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BEGIN:VEVENT
SUMMARY:Ryan Matzke (University of Minnesota)
DTSTART:20200504T150000Z
DTEND:20200504T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/1
DESCRIPTION:Title: Discreteness of energy-minimizing measures.\nby Ryan Matzke (Un
iversity of Minnesota) as part of HA-GMT-PDE Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillermo Rey (Wing)
DTSTART:20200511T150000Z
DTEND:20200511T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/2
DESCRIPTION:Title: Another counterexample to Zygmund's conjecture\nby Guillermo Re
y (Wing) as part of HA-GMT-PDE Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Burkart (Stony Brook University)
DTSTART:20200618T150000Z
DTEND:20200618T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/3
DESCRIPTION:Title: Transcendental Julia sets with fractional packing dimension\nby
Jack Burkart (Stony Brook University) as part of HA-GMT-PDE Seminar\n\n\n
Abstract\nIn this talk\, we will define and compare different definitions
of dimension (Hausdorff\, Minkowski\, and packing) used to analyze fractal
sets. We will then define the basic objects in complex dynamics\, and dis
cuss some history of results about the dimension of the fractal Julia sets
that famously show up in this area. No prior knowledge of complex dyanmic
s will be assumed. We will conclude by discussing my recent construction o
f a Julia set of a non-polynomial entire function with packing dimension s
trictly between one and two. We will see that Whitney decompositions\, a f
oundational tool in harmonic analysis\, play a vital role in the dimension
calculation.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenjie Lu (University of Minnesota)
DTSTART:20200521T150000Z
DTEND:20200521T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/4
DESCRIPTION:Title: On the De Gregorio modification of the Constantin-Lax-Majda model\nby Wenjie Lu (University of Minnesota) as part of HA-GMT-PDE Seminar\n
\n\nAbstract\nI will introduce the Constantin-Lax-Majda model with De Greg
orio modifications. More specifically\, I will focus on the problems relat
ed to stationary solutions and well-posedness.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Naples (University of Connecticut)
DTSTART:20200526T150000Z
DTEND:20200526T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/5
DESCRIPTION:Title: Rectifiability of pointwise doubling measures in Hilbert space\nby Lisa Naples (University of Connecticut) as part of HA-GMT-PDE Semina
r\n\n\nAbstract\nJones’ beta numbers measure the flatness of a set at v
arious scales and windows. Since their introduction\, beta numbers have s
erved as an important tool to relate the geometric structure of sets and m
easures and to measure-theoretic quantities. We will extend results of Ba
dger and Schul to show that an $L^2$ variant of the beta numbers can be us
ed to characterize rectifiable pointwise doubling measures in Hilbert spa
ce. We will also discuss results for the related notions of graph rectifi
ability and fractional rectifiability.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Brocchi (University of Birmingham)
DTSTART:20200528T150000Z
DTEND:20200528T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/6
DESCRIPTION:Title: Random dyadic grids and what they can do for you\nby Gianmarco
Brocchi (University of Birmingham) as part of HA-GMT-PDE Seminar\n\n\nAbst
ract\nIn the last decade dyadic analysis and probabilistic methods have be
en successfully used to obtain optimal weighted estimates. In this talk w
e introduce dyadic grids and their random shifted analogue. We discuss in
an informal way some of the advantages of this tool and how it can be used
to decompose your operator.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Turner (University of Birmingham)
DTSTART:20200604T150000Z
DTEND:20200604T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/8
DESCRIPTION:Title: Solvability of boundary value problems for the Schrodinger equation
with nonnegative potentials\nby Andrew Turner (University of Birmingh
am) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nAbstract pdf: https://dri
ve.google.com/file/d/17Kzg-Zp2a9fhr8_2E9IWM_w4v7O3b383/view\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrije Cicmilovic (University of Bonn)
DTSTART:20200608T150000Z
DTEND:20200608T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/9
DESCRIPTION:Title: Symplectic non-squeezing and Hamiltonian PDE\nby Dimitrije Cicm
ilovic (University of Bonn) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nI
n this talk we shall discuss infinite dimensional generalization of\nGromo
v's sympelctic nonsqueezing result. As an application we will present\nmas
s subcritical and critical nonlinear Schrodinger equation. Nonsqueezing\np
roperty of the said flows was already known\, however the techniques used\
nare based on finite dimensional Gromov's result\, while ours presents a\n
more natural way of looking at the Hamiltonian structure of the equations.
