 2018]. There it was shown that a one-dimensional F
ourier transform applied to the spectral parameter of Complex Geometric Op
tics (CGO) solutions to a Beltrami equation is a useful technique. Microlo
cal analysis of the involved complex principal type operators reveals sing
ularities propagating in curious ways. They enable a novel filtered back-p
rojection type nonlinear reconstruction algorithm for EIT. This approach i
s called Virtual Hybrid Edge Detection (VHED). \n\nOne of the medically mo
st promising applications of EIT is stroke imaging. There are two main typ
es of stroke: (1) brain hemorrhage and (2) ischemic stroke caused by a blo
od clot. The symptoms for those two conditions are the same\, but the trea
tments are completely the opposite. There are two main uses for EIT here:
(a) classifying the type of stroke already in the ambulance with a cost-ef
fective portable device\, and (b) monitoring the state of recovering strok
e patients in the intensive care unit. \n\nThe main difficulty in using EI
T for head imaging is the resistive skull. Because of that\, the relevant
signal from the brain is weak and almost buried in noise. Given the extrem
e ill-posedness of the inverse conductivity problem\, it is quite a challe
nge to design a robust EIT algorithm for either (a) or (b). \n\nVHED offer
s a way to divide the information in EIT measurements into geometrically u
nderstood pieces. One could wish that those pieces are less sensitive to n
oise than a full reconstructed image of the conductivity. This presentatio
n shows how machine learning can be used for classifying stroke (problem (
a)) above based on VHED profiles. Examined are fully connected neural netw
orks (FCNN)\, convolutional neural networks (CNN) and recurrent neural net
works (RNN). Perhaps surprisingly\, CNNs offer the worst performance\, whi
le RNNs are slightly better than FCNNs.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Kutyniok (Ludwig-Maximilians-Universität München)
DTSTART:20210311T170000Z
DTEND:20210311T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/37
DESCRIPTION:Title: Graph Convolutional Neural Networks: The Mystery of Generalization
\nby Gitta Kutyniok (Ludwig-Maximilians-Universität München) as part
of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\
nThe tremendous importance of graph structured data due to\nrecommender sy
stems or social networks led to the introduction of\ngraph convolutional n
eural networks (GCN). Those split into spatial\nand spectral GCNs\, where
in the later case filters are defined as\nelementwise multiplication in th
e frequency domain of a graph.\nSince often the dataset consists of signal
s defined on many\ndifferent graphs\, the trained network should generaliz
e to signals\non graphs unseen in the training set. One instance of this p
roblem\nis the transferability of a GCN\, which refers to the condition th
at\na single filter or the entire network have similar repercussions on\nb
oth graphs\, if two graphs describe the same phenomenon. However\,\nfor a
long time it was believed that spectral filters are not\ntransferable.\n\n
In this talk we aim at debunking this common misconception by\nshowing tha
t if two graphs discretize the same continuous metric\nspace\, then a spec
tral filter or GCN has approximately the same\nrepercussion on both graphs
. Our analysis also accounts for large\ngraph perturbations as well as all
ows graphs to have completely\ndifferent dimensions and topologies\, only
requiring that both\ngraphs discretize the same underlying continuous spac
e. Numerical\nresults then even imply that spectral GCNs are superior to s
patial\nGCNs if the dataset consists of signals defined on many different\
ngraphs.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Isakov (Wichita State University)
DTSTART:20210318T160000Z
DTEND:20210318T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/38
DESCRIPTION:Title: On increasing stability and minimal data in inverse problems\n
by Victor Isakov (Wichita State University) as part of International Zoom
Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe expose (with basic
ideas of proofs) recent results about improving stability in the Cauchy pr
oblem for general elliptic partial differential equations of second order
of Helmholtz type without any geometrical assumptions on domains and oper
ators when the wave number is growing. The next topic is better stability
in in the inverse source scattering problems with the boundary data at an
interval of wave numbers when this interval is getting larger. We give ra
ther complete theory for the Helmholtz equation (based on sharp bounds of
analytic and exact observability for the wave equation)\, as well as conv
incing numerical examples. Similarly we discuss recovery of the Schroeding
er potential from the Dirichlet-to Neumann map. Finally\, we report on fir
st results on the inverse problems where the wave number is zero (or small
)\, showing that in the two dimensional case of inverse gravimetry in a re
alistic practical situation one can stably find only 5 real parameters of
gravity force at the boundary and with this data uniquely determine an ell
ipse.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angkana Rüland (Heidelberg University)
DTSTART:20210325T160000Z
DTEND:20210325T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/39
DESCRIPTION:Title: On instability mechanisms in inverse problems\nby Angkana Rül
and (Heidelberg University) as part of International Zoom Inverse Problems
Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaik Ambartsoumian (University of Texas at Arlington)
DTSTART:20210401T160000Z
DTEND:20210401T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/40
DESCRIPTION:Title: 2D vector tomography with broken rays and stars\nby Gaik Ambar
tsoumian (University of Texas at Arlington) as part of International Zoom
Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nMultiple classical wor
ks of integral geometry have been dedicated to the reconstruction of vecto
r fields from various integral transforms of such fields\, including the l
ongitudinal ray transform (Doppler transform)\, transverse ray transform\,
and their integral moments. We consider a generalization of these transfo
rms\, in which the straight-line path of integration is substituted either
by broken rays or by stars (a finite union of rays emanating from a commo
n vertex). We present several exact closed-form inversion formulas for cer
tain pairs of these transforms on 2D compactly supported vector fields in
the plane\, discuss their properties and present results of numerical simu
lations. The talk is based on joint work with Mohammad Latifi (University
of Arizona) and Rohit Mishra (University of Texas at Arlington).\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mourad Bellassoued (University of Tunis El Manar\, Tunisia)
DTSTART:20210408T160000Z
DTEND:20210408T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/41
DESCRIPTION:Title: Stable recovery of a metric tensor from the partial hyperbolic Dir
ichlet to Neumann map\nby Mourad Bellassoued (University of Tunis El M
anar\, Tunisia) as part of International Zoom Inverse Problems Seminar\, U
C Irvine\n\n\nAbstract\nIn this talk we consider the inverse problem of de
termining on a compact Riemannian manifold the metric tensor in the wave e
quation with Dirichlet data from measured Neumann sub-boundary observatio
ns. This information is enclosed in the dynamical partial Dirichlet-to-Neu
mann map associated to the wave equation. We prove in dimension $n\\geq 2$
that the knowledge of the partial Dirichlet-to-Neumann map for the wave
equation uniquely determines the metric tensor and we establish logarithm-
type stability.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antônio Sá Barreto (Purdue University)
DTSTART:20210415T160000Z
DTEND:20210415T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/42
DESCRIPTION:Title: Inverse Scattering for Critical Semilinear Wave Equations\nby
Antônio Sá Barreto (Purdue University) as part of International Zoom Inv
erse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe show that the scatteri
ng operator for defocusing energy critical semilinear wave equations $\\s
quare u+f(u)=0\,$ $f\\in C^\\infty(\\mr)$ and $f\\sim u^5\,$ in three spa
ce dimensions\, determines $f$. This is joint work with Gunther Uhlmann an
d Yiran Wang.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ting Zhou (Northeastern University)
DTSTART:20210422T160000Z
DTEND:20210422T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/43
DESCRIPTION:Title: Inverse Problems for Nonlinear PDEs\nby Ting Zhou (Northeaster
n University) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\n\nAbstract\nIn this talk\, I will demonstrate the higher order l
inearization approach to solve several inverse boundary value problems for
nonlinear PDEs modeling nonlinear electromagnetic optics including nonlin
ear time-harmonic Maxwell’s equations with Kerr-type and second harmonic
generation nonlinearity. The problem will be reduced to solving for the c
oefficient functions from their integrals against multiple linear solution
s. We will focus our discussion on different choices of linear solutions.