\nAdditionally\, we shall remark on future projects in terms of applicatio
n\nof the non-squeezing property.\nJoint work with Herbert Koch.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damian Dabrowski (Universitat Autonoma de Barcelona)
DTSTART:20200615T150000Z
DTEND:20200615T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/10
DESCRIPTION:Title: Cones\, rectifiability and singular integral operators.\nby Da
mian Dabrowski (Universitat Autonoma de Barcelona) as part of HA-GMT-PDE S
eminar\n\n\nAbstract\nLet K(x\, V\, s) be the open cone centred at x\, wit
h direction V\, and aperture s. It is easy to see that if a set E satisfie
s for some V and s the condition:\n"if x belongs to E\, then E has an empt
y intersection with K(x\, V\, s)"\,\nthen E is a subset of a Lipschitz gra
ph. To what extent can we weaken the condition above and still get meaning
ful information about the geometry of E? It depends on what we mean by "me
aningful information''\, of course. For example\, one could ask for rectif
iability of E\, or if E contains big pieces of Lipschitz graphs\, or if ni
ce singular integral operators are bounded in L^2(E). In the talk I will d
iscuss these three closely related questions.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yijing Wu (University of Maryland)
DTSTART:20200629T150000Z
DTEND:20200629T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/12
DESCRIPTION:Title: Existence\, uniqueness and regularity of the minimizer of energy r
elated to perimeter minus fractional perimeter\nby Yijing Wu (Universi
ty of Maryland) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nWe are intere
sted in the asymptotic behaviors of the following energy functional $E(\\O
mega)=\\sigma Per(\\Omega)+\\beta V_K(\\Omega)$ defined for $|\\Omega|=m$.
Here the perimeter tries to keep the mass together in a ball\, and $V_K$
is a non-local repulsive interaction energy trying to spread the mass arou
nd. We will then discuss the existence\, uniqueness snd regularity propert
ies of the minimizers of the energy especially in the regime where the ene
rgy $E(\\Omega)$ converges to Perimeter minus fractional perimeter.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gael Diebou (University of Bonn)
DTSTART:20200716T150000Z
DTEND:20200716T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/14
DESCRIPTION:Title: The Dirichlet problem for weakly harmonic maps with rough data
\nby Gael Diebou (University of Bonn) as part of HA-GMT-PDE Seminar\n\n\nA
bstract\nIn this talk\, we will discuss the well-posedness issues for weak
ly harmonic maps subject to Dirichlet boundary data assuming a minimal reg
ularity. After a brief description of the problem we will present our tech
niques which partly rely on certain fundamental notions in harmonic analys
is such as Carleson measures\, its intrinsic connection to the John-Nirenb
erg space BMO and the Laplace operator... With an appropriate reformulatio
n of our problem\, various solvability results (existence\, uniqueness and
regularity) will then be reviewed. Our approach (nonvariational)\, as we
will see\, is suitable for the analysis of critical or endpoint elliptic b
oundary value problems and hence can unambiguously be applicable to simila
r type of equations or systems driven by classical operators. For this tal
k\, we only mention a generalization of our results to second-order consta
nt elliptic systems.\n\nThis is a joint work with Herbert Koch.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lois Okereke (African University of Science and Technology)
DTSTART:20200720T150000Z
DTEND:20200720T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/15
DESCRIPTION:Title: Iterative methods for nonlinear optimisation problems - Prospects
and applications\nby Lois Okereke (African University of Science and T
echnology) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nAn important class
of extremal problems in nonlinear functional analysis is the nonlinear op
timisation problem where some of the objective functions are nonlinear. I
n many cases where existence of solutions is guaranteed\, these solutions
are not usually affordable in a direct way. Iterative methods (or algorith
ms)\, therefore provide a convenient way of approximating these solutions.
To a large extent\, most of these iterative methods can be traced to the
popular gradient descent algorithm. This talk presents the prospects that
may result in using a different approach\, and its usefulness even to equi
valent reformulations of the nonlinear optimisation problem. Its applicabi
lity in some areas of science and technology is highlighted and a spectac
ular application in radiotherapy treatment planning where algorithmic effi
ciency is especially required is demonstrated.\n\nThis work is Joint with
Charles Ejike Chidume.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Luis Luna García (University of Missouri)
DTSTART:20200727T150000Z
DTEND:20200727T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/16
DESCRIPTION:Title: Critical Perturbations for Linear Elliptic Equations\nby José
Luis Luna García (University of Missouri) as part of HA-GMT-PDE Seminar\
n\n\nAbstract\nIn this talk we develop a perturbation theory for the L^2 s
olvability of certain Boundary Value Problems for linear elliptic equation
s with complex coefficients in the upper half space. While we expect the m
ethods to apply to general systems and higher order equations\, we will fo
cus here on the general scalar second order equation\, for which most of t
he main difficulties are already present: For instance a lack of boundedne
ss and continuity of solutions\, precluding the use of a pointwise-defined
fundamental solution.\n\nOur theory is based on solvability via the metho
d of layer potentials. As such the main points to consider are boundedness
and invertibility\, in the appropriate functional spaces\, of the corresp
onding operators and their boundary traces. For the boundedness issue we e
mploy the theory of local Tb theorems\, to obtain control on certain squar
e functions that allow us to conclude the desired bounds on the layer pote
ntials. The invertibility will be treated through the analyticity of the
boundary traces as a function of the coefficients of the equation.\n\nOf t
echnical interest is that our methods allow us to obtain nontangential max
imal function estimates for the layer potential solutions so constructed.\
n\nThis is joint work with Simon Bortz\, Steve Hofmann\, Svitlana Mayborod
a\, and Bruno Poggi.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zihui Zhao (University of Chicago)
DTSTART:20200810T150000Z
DTEND:20200810T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/17
DESCRIPTION:Title: Boundary regularity of area-minimizing currents: a linear model wi
th analytic interface\nby Zihui Zhao (University of Chicago) as part o
f HA-GMT-PDE Seminar\n\n\nAbstract\nGiven a curve \\Gamma \, what is the s
urface T that has least area among all surfaces spanning \\Gamma? This cl
assical problem and its generalizations are called Plateau's problem. In t
his talk we consider area minimizers among the class of integral currents\
, or roughly speaking\, orientable manifolds. Since the 1960s a lot of wor
k has been done by De Giorgi\, Almgren\, et al to study the interior regul
arity of these minimizers. Much less is known about the boundary regularit
y\, in the case of codimension greater than 1. I will speak about some rec
ent progress in this direction and my joint work with C. De Lellis.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jungang Li (Brown University)
DTSTART:20200813T150000Z
DTEND:20200813T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/21
DESCRIPTION:Title: The L^p-ellipticity and L^p-Dirichlet problems of second order ell
iptic systems\nby Jungang Li (Brown University) as part of HA-GMT-PDE
Seminar\n\n\nAbstract\nIn this talk we will discuss a structural condition
of second order elliptic systems with complex coefficients\, namely the L
^p-ellipticity condition\, which can be viewed as an L^p version of the cl
assical ellipticity condition. Such condition naturally implies both inter
ior and boundary estimates\, which act as a proper substitution of the De
Giorgi-Nash-Moser regularity theory. The new regularity result will help u
s to prove an extrapolation theorem of the L^p-Dirichlet problem and we wi
ll apply it to two well-studied cases: Lam\\'e equations and homogenizatio
n problems. This is a joint work with M. Dindos and J. Pipher.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajula Srivastava (University of Wisconsin-Madison)
DTSTART:20200820T150000Z
DTEND:20200820T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/24
DESCRIPTION:Title: Orthogonal Systems of Spline Wavelets as Unconditional Bases in So
bolev Spaces\nby Rajula Srivastava (University of Wisconsin-Madison) a
s part of HA-GMT-PDE Seminar\n\n\nAbstract\nWe exhibit the necessary range
for which functions in the Sobolev spaces $L^s_p$ can be represented as a
n unconditional sum of orthonormal spline wavelet systems\, such as the Ba
ttle-Lemarié wavelets. We also consider the natural extensions to Triebel
-Lizorkin spaces. This builds upon\, and is a generalization of\, previous
work of Seeger and Ullrich\, where analogous results were established for
the Haar wavelet system.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Duncan (University of Birmingham)
DTSTART:20200723T150000Z
DTEND:20200723T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/25
DESCRIPTION:Title: An Algebraic Brascamp-Lieb Inequality\nby Jennifer Duncan (Uni
versity of Birmingham) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nThe Br
ascamp-Lieb inequalities are a natural generalisation of many familiar mul
tilinear inequalities that arise in mathematical analysis\, classical exam
ples of which include Holder’s inequality\, Young’s convolution inequa
lity\, and the Loomis-Whitney inequality. Each Brascamp-Lieb inequality is
uniquely defined by a 'Brascamp-Lieb datum'\, which is a pair consisting
of a set of linear surjections between euclidean spaces and a set of expon
ents corresponding to these maps. It is common in applications to encounte
r nonlinear variants\, where the linear maps are replaced with nonlinear m
aps between manifolds. By incorporating a dampening factor that compensate
s for local degeneracies\, we establish a global nonlinear Brascamp-Lieb i
nequality for a broad class of maps that exhibit a certain algebraic struc
ture\, with a constant that explicitly depends only on the associated 'deg
rees' of these maps.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiao He (University of Evry - Paris Saclay)
DTSTART:20200709T150000Z
DTEND:20200709T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/27
DESCRIPTION:Title: Regularity criteria for weak solutions to the three-dimensional MH
D system\nby Jiao He (University of Evry - Paris Saclay) as part of HA
-GMT-PDE Seminar\n\n\nAbstract\nIn this talk we will first review various
known regularity criteria and partial regularity theory for 3D incompressi
ble Navier-Stokes equations.\n\nI will then present two generalizations of
partial regularity theory of Caffarelli\, Kohn and Nirenberg to the weak
solutions of MHD equations. The first one is based on the framework of par