A similar problem for nonlinear magnetic Schrodinger equation will be cons
idered as a comparison.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanming Zhou (UC Santa Barbara)
DTSTART:20210429T160000Z
DTEND:20210429T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/44
DESCRIPTION:Title: Travel time tomography in stationary spacetimes\nby Hanming Zh
ou (UC Santa Barbara) as part of International Zoom Inverse Problems Semin
ar\, UC Irvine\n\n\nAbstract\nIn this talk\, I will discuss the boundary r
igidity problem on a cylindrical domain in $\\mathbb R^{1+n}$\, $n\\geq 2$
\, equipped with a stationary (time-invariant) Lorentzian metric. We show
that the time separation function between pairs of points on the boundary
of the cylindrical domain determines the stationary spacetime\, up to some
time-invariant diffeomorphism\, assuming that the metric is close to the
Minkowski metric\, and satisfies some a-priori conditions. The talk is bas
ed on joint work with Gunther Uhlmann (UW) and Yang Yang (MSU).\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joonas Ilmavirta (Tampere University)
DTSTART:20210506T160000Z
DTEND:20210506T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/45
DESCRIPTION:Title: Geometric inverse problems arising from geophysics\nby Joonas
Ilmavirta (Tampere University) as part of International Zoom Inverse Probl
ems Seminar\, UC Irvine\n\n\nAbstract\nI will describe how geometrization
of some seismological problems leads to geometric inverse problems\, focus
ing on broader ideas rather than specific details or theorems. The talk wi
ll mostly revolve around seismology\, modelling\, PDEs\, differential geom
etry\, and inverse problems.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Liimatainen (University of Helsinki)
DTSTART:20210513T160000Z
DTEND:20210513T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/46
DESCRIPTION:Title: Linearized Calderón problem and exponentially accurate quasimodes
for analytic manifolds\nby Tony Liimatainen (University of Helsinki)
as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAb
stract\nI will discuss a new method for the linearized anisotropic Calder
ón problem on cylindrical Riemannian manifolds. I will present our recent
result with Katya Krupchyk and Mikko Salo\, https://arxiv.org/abs/2009.05
699. Crucial ingredients in the proof of our result are the construction o
f Gaussian beam quasimodes with exponentially small errors\, as well as th
e FBI transform characterization of the analytic wave front set. These mig
ht have applications in other inverse problems as well.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ru-Yu Lai (University of Minnesota)
DTSTART:20210520T160000Z
DTEND:20210520T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/47
DESCRIPTION:Title: An inverse problem for the Boltzmann equation\nby Ru-Yu Lai (U
niversity of Minnesota) as part of International Zoom Inverse Problems Sem
inar\, UC Irvine\n\n\nAbstract\nThe Inverse problem for the Boltzmann equa
tion finds applications in many fields such as optical imaging. It seeks t
o reconstruct certain physical properties of a medium from the data measur
ed on the boundary. In this talk\, I will discuss an inverse problem for t
he Boltzmann equation with nonlinear collision operator. We show that the
collision kernel can be reconstructed from the incoming-to-outgoing mappin
gs on the boundary of the domain. This talk is based on a joint work with
Gunther Uhlmann (UW) and Yang Yang (MSU).\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Novikov (Penn State University)
DTSTART:20210527T160000Z
DTEND:20210527T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/48
DESCRIPTION:Title: Imaging with highly incomplete and corrupted data\nby Alexei N
ovikov (Penn State University) as part of International Zoom Inverse Probl
ems Seminar\, UC Irvine\n\n\nAbstract\nWe consider the problem of imaging
sparse scenes from a few noisy data using an l1-minimization approach. Thi
s problem can be cast as a linear system of the form Ax=b. The dimension o
f the unknown sparse vector x is much larger than the dimension of the dat
a vector b. The l1-minimization alone\, however\, is not robust for imagin
g with noisy data. To improve its performance we propose to solve instead
the augmented linear system [A|C]x=b\, where the matrix C is a noise colle
ctor. It is constructed so as its column vectors provide a frame on which
the noise of the data can be well approximated with high probability. This
approach gives rise to a new hyper-parameter free imaging method that ha
s a zero false discovery rate for any level of noise. We further apply the
idea of the noise collector to signal recovery from cross-correlated data
matrix bb’. Cross-correlations naturally arise in many fields of imagin
g\, such as optics\, holography and seismic interferometry. The unknown is
now a matrix xx’ formed by the cross correlation of the unknown signa
l. Hence\, the bottleneck for inversion is the number of unknowns that gro
ws quadratically with dimension of x. The noise collector helps to reduce
the dimensionality of the problem by recovering only the diagonal of xx’
\, whose dimension grows linearly with the size of x. I will demonstrate t
he effectiveness of our approach for radar imaging. The method itself\, ho
wever\, can be applied in\, among others\, medical imaging\, structural bi
ology\, geophysics and high-dimensional linear regression in statistics. T
his is a joint work with M. Moscoso\, G.Papanicolaou and C. Tsogka.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis Chung (University of Kentucky)
DTSTART:20210603T160000Z
DTEND:20210603T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/49
DESCRIPTION:Title: Optical Inverse Problems with Local Data\nby Francis Chung (Un
iversity of Kentucky) as part of International Zoom Inverse Problems Semin
ar\, UC Irvine\n\n\nAbstract\nOptical tomography is the process of reconst
ructing internal properties of an object by making optical measurements at
the boundary. By considering both diffusion and transport models for ligh
t propagation\, this process gives rise to a number of interesting inverse
problems. Although many of these problems are solved in the case of full
boundary data\, most are still at least partially open in the case of loca
l data\, where measurements are restricted to a fixed subset of the bounda
ry. In this talk I will describe four of these problems\, and discuss some
of what is known in each case.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Albert Fannjiang (UC Davis)
DTSTART:20210610T160000Z
DTEND:20210610T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/50
DESCRIPTION:Title: Ptychography: Theory and Algorithms\nby Albert Fannjiang (UC D
avis) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n
\n\nAbstract\nPtychography is a scanning version of coded-aperture phase r
etrieval\, a versatile method that finds its way to many applications in m
olecular and materials imaging. Its operating principle is that measuremen
t redundancy due to overlap of scanning probe removes the usual ambiguitie
s in standard phase retrieval by providing extra constraint for unique cha
racterization of the underlying extended object. \n\nA remarkable effect o
f ptychography emerged in physics experiments more than 10 years ago that
the coded aperture can be recovered along with the unknown object\, up to
a constant phase factor\, for certain measurement schemes with sufficient
probe overlap (i.e. blind ptychography). We review recent progress in math
ematical theory and algorithms developed for blind ptychography operating
at realistic level of measurement resources.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenneth Golden (University of Utah)
DTSTART:20210617T160000Z
DTEND:20210617T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/51