abolic Morrey spaces. We will show parabolic Hölder regularity for the "s
uitable weak solutions" to the MHD system in small neighborhoods. This typ
e of parabolic generalization using Morrey spaces appears to be crucial wh
en studying the role of the pressure in the regularity theory and makes it
possible to weaken the hypotheses on the pressure.\n\nThe second one is a
regularity result relying on the notion of "dissipative solutions". By ma
king use of the first result\, we will show the regularity of the dissipat
ive solutions to the MHD system with a weaker hypothesis on the pressure (
$P \\in \\mathcal{D}'$).\n\nThis is a joint work with Diego Chamorro.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Montie Avery (University of Minnesota)
DTSTART:20200625T150000Z
DTEND:20200625T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/28
DESCRIPTION:Title: Nonlinear stability of critical pulled fronts via resolvent expans
ions\nby Montie Avery (University of Minnesota) as part of HA-GMT-PDE
Seminar\n\n\nAbstract\nWe consider invasion processes mediated by propagat
ing fronts in spatially extended systems\, in which a stable rest state in
vades an unstable rest state. We focus on the case of pulled fronts\, for
which the speed of propagation is the linear spreading speed\, which marks
the transition between pointwise decay and pointwise growth for the linea
rization about the unstable rest state in a co-moving frame. In a general
setting of scalar parabolic equations on the real line of arbitrary order\
, we establish sharp decay rates and temporal asymptotics for perturbation
s to the front\, under conceptual assumptions on the existence and spectra
l stability of fronts. Some of these results are known for the specific ex
ample of the Fisher-KPP equation\, and so our work can be viewed as establ
ishing universality of certain aspects of this classical model. Technicall
y\, our approach is based on a detailed study of the resolvent operator fo
r the linearization about the critical front\, near its essential spectrum
.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Sakellaris (Autonomous University of Barcelona)
DTSTART:20200611T150000Z
DTEND:20200611T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/29
DESCRIPTION:Title: Green's function for second order elliptic equations with singula
r lower order coefficients and applications\nby Georgios Sakellaris (A
utonomous University of Barcelona) as part of HA-GMT-PDE Seminar\n\n\nAbst
ract\nWe will discuss Green's function for second order elliptic \noperato
rs of the form $\\mathcal{L}u=-\\text{div}(A\\nabla u+bu)+c\\nabla \nu+du$
in domains $\\Omega\\subseteq\\mathbb R^n$\, for $n\\geq 3$. We will \nas
sume that $A$ is elliptic and bounded\, and also that \n$d\\geq\\text{div}
b$ or $d\\geq\\text{div}c$ in the sense of distributions.\n\nIn the settin
g of Lorentz spaces\, we will explain why the assumption \n$b-c\\in L^{n\,
1}(\\Omega)$ is optimal in order to obtain a pointwise \nbound of the form
$G(x\,y)\\leq C|x-y|^{2-n}$. Under the assumption \n$d\\geq\\text{div}b$\
, we will also discuss why this assumption is \nnecessary to even have wea
k type bounds on Green's function. Finally\, \nfor the case $d\\geq\\text{
div}c$\, we will deduce a maximum principle \nand a Moser type estimate\,
showing again that the assumption $b-c\\in \nL^{n\,1}(\\Omega)$ is optimal
.\n\nOur estimates will be scale invariant and no regularity on \n$\\parti
al\\Omega$ will be imposed. In addition\, $\\mathcal{L}$ will not \nbe ass
umed to be coercive\, and there will be no smallness assumption \non the l
ower order coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Ángeles García-Ferrero (University of Heidelberg)
DTSTART:20200730T150000Z
DTEND:20200730T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/30
DESCRIPTION:Title: Unique continuation properties for nonlocal operators\nby Mar
ía Ángeles García-Ferrero (University of Heidelberg) as part of HA-GMT-
PDE Seminar\n\n\nAbstract\nRoughly speaking\, a unique continuation proper
ty states that a solution of certain partial differential equation is dete
rmined by its behaviour in a subset. In this talk we will see this kind of
properties\, including their strong and quantitative versions\, for some
classes of nonlocal operators like the Hilbert transform\, which arise in
medical imaging\, or the (higher order) fractional Laplacian. The results
I will present rely on commonly used tools as Carleman estimates and the C
affareli-Silvestre extension\, but also on two alternative mechanisms. As
an application we will see Runge approximation results.\n\nThis is joint w
ork with Angkana Rüland.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joao Pedro Ramos (Instituto Nacional de Matematica Pura e Aplicada
- ETH Zurich)
DTSTART:20200713T150000Z
DTEND:20200713T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/31
DESCRIPTION:Title: Recent progress on Fourier uncertainty\nby Joao Pedro Ramos (I
nstituto Nacional de Matematica Pura e Aplicada - ETH Zurich) as part of H
A-GMT-PDE Seminar\n\n\nAbstract\nThe classical Heisenberg Uncertainty Prin
ciple shows that a function and its Fourier transform cannot be too concen
trated around a point simultaneously. In other words\, if we force a funct
ion and its Fourier transform to vanish outside a small neighborhood of a
point\, then the function is zero. This classical principle has been gener
alized to many levels in the past\, including results of Hardy\, Beurling
and many others. In this talk\, we will recall old and new results about F
ourier ncertainty\, focusing more on the most recent developments on the f