DESCRIPTION:Title: On Thinning Ice: Modeling and monitoring sea ice in a warming clim
ate\nby Kenneth Golden (University of Utah) as part of International Z
oom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nPolar sea ice is a
key component of Earth’s climate system. As a material it is a composit
e which is structured on length scales ranging over ten orders of magnitud
e. A principal challenge in modeling sea ice is how to use information on
small scale structure to find the effective or homogenized properties on l
arger scales relevant to climate models. Moreover\, the inverse problem of
estimating parameters controlling small scale processes from large scale
observations is also of interest. For example\, electromagnetic remote sen
sing of sea ice is central to assessing the impact of climate change. We w
ill discuss recent results on forward and inverse homogenization for sea i
ce over a broad range of scales. We consider electromagnetic and fluid tra
nsport through the brine and polycrystalline microstructure\, advection di
ffusion processes\, ocean wave propagation through the ice pack\, melt pon
ds\, and the sea ice concentration field over the Arctic Ocean. This work
is helping to advance how sea ice is represented in climate models\, and t
o improve projections of the fate of Earth’s sea ice packs and the ecosy
stems they support.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Faraco Hurtado (Universidad Autónoma de Madrid)
DTSTART:20210624T160000Z
DTEND:20210624T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/52
DESCRIPTION:Title: Mathematics with Slava Kurylev: Homogenization and Inverse Proble
ms\nby Daniel Faraco Hurtado (Universidad Autónoma de Madrid) as part
of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\
nI wil describe two theorems of Y. Kurylev with the Madrid group in relat
ion with homogenization and inverse problems. In between those theorems I
will revisit the relation between quasiconformal maps and the stability of
Calderón problemand how a suitable average of the time dependent non el
liptic Schrödinger equation provides a seemly stable Buckgheim type reco
very algorthim for irregular potentials. The talk is aimed to be not techn
ical and highlighting the new viewpoints.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunther Uhlmann (University of Washington)
DTSTART:20210819T160000Z
DTEND:20210819T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/53
DESCRIPTION:Title: The Dirichlet-to-Neumann Map\, the Boundary Distance Function\, an
d the Geodesic X-Ray Transform\nby Gunther Uhlmann (University of Wash
ington) as part of International Zoom Inverse Problems Seminar\, UC Irvine
\n\n\nAbstract\nWe will discuss some connections between these three topic
s.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Nachman (University of Toronto)
DTSTART:20210826T160000Z
DTEND:20210826T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/54
DESCRIPTION:Title: A nonlinear Plancherel Theorem with applications to global well-po
sedness for the Defocusing Davey-Stewartson Equation and to the Calderón
Inverse Problem in dimension 2\nby Adrian Nachman (University of Toron
to) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n
\nAbstract\nI’ll describe a well-studied nonlinear Fourier transform in
two dimensions for which a proof of the Plancherel theorem had been a chal
lenging open problem. I’ll sketch out the main ideas of the solution of
this problem\, as well as the solution of two other problems that motivate
d it: global well-posedness for the Defocusing DSII Equation in the mass c
ritical case\, and global uniqueness for the Inverse Boundary Value Proble
m of Calderón for a class of unbounded conductivities. On the way\, there
will also be new estimates for classical fractional integrals\, and a new
result on L^2 boundedness of pseudodifferential operators with non-smooth
symbols. (This is joint work with Idan Regev and Daniel Tataru.)\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Rundell (Texas A&M University)
DTSTART:20210902T160000Z
DTEND:20210902T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/55
DESCRIPTION:Title: Inverse Problems for Fractional Partial Differential Equations
\nby William Rundell (Texas A&M University) as part of International Zoom
Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nFractional derivatives
and powers of operators have been a well-studied topic over the last deca
de — and for good reason. Not only is there interesting mathematics invo
lved but a myriad of applications have shown that such operators have defi
nitely left any curiousity-level label. Also\, many inverse problems for P
DE are characterised by the fact that their solution is often highly ill-p
osed. In this talk we shall look at several inverse problems involving bot
h classical derivatives and some of their fractional counterparts. The rec
urring question\, which will come with some answers\, is whether these two
paradigms give similar uniqueness results and if the levels of ill-posedn
ess are the same and\, of course\, why this should be so.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Kunyansky (University of Arizona)
DTSTART:20210909T160000Z
DTEND:20210909T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/56
DESCRIPTION:Title: Parametrix for the inverse source problem of thermoacoustic tomogr
aphy with reduced data\nby Leonid Kunyansky (University of Arizona) as
part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbst
ract\nWe consider the inverse source problem of thermo- and photoacoustic
tomography\, with data registered on an open surface partially surrounding
the source of acoustic waves. Our goal is to find efficient non-iterative
\nsolutions to this problem.\n\nI will present two different methods:\n\n(
1) A procedure based on solving the exterior Dirichlet problem and computi
ng the Radon transform of the solution. This technique works under assumpt
ion of a constant speed of sound.\n\n(2) A procedure based on modifying th
e time-reversed solution by two Hilbert transforms\, one in time and one i
n a certain spatial variable. This techniques works for a smooth known spe
ed of sound\, subject to an additional geometric condition.\n\nBoth techni
ques produce microlocally accurate approximations to the sought initial co
ndition. In certain geometries these methods can be implemented as fast al
gorithms. Performance of these techniques will be demonstrated in numerica
l simulations.\n\nJoint work with M. Eller and P. Hoskins\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tracey Balehowsky (University of Helsinki)
DTSTART:20210916T160000Z
DTEND:20210916T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/57
DESCRIPTION:Title: Determining a Riemannian metric from least-area data\nby Trace
y Balehowsky (University of Helsinki) as part of International Zoom Invers
e Problems Seminar\, UC Irvine\n\n\nAbstract\nIn this talk\, we address th
e following question: Given any simple closed curve $\\gamma$ on the bound
ary of a Riemannian 3-manifold $(M\,g)$\, suppose the area of the least-ar
ea surfaces bounded by $\\gamma$ are known. From this data may we uniquely
recover $g$? \n\nIn several settings\, we show the the answer is yes. In
fact\, we prove both global and local uniqueness results given least-area
data for a much smaller class of curves on the boundary. We demonstrate un
iqueness for $g$ by reformulating parts of the problem as a 2-dimensional
inverse problem on an area-minimizing surface. In particular\, we relate o
ur least-area information to knowledge of the Dirichlet-to-Neumann map for
the stability operator on a minimal surface. \n\nBroadly speaking\, the q
uestion we address is a dimension 2 version of the classical boundary rigi
dity problem for simply connected\, Riemannian 3-manifolds with boundary.
We will briefly review this problem of boundary rigidity as it relates to
aspects of our question of recovering $g$ from knowledge of areas. \n\nThi
s is joint work with S. Alexakis and A. Nachman.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihajlo Cekić (Université Paris-Saclay)
DTSTART:20210923T160000Z
DTEND:20210923T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/58
DESCRIPTION:Title: The Holonomy Inverse Problem\nby Mihajlo Cekić (Université P
aris-Saclay) as part of International Zoom Inverse Problems Seminar\, UC I
rvine\n\n\nAbstract\nGiven a compact Riemannian manifold (M\, g) and a vec
tor bundle over M equipped with a connection\, we consider the following q
uestion: does the holonomy along closed geodesics determine the gauge (equ
ivalence) class of the connection? If (M\, g) has negative curvature or mo
re generally its geodesic flow is Anosov\, in this talk I will explain how
in fact\, only the traces of the holonomy along closed geodesics locally
determine a generic connection\; global uniqueness results are obtained in
some cases. A direct consequence is an inverse spectral result for the co
nnection (magnetic) Laplacian. The proof relies on two new ingredients: a
Livšic type theorem in hyperbolic dynamics for unitary cocycles\, and the
interplay between the local geometry of the moduli space of connections w
ith Pollicott-Ruelle resonances of a certain natural transport operator. J
oint work with Thibault Lefeuvre.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Cherkaev (University of Utah)
DTSTART:20210930T160000Z
DTEND:20210930T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/59
DESCRIPTION:Title: Inverse homogenization: Can one hear the structure of a composite?
\nby Elena Cherkaev (University of Utah) as part of International Zoom
Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nInverse homogenizatio
n is a problem of deriving information about the microgeometry of a finely
structured medium from its known effective properties. I will discuss an
approach to this problem based on reconstructing the matrix-valued spectra
l measure in the Stieltjes integral representation of the effective proper
ties of a two-component composite. This integral representation relates th
e n-point correlation functions of the microstructure to the moments of th
e spectral measure of an operator depending on the composite’s geometry.
I will show that the spectral measure which contains all information abou
t the microstructure\, can be uniquely recovered from frequency dependent
effective data\; this allows to view the problem as an inverse spectral pr
oblem. In particular\, the moments of the measure and the spectral gaps at
the ends of the spectral interval can be uniquely reconstructed\, which r
esults in the unique identification of the volume fractions of materials i
n the composite and estimates for the connectedness of its phases. I will
discuss the recovery of microstructural parameters from electromagnetic an
d viscoelastic effective measurements and show that the resulting spectros
copic imaging method provides an efficient way to construct spectrally mat
ched microstructures.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fioralba Cakoni (Rutgers University)
DTSTART:20211007T160000Z
DTEND:20211007T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/60
DESCRIPTION:Title: Singularities Almost Always Scatter: Regularity Results for Non-sc
attering Inhomogeneities\nby Fioralba Cakoni (Rutgers University) as p
art of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstra
ct\nA perplexing question in scattering theory is whether there are incom
ing time harmonic waves\, at particular frequencies\, that are not scatter
ed by a given inhomogeneity\, in other words the inhomogeneity is invisibl
e to probing by such waves. We refer to wave numbers\, that correspond to
frequencies for which there exists a non-scattering incoming wave\, as no
n-scattering. This question is inherently related to the solution of inver
se scattering problem for inhomogeneous media. The attempt to provide an
answer to this question has led to the so-called transmission eigenvalue p
roblem with the wave number as the eigen-parameter. This is non-selfadjoi
nt eigenvalue problem with challenging mathematical structure. The non-sca
ttering wave numbers form a subset of real transmission eigenvalues. A po
sitive answer to the existence of non-scattering wave numbers is already k
nown for spherical inhomogeneities and a negative answer was given for
inhomogeneities with corners. Up to very recently little was known about n
on-scattering inhomogeneities that are neither spherical symmetric nor hav
ing support that contains a corner. In this presentation we discuss some
new results for general inhomogeneities. More specifically we examine nece
ssary conditions for an inhomogeneity to be non-scattering\, or equivalent
ly\, by negation\, sufficient conditions for it to be scattering. These co
nditions are formulated in terms of the regularity of the boundary and ref
ractive index of the inhomogeneity. Our approach makes a connection betwee
n non-scattering configuration and free boundary methods. \n\nThis present
ation is based on a joint work with Michael Vogelius.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Beretta (Politecnico di Milano)
DTSTART:20211014T160000Z
DTEND:20211014T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/61
DESCRIPTION:Title: Title: Identification of cavities in a nonlinear model arising fro
m cardiac electrophysiology via Gamma-convergence\nby Elena Beretta (P
olitecnico di Milano) as part of International Zoom Inverse Problems Semin
ar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingni Xiao (Rutgers University)
DTSTART:20211021T160000Z
DTEND:20211021T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/62
DESCRIPTION:Title: Nonscattering Wavenumbers\nby Jingni Xiao (Rutgers University)
as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nA
bstract\nIn this talk\, I will survey some recent results on the existence
or nonexistence of nonscattering wavenumbers under various settings\, inc
luding medium scatterers with corners or with regular boundaries. This tal
k is partially based on joint papers with F. Cakoni\, M. Vogelius\, H. Liu
\, and E. Blåsten.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otmar Scherzer (University of Vienna & RICAM)
DTSTART:20211028T160000Z
DTEND:20211028T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/63
DESCRIPTION:Title: Projection and Diffraction Tomography of Particles in a Trap\n
by Otmar Scherzer (University of Vienna & RICAM) as part of International
Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nTomographic imagi
ng of particles in a trap is a recent research topic in microscopy. There
a particle is moved by tweezers for tomographic imaging. Mathematically\,
this results in a tomographic imaging problem with irregular movement. Typ
ically the problem is split up into two problems: The first is motion dete
ction and the second is 3D tomographic imaging. We consider motion detecti
on based on optical projection imaging and 3D tomographic imaging based on
a diffraction forward model. Open problems and relations to mathematical
problems in Cryo imaging are discussed.\n\nThis is joint work with Peter
Elbau\, Florian Faucher\, Clemens Kirisits\, Michael Quellmalz\, Monika Ri
tsch-Marte\, Eric Setterqvist\, Gabriele Steidl.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Passamani Zubelli (Khalifa University)
DTSTART:20211104T160000Z
DTEND:20211104T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/64
DESCRIPTION:Title: A Splitting Strategy for the Calibration of Jump-Diffusion Models<
/a>\nby Jorge Passamani Zubelli (Khalifa University) as part of Internatio
nal Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nThis talk con
cerns the calibration of Dupire’s model in the presence of jumps. This l
eads to an integro-differential equation whose parameters have to be calib
rated so as to fit market data. We present a detailed analysis and impleme
ntation of a splitting strategy to identify simultaneously the local-volat
ility surface and the jump-size distribution from quoted European prices.