ield and its relationship to various topics\, such as the sphere packing p
roblem\, interpolation formulae and many others.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Jarrin (Universidad Tecnica de Ambato)
DTSTART:20200806T150000Z
DTEND:20200806T155000Z
DTSTAMP:20260404T094940Z
UID:anpdews/32
DESCRIPTION:Title: On the Liouville problem for the stationary Navier-Stokes equation
s\nby Oscar Jarrin (Universidad Tecnica de Ambato) as part of HA-GMT-P
DE Seminar\n\n\nAbstract\nUniqueness of weak solutions of the 3D Navier-St
okes equations is a challenging open problem. In this talk\, we will discu
ss some recent results of this problem for the 3D stationary Navier-Stokes
equations. More precisely\, within the framework of the Lebesgue\, Lorent
z and Morrey spaces\, we will observe that the null solution of these equ
ations is the unique one. This kind of results are also known as Liouville
-type results.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Poggi Cevallos (University of Minnesota)
DTSTART:20200914T160000Z
DTEND:20200914T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/33
DESCRIPTION:Title: Additive and scalar-multiplicative Carleson perturbations of ellip
tic operators on domains with low dimensional boundaries.\nby Bruno Po
ggi Cevallos (University of Minnesota) as part of HA-GMT-PDE Seminar\n\n\n
Abstract\nAt the beginning of the 90s\, Fefferman\, Kenig and Pipher (FKP)
obtained a rather sharp (additive) perturbation result for the Dirichlet
problem of divergence form elliptic operators. Without delving into detail
s\, the point is that if the (additive) disagreement of two operators sati
sfies what is known as a Carleson measure condition\, then quantitative ab
solute continuity of the elliptic measure is transferred from one operator
to the other\, if one of the operators already possesses this property. T
heir (additive) perturbation result has since then been generalized to inc
reasingly weaker geometric and topological assumptions on boundaries of co
-dimension 1\, by multiple authors. \n\nThis talk will consist of two mai
n parts. In the first part\, we will see an extension of the FKP result t
o the degenerate elliptic operators of David\, Feneuil and Mayboroda\, whi
ch were developed to study geometric and analytic properties of sets with
boundaries whose co-dimension is higher than 1. These operators are of the
form -div A∇ \, where A is a degenerate elliptic matrix crafted to weig
h the distance to the low-dimensional boundary in a way that allows for th
e nourishment of an elliptic theory. When this boundary is a d-Alhfors-Dav
id regular set in R^n with d in [1\, n-1)\, and n≥ 3\, we prove that the
membership of the elliptic measure in A_∞ is preserved under (additive
) Carleson measure perturbations of the matrix of coefficients\, yielding
in turn that the L^p-solvability of the Dirichlet problem is also stable u
nder these perturbations (with possibly different p). If the Carleson mea
sure perturbations are suitably small\, we establish solvability of the Di
richlet problem in the same L^p space. One of the corollaries of our resul
ts together with a previous result of David\, Engelstein and Mayboroda\, i
s that\, given any d-ADR boundary Γ with d in [1\, n-2)\, n≥ 3\, there
is a family of degenerate operators of the form described above whose ell
iptic measure is absolutely continuous with respect to the d-dimensional
Hausdorff measure on Γ. Our method of proof uses the method of Carleson
measure extrapolation\, as developed by Lewis and Murray\, and adapted to
a dyadic setting by Hofmann and Martell in the past decade. This is joint
work with Svitlana Mayboroda.\n\nIn the second part of the talk\, we will
adopt a slightly different perspective than has been customary in the lite
rature of these perturbation results\, by considering scalar-multiplicativ
e Carleson perturbations\, as communicated to us by Joseph Feneuil and ins
pired by the work on equations with drift terms of Hofmann and Lewis\, and
Kenig and Pipher\, at the start of the 21st century. Essentially\, if we
may write A=bA_0 with b a scalar function bounded above and below by a po
sitive number\, and ∇b·dist(· \,Γ) satisfying a Carleson measure cond
ition\, then we still retain the transference of the quantitative absolute
continuity of the elliptic measure for -div A∇\, if -div A_0∇ already
has this property. By way of examples in the setting of low dimensional b
oundaries\, we will see that one ought to consider these two types of pert
urbations (namely\, additive and scalar-multiplicative) to reckon a more c
omplete picture of the absolute continuity of elliptic measure. This is jo
int work with Joseph Feneuil.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arunima Bhattacharya (University of Washington)
DTSTART:20200909T160000Z
DTEND:20200909T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/34
DESCRIPTION:Title: Hessian Estimates for the Lagrangian mean curvature equation\n
by Arunima Bhattacharya (University of Washington) as part of HA-GMT-PDE S
eminar\n\n\nAbstract\nIn this talk\, we will derive a priori interior Hess
ian estimates for the Lagrangian mean curvature equation under certain nat
ural restrictions on the Lagrangian phase. As an application\, we will use
these estimates to solve the Dirichlet problem for the Lagrangian mean cu
rvature equation with continuous boundary data\, on a uniformly convex\, b
ounded domain in R^n.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bingyang Hu (Purdue University)
DTSTART:20200924T160000Z
DTEND:20200924T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/35
DESCRIPTION:Title: On the adjacency of general dyadic grids in Euclidean spaces .