The underlying model consists of a jump-diffusion driven asset with\ntime
and price dependent volatility. Our approach uses a forward Dupire-type pa
rtial-integro-differential equation for the option prices to produce a par
ameter-to-solution map. The ill-posed inverse problem for such a map is th
en solved by means of a Tikhonov-type convex regularization. We present nu
merical examples that substantiate the robustness of the method both for
synthetic and real data. This is joint work with Vinicius Albani (UFSC) th
at appeared in Finance and Stochastics.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Guevara Vasquez (University of Utah)
DTSTART:20211118T170000Z
DTEND:20211118T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/65
DESCRIPTION:Title: Active thermal cloaking and mimicking\nby Fernando Guevara Vas
quez (University of Utah) as part of International Zoom Inverse Problems S
eminar\, UC Irvine\n\n\nAbstract\nWe show how to hide objects or sources b
y using an active source and dipole distribution on a surface enclosing th
e region to be cloaked\, allowing for cloaking even in transient regimes.
This technique does assume a homogeneous medium and knowledge of the probi
ng field\, but applies to a variety of physical phenomena that can be mode
led by the heat equation (including mass or light diffusion). The same ide
a can be used to make an object (or source) appear as another one. This is
work in collaboration with Maxence Cassier\, Trent DeGiovanni and Sebasti
en Guenneau.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xue-Cheng Tai (Hong Kong Baptist University)
DTSTART:20211209T170000Z
DTEND:20211209T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/66
DESCRIPTION:Title: Deep neural networks in image processing\nby Xue-Cheng Tai (Ho
ng Kong Baptist University) as part of International Zoom Inverse Problems
Seminar\, UC Irvine\n\n\nAbstract\nIn this talk\, we present our recent r
esearch on using variational models as layers for deep neural networks (DN
Ns). We use image segmentation as an example. The technique can also be us
ed for high dimensional data classification as well. Through this techniqu
e\, we could integrate many well-know variational models for image segment
ation into deep neural networks. The new networks will have the advantages
of traditional DNNs. At the same time\, the outputs from the new networks
can also have many good properties of variational models for image segmen
tation. We will present some techniques to incorporate shape priors into t
he networks through the variational layers. We will show how to design net
works with spatial regularization and volume preservation. We can also des
ign networks with guarantee that the output shapes from the network for im
age segmentation must be convex shapes/star-shapes. It is numerically veri
fied that these techniques can improve the performance when the true shape
s satisfy these priors. \n\nThe ideas of these new networks is based on so
me relationship between the softmax function\, the Potts models and the st
ructure of traditional DNNs. We will explain this in detail which leads na
turally to the newly designed networks. \n\nThis talk is based on joint wo
rks with Jun Liu\, S. Luo and several other collaborators.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi-Hsuan Lin (National Yang Ming Chiao Tung University)
DTSTART:20211202T170000Z
DTEND:20211202T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/67
DESCRIPTION:Title: Simultaneous recovery inverse problems for nonlinear and nonlocal
equations\nby Yi-Hsuan Lin (National Yang Ming Chiao Tung University)
as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAb
stract\nWe study inverse problems associated with semilinear parabolic and
hyperbolic systems in several scenarios where both the nonlinearities and
the initial data can be unknown. We also show that some simultaneous reco
very results hold for both nonlocal and nonlinear elliptic equations. It t
urns out that the nonlinearity and nonlocality play critical roles in deri
ving these simultaneous recovery results.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Covi (Heidelberg University)
DTSTART:20211216T170000Z
DTEND:20211216T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/68
DESCRIPTION:Title: Uniqueness for the fractional Calderon problem with quasilocal per
turbations\nby Giovanni Covi (Heidelberg University) as part of Intern
ational Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe will b
e talking about the fractional Schrodinger equation with quasilocal pertur
bations. Quasilocal operators are a special kind of nonlocal operators tra
nsforming compactly supported functions into functions of unbounded suppor
t with a decay estimate at infinity. These include\, among the others\, co
nvolutions operators against Schwartz functions. We will show that both qu
alitative and quantitative unique continuation and Runge approximation pro
perties hold in the assumption of sufficient decay. The results are then u
sed to show uniqueness in the inverse problem of retrieving a quasilocal p
erturbation from DN data under suitable geometric assumptions. This work g
eneralizes recent results regarding the locally perturbed fractional Calde
ron problem\, and is based on the following paper: https://arxiv.org/abs/2
110.11063\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Kenig (University of Chicago)
DTSTART:20220113T170000Z
DTEND:20220113T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/69
DESCRIPTION:Title: Wave maps into the sphere\nby Carlos Kenig (University of Chic
ago) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\
n\nAbstract\nWe will introduce wave maps and discuss some of their basic p
roperties\, leading to recent works on the soliton resolution conjecture f
or critical wave maps and related equations.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State University)
DTSTART:20220120T170000Z
DTEND:20220120T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/70
DESCRIPTION:Title: An inverse problem in fault detection\nby Anna Mazzucato (Penn
State University) as part of International Zoom Inverse Problems Seminar\
, UC Irvine\n\n\nAbstract\nI will discuss a model for dislocations in an e
lastic medium\, modeling faults in the Earth’s crust. The direct problem
consists in solving a non-standard boundary value/interface problem for i
sotropic linear elasticity with piecewise Lipschitz Lame’ parameters. Th
e inverse problem consists in determining the fault surface and slip vecto
r from displacement measurements made at the surface. We prove uniqueness
under some geometric conditions\, using unique continuation results. The r
esults extend to certain anisotropic media in 2 dimensions.\nWe also estab
lish shape derivative formulas under infinitesimal movements of the fault
and changes in the slip. . This is joint work with Andrea Aspri (Milan Un
iversity)\, Elena Beretta (NYU-Abu Dhabi)\, and Maarten de Hoop (Rice Univ
ersity).\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Zelditch (Northwestern University)
DTSTART:20220127T170000Z
DTEND:20220127T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/71
DESCRIPTION:Title: Spatial and Fourier restriction problems for eigenfunctions\nb
y Steve Zelditch (Northwestern University) as part of International Zoom I
nverse Problems Seminar\, UC Irvine\n\n\nAbstract\nThere are two different
types of “restriction theorems” for Laplace (or related) operators. O
ne type is “Fourier restriction theorems” where the Fourier transform
is restricted to a hypersurface or submanifold. Another type is spatial re
striction theorems\, where an eigenfunction $\\phi$ of the Laplacian $\\De
lta_M$ of a Riemannian manifold is restricted to a submanifold $H$. My tal
k is about joint restriction theorems: one first restricts an eigenfunctio
n $\\phi$ to a submanifold $H$\, expands it in eigenfunctions $e_k$ of $\
\Delta_H$\, and then studies the Fourier restriction of $\\phi |_H$ to sho
rt window of Fourier coefficients w.r.t. $H$. How much of the $L^2$-mass
of $\\phi |_H$ lies in a short window of frequencies of $H$? This kind of
problem arises in several branches of analysis. My talk is in part a surv
ey of joint restriction phenomena and in part a description of recent resu
lts\, partly in collaboration with Yakun Xi and Emmett Wyman.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Teemu Tyni (University of Toronto)
DTSTART:20220210T170000Z
DTEND:20220210T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/72
DESCRIPTION:Title: Stability of an inverse problem for a semi-linear wave equation\nby Teemu Tyni (University of Toronto) as part of International Zoom Inv
erse Problems Seminar\, UC Irvine\n\n\nAbstract\nStability of an inverse p
roblem deals with the question about whether small errors in the measureme
nt lead only to small errors in the reconstruction. I will discuss the sta
bility and unique recovery of a potential function in a semi-linear wave e
quation. The inverse problem is formulated on a Lorentzian manifold. Using
the nonlinearity of the wave equation\, we show that the potential functi
on can be recovered in a H\\"older stable way from the Dirichlet-to-Neuman
n map. This talk is based on a joint work with Matti Lassas\, Tony Liimata
inen and Leyter Potenciano-Machado.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruchi Guo (UC Irvine)
DTSTART:20220303T170000Z
DTEND:20220303T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/73
DESCRIPTION:Title: A Deep Direct Sampling Method for Electrical Impedance and Diffuse
Optical Tomography\nby Ruchi Guo (UC Irvine) as part of International
Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nElectrical imped
ance tomography (EIT) and Diffuse Optical Tomography (DOT) are promising t
echniques for non-invasive and radiation-free type of medical imaging. The
y all can be considered as inverse boundary value problems to identify PDE
coefficients. But a high-quality reconstruction is always challenging due
to its severe ill-posedness. Based on the idea of direct sampling methods
(DSMs)\, we present a framework to construct deep neural networks for sol
ving these two problems. It is able to capture the underlying mathematical
structure from background projection of boundary measurement to coefficie
nt distribution. The resulting Deep DSM (DDSM) is easy for implementation
and its offline-online decomposition inherits efficiency from the original
DSM that does not need any optimization process in reconstruction. Additi
onally\, it is capable of systematically incorporating multiple Cauchy dat
a pairs to achieve high-quality reconstruction and is also highly robust t
o large noise.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Zhang (University of Washington)
DTSTART:20220310T170000Z
DTEND:20220310T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/74
DESCRIPTION:Title: Inverse boundary value problems for a quasilinear wave equation on
Lorentzian manifolds\nby Yang Zhang (University of Washington) as par
t of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract
\nInverse problems of recovering the metric and nonlinear terms were origi
nated in the work by Kurylev\, Lassas\, and Uhlmann for the semilinear wav
e equation $\\square_g u(x) + a(x)u^2(x) = f(x)$ in a manifold without bou
ndary. The idea is to use the linearization and the nonlinear interactions
of distorted planes waves to produce point source like singularities in a
n observable set. In this talk\, I will discuss the joint work with Gunthe
r Uhlmann which considers the recovery of the metric and the nonlinear ter
m for a quadratic derivative nonlinear wave equation on a Lorentzian manif
old with boundary. The main difficulty that we need to handle here is caus
ed by the presence of the boundary. Our work builds on the previous result
s and I will discuss the methods to overcome these difficulties.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erkki Somersalo (Case Western Reserve University)
DTSTART:20220224T170000Z
DTEND:20220224T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/75
DESCRIPTION:Title: Bayesian inversion and data science methods to identify changes in
brain activity during meditation from MEG measurements\nby Erkki Some
rsalo (Case Western Reserve University) as part of International Zoom Inve
rse Problems Seminar\, UC Irvine\n\n\nAbstract\nMeditation as a potential
alternative for pharmaceutical intervention to mitigate conditions such a
s chronic pain or clinical depression continues to obtain significant atte
ntion. One of the problems is that often the positive effects of meditatio
n that have been reported are anecdotal or are based on self reporting. To
quantify the effects of meditation\, it is therefore important to develop
methods based on medical imaging to identify brain regions that are invol
ved in the meditation practice. In this talk\, we review some recent resul
ts about this topic\, addressed by using magnetoencephalography (MEG) to m
ap brain activity during meditation. One of the difficulties here is that
the data are less sensitive to activity taking place in the deep brain reg
ions\, including the limbic system that is believed to play an important r
ole in meditation. The MEG inverse problem is addressed by using novel Bay
esian methods combined with advanced numerical techniques\, applied on dat
a from professional Buddhist meditators. The reconstructed activity is the
n analyzed using data science techniques to distill the information about
the activation changes during meditation.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Kaltenbacher (University of Klagenfurt)
DTSTART:20220428T160000Z
DTEND:20220428T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/76
DESCRIPTION:Title: Imaging with nonlinear and fractionally damped waves\nby Barba
ra Kaltenbacher (University of Klagenfurt) as part of International Zoom I
nverse Problems Seminar\, UC Irvine\n\n\nAbstract\nThe importance of ultra
sound is well established in the imaging of human tissue. In order to enha
nce image quality by exploiting nonlinear effects\, recently techniques su
ch as harmonic imaging and nonlinearity parameter tomography have been put
forward. The latter leads to a coefficient identification problem for a q
uasilinear wave equation. Another characteristic property of ultrasound pr
opagating in human tissue is frequency power law attenuation leading to fr
actional derivative damping models in time domain. In this talk we will fi
rst of all dwell on modeling of nonlinearity on one hand and fractional da
mping on the other hand. Then we will discuss the linear inverse problem o
f photoacoustic tomography with fractional damping. Finally we return to t
he inverse problem of nonlinearity parameter imaging and show some first r
esults.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Vogelius (Rutgers University)
DTSTART:20220331T160000Z
DTEND:20220331T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/77
DESCRIPTION:Title: Recent results concerning ``small" change in boundary conditions\nby Michael Vogelius (Rutgers University) as part of International Zoom
Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nThe study of the effe
ct of (volumetric) small changes of material parameters is an area of rese
arch that has had significant impact on inverse problems\, and in addition
to the very recent (boundary) results\, I will attempt to give a brief s
urvey of some of the earlier work.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bastian von Harrach (Goethe University Frankfurt)
DTSTART:20220407T160000Z
DTEND:20220407T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/78
DESCRIPTION:Title: Uniqueness and convex reformulation for inverse coefficient proble
ms with finitely many measurements\nby Bastian von Harrach (Goethe Uni
versity Frankfurt) as part of International Zoom Inverse Problems Seminar\
, UC Irvine\n\n\nAbstract\nSeveral applications in medical imaging and non
-destructive material testing lead to inverse elliptic coefficient problem
s\, where an unknown coefficient function in an elliptic PDE is to be dete
rmined from partial knowledge of its solutions. This is usually a highly n
on-linear ill-posed inverse problem\, for which unique reconstructability
results\, stability estimates and global convergence of numerical methods
are very hard to achieve.\n\nIn this talk we will consider an inverse coef
ficient problem with finitely many measurements and a finite desired resol
ution. We will present a criterion based on monotonicity\, convexity and l
ocalized potentials arguments that allows us to explicitly estimate the nu
mber of measurements that is required to achieve the desired resolution. W
e also obtain an error estimate for noisy data\, and overcome the problem
of local minima by rewriting the problem as an equivalent uniquely solvabl
e convex non-linear semidefinite optimization problem.\n\nReferences\n\nB.