\nby Bingyang Hu (Purdue University) as part of HA-GMT-PDE Seminar\n\n\nAb
stract\nIn this talk\, we will briefly introduce the recent development on
study the adjacent grids in Euclidean spaces. This talk contains three 3
parts\, the real line case\, the higher dimension case and the different b
ases case. The first part is a joint work with Tess Anderson\, Liwei Jiang
\, Connor Olson and Zeyu Wei\, which is due to a summer REU project at UW-
Madison in 2018\; while the second and third parts are taken from joint wo
rks with Tess Anderson.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyunwoo Kwon (Republic of Korea Air Force Academy)
DTSTART:20200928T160000Z
DTEND:20200928T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/36
DESCRIPTION:Title: Elliptic equations with singular drifts term on Lipschitz domains.
\nby Hyunwoo Kwon (Republic of Korea Air Force Academy) as part of HA-
GMT-PDE Seminar\n\n\nAbstract\nIn this talk\, we consider linear elliptic
equation of second-order with the first term given by a singular vector fi
eld $\\mathbf{b}$ on bounded Lipschitz domains $\\Omega$ in $\\mathbb{R}^n
$\, $(n\\geq 3)$. Under the assumption $\\mathbf{b}\\in L^n(\\Omega)^n$\,
we establish unique solvability in $L_{\\alpha}^p(\\Omega)$ for Dirichlet
and Neumann problems. Here $L_{\\alpha}^p(\\Omega)$ denotes the standard S
obolev spaces(or Bessel potential space) with the pair $(\\alpha\,p)$ sati
sfying certain condition. These results extend the classical works of Jeri
son-Kenig (1995) and Fabes-Mendez-Mitrea (1999) for the Poisson equation.
In addition\, we study the Dirichlet problem for such linear elliptic equa
tion when the boundary data is in $L^2(\\partial\\Omega)$. Necessary revie
w on this topics is also presented in this talk. This is a joint work with
Hyunseok Kim(Sogang University).\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (Institute for Advanced Study\, New Jersey)
DTSTART:20201005T160000Z
DTEND:20201005T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/37
DESCRIPTION:Title: Distinct distances on the plane\nby Hong Wang (Institute for A
dvanced Study\, New Jersey) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nG
iven N distinct points on the plane\, what is the minimal number of distin
ct distances between them? This problem was posed by Paul Erdos in 1946 an
d essentially solved by Guth and Katz in 2010. \n\nWe are going to consid
er a continuous analogue of this problem\, the Falconer distance problem.
Given a set $E$ of dimension $s>1$\, what can we say about its distance s
et $\\Delta(E)=\\{ |x-y|: x\,y\\in E\\}$? Falconer conjectured in 1985 tha
t $\\Delta(E)$ should have positive Lebesgue measure. In the recent year
s\, people have attacked this problem in different ways (including geomet
ric measure theory\, Fourier analysis\, and combinatorics) and made some p
rogress for various examples and for some range of $s$.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dallas Albritton (Courant Institute\, New York)
DTSTART:20201019T160000Z
DTEND:20201019T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/38
DESCRIPTION:Title: Self-similar solutions of active scalars with critical dissipation
\nby Dallas Albritton (Courant Institute\, New York) as part of HA-GMT
-PDE Seminar\n\n\nAbstract\nIn PDE analyses of fluid models\, often we may
identify a so-called critical space that lives precisely at the borderlin
e between well-posedness and ill-posedness. What happens at this borderlin
e? We explore this question in two active scalar equations with critical d
issipation. In the surface quasi-geostrophic equations\, we investigate th
e connection between non-uniqueness and large self-similar solutions that
was established by Jia\, Sverak\, and Guillod in the Navier-Stokes equatio
ns. This is joint work with Zachary Bradshaw. In the critical Burgers equa
tion\, and more generally in scalar conservation laws\, the analogous self
-similar solutions are unique\, and we show that all front-like solutions
converge to a self-similar solution at the diffusive rates. This is joint
work with Raj Beekie.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Barron (University of Illinois-Urbana Champaign)
DTSTART:20201026T160000Z
DTEND:20201026T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/39
DESCRIPTION:Title: A sharp global Strichartz estimate for the Schrodinger equation on
the cylinder\nby Alex Barron (University of Illinois-Urbana Champaign
) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nThe classical Strichartz es
timates show that a solution to the linear Schrodinger equation on Euclide
an space is in certain Lebesgue spaces globally in time provided the initi
al data is in $L^2$. On compact manifolds one can no longer have global co
ntrol\, and some loss of derivatives is necessary (meaning the initial dat
a needs to be in a Sobolev space rather than $L^2$). In 'intermediate' cas
es it is a challenging question to understand when one can have good space
-time estimates with no loss of derivatives. \n\nIn this talk we discuss a
global-in-time Strichartz-type estimate for the linear Schrodinger equati
on on the cylinder. Our estimate is sharp\, scale-invariant\, and requires