Harrach\, Uniqueness\, stability and global convergence for a discrete in
verse elliptic Robin transmission problem\, Numer. Math. 147 (2021)\, pp.
29-70\, https://doi.org/10.1007/s00211-020-01162-8\n\nB. Harrach\, Solving
an inverse elliptic coefficient problem by convex non-linear semidefinite
programming\, Optim Lett (2021)\, arXiv preprint (2021)\, https://doi.org
/10.1007/s11590-021-01802-4\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yimin Zhong (Duke University)
DTSTART:20220203T170000Z
DTEND:20220203T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/79
DESCRIPTION:Title: Quantitative PAT with simplified PN approximation\nby Yimin Zh
ong (Duke University) as part of International Zoom Inverse Problems Semin
ar\, UC Irvine\n\n\nAbstract\nThe photoacoustic tomography (PAT) is a hybr
id modality that combines the optics and\nacoustics to obtain high resolut
ion and high contrast imaging of heterogeneous media. In this\nwork\, our
objective is to study the inverse problem in the quantitative step of PAT
which aims\nto reconstruct the optical coefficients of the governing radia
tive transport equation from the\nultrasound measurements. In our analysis
\, we take the simplified PN approximation of the\nradiative transport equ
ation as the physical model and then show the uniqueness and stability\nfo
r this modified inverse problem. Numerical simulations based on synthetic
data are presented\nto validate our analysis.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolas Eptaminitakis (Purdue University)
DTSTART:20220217T170000Z
DTEND:20220217T180000Z
DTSTAMP:20260404T110823Z
UID:Inverse/80
DESCRIPTION:Title: The Solid-Fluid Transmission Problem\nby Nikolas Eptaminitakis
(Purdue University) as part of International Zoom Inverse Problems Semina
r\, UC Irvine\n\n\nAbstract\nWe will discuss a problem motivated from geop
hysics\, where one is interested in understanding the propagation of seism
ic waves in the interior of the Earth. It is known that the interior of th
e Earth consists of several layers\, some of which are solid and some of w
hich are fluid. When a seismic wave meets the interface between two layers
\, part of its energy is reflected back (possibly with mode conversion)\,
and\, if the angle of incidence is not too large\, part of it is transmitt
ed to the other side of the interface. We are particularly interestred in
understanding reflection\, transmission and mode conversion of waves at th
e interface between a linear elastic solid and an inviscid fluid. For simp
licity\, we consider the case of two layers\, with the fluid layer being e
nclosed by the solid one. The two media are described by a system of PDEs
modeling the displacement in the solid and pressure-velocity in the fluid\
, with these quantities being coupled at the interface by transmission con
ditions. We study the problem microlocally: to understand the behavior of
singularities of solutions of the system\, we construct a parametrix for i
t (approximate solution up to smooth error) using geometric optics. As an
application of our study\, we consider the inverse problem of recovering t
he wave speeds in the two layers and the material density in the solid out
er layer from the Neumann-to-Dirichlet map for the solid-fluid system corr
esponding to the exterior boundary. Based on joint work with Plamen Stefan
ov.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuzhou (Joey) Zou (UC Santa Cruz)
DTSTART:20220421T160000Z
DTEND:20220421T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/81
DESCRIPTION:Title: The $C^\\infty$-isomorphism property for a class of singularly-wei
ghted X-ray transforms\nby Yuzhou (Joey) Zou (UC Santa Cruz) as part o
f International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nW
e consider the mapping properties of singularly-weighted normal operators
associated to X-ray transforms on manifolds with boundary. While normal op
erators associated to geodesic X-ray transforms in "simple" settings are k
nown to be elliptic pseudodifferential operators in the interior\, their b
ehavior near the boundary is more subtle\; in particular the normal operat
ors need to be precomposed with weights in order to even map $C^\\infty$ o
f a manifold with boundary back to itself. This motivates asking which cho
ice of weights guarantee the normal operator to be an isomorphism of $C^\\
infty$\; such questions arise in considering theoretical guarantees for th
e consistency and uncertainty quantification of statistical recovery algor
ithms\, where one needs to know on what spaces the operator can be conside
red invertible. In this talk\, we will show that a particular family of we
ights on the Euclidean disk and on simple disks of constant curvature do g
ive rise to normal operators which are isomorphisms on $C^\\infty$. The pr
oof involves deriving the Singular Value Decomposition of a weighted X-ray
transform and studying certain function spaces based on the singular vect
ors of the X-ray transform\, which coincides with the eigenfunctions of a
particular degenerately elliptic Kimura-type differential operator. Joint
work with Rohit Kumar Mishra and Francois Monard.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Li (Institute for Pure and Applied Mathematics\, UCLA)
DTSTART:20220512T160000Z
DTEND:20220512T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/82
DESCRIPTION:Title: Inverse problems for fractional parabolic equations with power typ
e nonlinearities\nby Li Li (Institute for Pure and Applied Mathematics
\, UCLA) as part of International Zoom Inverse Problems Seminar\, UC Irvin
e\n\n\nAbstract\nI will first introduce classical and fractional Calderón
problems. Then I will focus on two inverse problems for fractional parabo
lic equations with power type nonlinearities. Both can be viewed as nonlin
ear parabolic variants of the fractional Calderón problem. The goal is to
determine nonlinearities/coefficients in fractional equations from exteri
or partial measurements of the Dirichlet-to-Neumann map. The approach reli
es on the unique continuation property of the fractional operator as well
as techniques relating nonlinear problems to linear ones.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Wunsch (Northwestern University)
DTSTART:20220317T160000Z
DTEND:20220317T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/83
DESCRIPTION:Title: Semiclassical analysis and the convergence of the finite element m
ethod\nby Jared Wunsch (Northwestern University) as part of Internatio
nal Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nAn important
problem in numerical analysis is the solution of the Helmholtz equation in
exterior domains\, in variable media\; this models the scattering of time
-harmonic waves. The Finite Element Method (FEM) is a flexible and powerf
ul tool for obtaining numerical solutions\, but difficulties are known to
arise in obtaining convergence estimates for FEM that are uniform as the f
requency of waves tends to infinity. I will describe some recent joint wo
rk with David Lafontaine and Euan Spence that yields new convergence resul
ts for the FEM which are uniform in the frequency parameter. The essentia
l new tools come from semiclassical microlocal analysis. No knowledge of
either FEM or semiclassical analysis will be assumed in the talk\, however
.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunther Uhlmann (University of Washington)
DTSTART:20220616T160000Z
DTEND:20220616T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/84
DESCRIPTION:by Gunther Uhlmann (University of Washington) as part of Inter
national Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tanya Christiansen (University of Missouri)
DTSTART:20220324T160000Z
DTEND:20220324T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/85
DESCRIPTION:Title: The semiclassical structure of the scattering matrix for a manifol
d with infinite cylindrical end\nby Tanya Christiansen (University of
Missouri) as part of International Zoom Inverse Problems Seminar\, UC Irvi
ne\n\n\nAbstract\nWe study the microlocal properties of the scattering\nma
trix associated to the semiclassical \nSchr\\"odinger operator $P=h^2\\Del
ta_X+V$ on a Riemannian\nmanifold with an infinite cylindrical end. Let $
Y$ denote the cross section of the end\, which is not necessarily connecte
d. We show that under suitable hypotheses\, microlocally the scattering
matrix is a Fourier integral operator associated to the graph of the scatt
ering map $\\kappa:\\mathcal{D}_{\\kappa}\\to T^*Y$\, with $\\mathcal{D}_\
\kappa\\subset T^*Y$. The scattering map\n$\\kappa$ and its domain $\\mat
hcal{D}_\\kappa$ are \ndetermined by the Hamilton flow of the principal sy
mbol of $P$.\nAs an application we prove that\, under additional hypothese
s on the scattering map\,\nthe eigenvalues of the associated unitary scatt
ering matrix are equidistributed on the unit circle.\n\nThis talk is based
on joint work with A. Uribe.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Per Christian Hansen (Technical University of Denmark)
DTSTART:20220519T160000Z
DTEND:20220519T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/86
DESCRIPTION:by Per Christian Hansen (Technical University of Denmark) as p
art of International Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Yang (Michigan State University)
DTSTART:20220602T160000Z
DTEND:20220602T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/87
DESCRIPTION:by Yang Yang (Michigan State University) as part of Internatio
nal Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Harris (Purdue University)
DTSTART:20220414T160000Z
DTEND:20220414T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/88
DESCRIPTION:Title: Regularization of the Factorization Method with Applications\n
by Isaac Harris (Purdue University) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\n\nAbstract\nIn this talk\, we discuss a ne
w regularized version of the Factorization Method. The Factorization Metho
d uses Picard’s Criteria to define an indicator function to image an unk
nown region. In most applications\, the data operator is compact which giv
es that the singular values can tend to zero rapidly which can cause numer
ical instabilities. The regularization of the Factorization Method present
ed here seeks to avoid the numerical instabilities in applying Picard’s
Criteria. This method allows one to image the interior structure of an obj
ect with little a priori information in a computationally simple and analy
tically rigorous way. Here we will focus on an application of this method
to diffuse optical tomography which will prove that this method can be use
d to recover an unknown subregion from the Dirichlet-to-Neumann mapping.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Eller (Georgetown University)
DTSTART:20220505T160000Z
DTEND:20220505T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/89
DESCRIPTION:Title: Hyperbolic boundary problems\, Carleman estimates\, and the Kreiss
-Sakamoto-Tataru condition\nby Matthias Eller (Georgetown University)
as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAb
stract\nA review of the theory of hyperbolic initial-boundary value proble
ms is presented. Since the 1970s there are two competing theories\, one fo
r symmetric hyperbolic systems mainly due to Friedrichs and one for strict
ly hyperbolic systems due to Kreiss and Sakamoto. The relationship of thes
e two theories has been clarified only during the last decade. A central p
art of both theories is played by a priori estimates. Carleman estimates s
hare some similarities with hyperbolic a priori estimates. Initially estab
lish for functions with compact support and as a tool for proving unique c
ontinuation for operators with non-analytic coefficients\, they have found
applications in Inverse Problems and Control Theory. Boundary data were i
ncluded in Carleman estimates by Lebeau\, Robbiano\, and Tataru establishe
d a condition similar to the one used by Kreiss and Sakamoto for hyperboli
c problems. The case of scalar second-order operators will be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Eskin (UCLA)
DTSTART:20220526T160000Z
DTEND:20220526T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/90
DESCRIPTION:Title: Rigidity for Lorentzian metrics having the same length of null-geo
desics\nby Gregory Eskin (UCLA) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\n\nAbstract\nWe study the Lorentzian metri
c independent of the time variable in the cylinder $\\R\\times\\Omega$
where $x_0\\in\\R$ is the time variable and $\\Omega$ is a bounde
d smooth domain in $\\R^n$.\n\nWe consider forward null-geodesics in
$\\R\\times \\Omega$ starting on $\\R\\times\\partial\\Omega$ at $
t=0$ and leaving $\\R\\times\\Omega$ at some later time. We prove the
following rigidity result:\n\nIf two Lorentzian metrics are close e
nough in some norm and if corresponding null-geodesics have equal
lengths in $(x_0\,x)$ space then the metrics are equal.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Todd Quinto (Tufts University)
DTSTART:20220609T160000Z
DTEND:20220609T170000Z
DTSTAMP:20260404T110823Z
UID:Inverse/91
DESCRIPTION:Title: Seismic imaging with generalized Radon transforms.\nby Todd Qu
into (Tufts University) as part of International Zoom Inverse Problems Sem
inar\, UC Irvine\n\n\nAbstract\nGeneralized Radon transforms are Fourier i
ntegral operators which are used\, for instance\, as imaging models in geo
physical exploration. They appear naturally when linearizing about a known
background compression wave speed. In this work we consider seismic opera
tors with two scanning geometries: zero-offset (the source and receiver ar
e at the same point and translated over the surface of the earth) and comm
on-offset (the source and receiver are offset a fixed distance from each o
ther and translated together). We first analyze the model with a linearly
increasing background velocity in two spatial dimensions. We verify the Bo
lker condition for the zero-offset scanning geometry and provide meaningfu
l arguments for it to hold even if the common-offset is positive. The Bolk
er condition allows us to infer that the normal operator is a pseudodiffer
ential operator. We calculate its top order symbol in the zero-offset case
to study how it maps singularities. Second\, to support the usage of back
ground models obtained from linear regression\, we prove that the Bolker c
ondition is stable under sufficiently small perturbations of the backgroun
d velocity or of the offset.\n\nAuthors: Peer Christian Kunstmann and Andr
eas Rieder\, Department of Mathematics\, Karlsruhe Institute of Technology
(KIT)\, D-76128\, Karlsruhe\, Germany\, Eric Todd Quinto\, Department of
Mathematics\, Tufts University\, Medford\, MA 02155\, USA.\n
LOCATION:https://stable.researchseminars.org/talk/Inverse/91/
END:VEVENT
END:VCALENDAR