only $L^2$ data. Joint work with M. Christ and B. Pausader.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Feneuil (Australian National University)
DTSTART:20201109T170000Z
DTEND:20201109T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/41
DESCRIPTION:Title: Uniform rectifiability implies $A_{\\infty}$-absolute continuity o
f the harmonic measure with respect to the Hausdorff measure in low dimens
ion.\nby Joseph Feneuil (Australian National University) as part of HA
-GMT-PDE Seminar\n\n\nAbstract\nUnder mild conditions of topology on the d
omain $\\Omega\\subset\\mathbb R^n$\, the harmonic measure is $A_{\\infty}
$-absolutely continuous with respect to the surface measure if and only if
the boundary ∂Ω is uniformly rectifiable of dimension n − 1.\n\nWe s
hall present the state of the art around the above statement\, and then di
scuss the strategy employed by Guy David\, Svitlana Mayboroda\, and the sp
eaker to extend this characterization of uniform rectifiability to sets of
dimension d < n − 1.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zanbing Dai (University of Minnesota)
DTSTART:20201116T170000Z
DTEND:20201116T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/42
DESCRIPTION:Title: The Regularity boundary value problem in domains with lower dimens
ional boundaries.\nby Zanbing Dai (University of Minnesota) as part of
HA-GMT-PDE Seminar\n\n\nAbstract\nRecently\, Guy David\, Joseph Feneuil a
nd Svitlana Mayboroda developed an elliptic theory in domains with lower d
imensional boundaries. They studied a class of degenerate second order ell
iptic operators $-\\textup{div} A\\nabla$ \, where A is a weighted matrix.
The Dirichlet boundary value problem associated with these operators in\n
higher codimension has already been solved by Joseph Feneuil\, Svitlana Ma
yboroda and Zihui Zhao. We currently focus on the regularity boundary prob
lem. Roughly speaking\, we are interested in the relation between the grad
ient of weak solutions and the gradient of boundary data whenever the boun
dary has higher regularity and coefficients satisfy a certain smoothness c
ondition . In this talk\, I will introduce our main results about the solv
ability of the regularity boundary value problem in the higher codimension
. This is joint work with Svitlana Mayboroda and Joseph Feneuil.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liding Yao (University of Wisconsin-Madison)
DTSTART:20201123T170000Z
DTEND:20201123T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/43
DESCRIPTION:Title: Frobenius Theorem for Log-Lipschitz Subbundles\nby Liding Yao
(University of Wisconsin-Madison) as part of HA-GMT-PDE Seminar\n\n\nAbstr
act\nIn differential geometry\, Frobenius theorem says that if a (smooth)
real tangential subbundle is involutive\, i.e. that X\,Y are sections impl
ies that [X\,Y] is also a section\, then this subbundle is spanned by some
coordinate vector fields. Recently we prove the Frobenius theorem in the
log-Lipschitz setting. In the talk I will go over the formulation of the t
heorem and show how harmonic analysis involves in the proof.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Hoffman (University of Missouri-Columbia)
DTSTART:20201130T170000Z
DTEND:20201130T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/44
DESCRIPTION:Title: Regular Lip(1\,1/2) Approximation of Parabolic Hypersurfaces\n
by John Hoffman (University of Missouri-Columbia) as part of HA-GMT-PDE Se
minar\n\n\nAbstract\nA classical result of David and Jerison states that a
regular\, n-dimensional set in R^{n+1} satisfying a two sided corkscrew c
ondition is quantitatively approximated by Lipschitz graphs. After review
ing this result\, we will discuss some recent advances in extending this r
esult to the parabolic setting. The proofs of these results are quite dif
ficult\, but many of the underlying principles are easy to understand and
quite geometric and presenting these geometric ideas will be the focus of
this talk. As such\, this talk will feature lots of pictures! Crucially\
, we highlight how fundamental differences of the parabolic setting requir
e us to consider additional nuances which are not present in the elliptic
setting. We will sketch the ideas of how to circumvent these difficulties
.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Chen (Massachusetts Institute of Technology)
DTSTART:20201207T170000Z
DTEND:20201207T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/45
DESCRIPTION:Title: Effective equations of quantum mechanics and phase transitions
\nby Li Chen (Massachusetts Institute of Technology) as part of HA-GMT-PDE
Seminar\n\n\nAbstract\nEffective equations of many-body quantum mechanics
form the backbone of many fields of modern physics. Notable examples of e
ffective equations include the Hartree-Fock\, Kohn-Sham\, and Bogoliubov-d
e Gennes (BdG) equations. Although their physical derivations vary\, we wi
ll review an unified formal mathematical frame work for their derivations
(if time permits). In this frame work\, the BdG equations are the most gen
eral form of effective equations. Physically\, they form a microscopic des
cription of superconductivity. When the temperature T is lower than a cert
ain critical Tc\, superconducting solutions emerge. In this talk\, we will
demonstrate the the existence of solutions to the BdG equations via varia
tional arguments and show energy instability (hence the formation of a sup
erconducting order parameter) when T < Tc. \n\nThis is a joint work with I
. M. Sigal\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Engelstein (University of Minnesota)
DTSTART:20210119T170000Z
DTEND:20210119T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/46
DESCRIPTION:Title: Lojasiewicz Inequalities and the Zero Sets of Harmonic Functions\nby Max Engelstein (University of Minnesota) as part of HA-GMT-PDE Semi
nar\n\n\nAbstract\nWhereas $C^\\infty$ functions can vanish (almost) arbit
rarily often to arbitrarily high order (e\,g\, $f(x) = e^{-1/x}$ vanishes
to infinite order at zero)\, the zero sets of analytic functions have a lo
t more structure. For example\, you learn in intro to complex analysis tha
t the zeroes of a Holomorphic function are isolated.\n\nThe Lojasiewicz in
equalities (partially) quantify this extra structure possessed by analytic
functions. Developed originally by algebraic geometers\, Lojasiewicz ineq
ualities have been used with great success to study geometric flows. In th
is talk\, I will give a brief introduction to these inequalities and then
discuss some joint work (and maybe some work in progress) with Matthew Bad
ger (UConn) and Tatiana Toro (U Washington)\, in which we use Lojasiewicz
inequalities to study the zero sets of harmonic functions and\, more inter
estingly\, sets which are infinitesimally approximated by the zero sets of
harmonic functions.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darío Mena Arias (Universidad de Costa Rica)
DTSTART:20210125T170000Z
DTEND:20210125T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/47
DESCRIPTION:Title: Sparse bounds for the Discrete Spherical Maximal Function\nby
Darío Mena Arias (Universidad de Costa Rica) as part of HA-GMT-PDE Semina
r\n\n\nAbstract\nWe prove sparse bounds for the spherical maximal operator
of Magyar\, Stein and Wainger. The bounds are conjecturally sharp\, and c
ontain an endpoint estimate. The new method of proof is inspired by ones b
y Bourgain and Ionescu\, is very efficient\, and has not been used in the
proof of sparse bounds before. The Hardy-Littlewood Circle method is used
to decompose the multiplier into major and minor arc components. The effic
iency arises as one only needs a single estimate on each element of the de
composition.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Bortz (University of Alabama)
DTSTART:20210201T170000Z
DTEND:20210201T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/48
DESCRIPTION:Title: New Developments in Parabolic Uniform Rectifiability\nby Simon
Bortz (University of Alabama) as part of HA-GMT-PDE Seminar\n\n\nAbstract
\nIn the 1980’s the $L^2$ boundedness of the Cauchy integral was establi
shed (by Coifman\, McIntosh and Meyer) and this $L^2$ boundedness was quic
kly generalized to `nice’ singular integral operators (Coifman\, David a
nd Meyer / David) on Lipschitz graphs. David and Semmes then asked the nat
ural question: For what sets are all `nice’ singular integral operators
$L^2$ bounded? They were remarkably successful in this endeavor\, providin
g more than 15 equivalent notions and called these sets “uniformly recti
fiable” or UR. These sets are still studied extensively today\, most rec
ently in their connection to elliptic partial differential equations.\n\n
\nAmong the characterizations of UR sets provided by David and Semmes is a
quadratic estimate on the so-called $\\beta$-numbers\, which measure the
flatness of the set at a particular location and scale. In a paper of Hofm
ann\, Lewis and Nyström a notion of “parabolic uniform rectictifiable s
ets” was introduced by taking the definition as a “quadratic estimate
on the parabolic $\\beta$-numbers”. There are no correct proofs of ANY o
f the analogues of the David Semmes theory\; for instance\, it is not know
n if $L^2$ boundedness of parabolic singular integral operators characteri
zes parabolic uniformly rectifiable sets.\n\n \nIn this talk I will discus
s some recent progress in the direction of establishing the parabolic Davi
d-Semmes theory and some open problems that remain. On one hand\, we have
made significant progress and provided some useful characterizations of pa
rabolic uniform rectifiability. On the other hand\, we have also discovere
d that many of the `elliptic’ characterizations do not hold in this para
bolic setting. This is joint work with J. Hoffman\, S. Hofmann\, J.L. Luna
and K. Nyström.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Manuel Conde Alonso (Universidad Autónoma de Madrid)
DTSTART:20210208T170000Z
DTEND:20210208T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/49
DESCRIPTION:Title: Weak endpoint estimates for Calderón-Zygmund operators in von Neu
mann algebras\nby José Manuel Conde Alonso (Universidad Autónoma de
Madrid) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nThe classical Calder
ón-Zygmund decomposition is a fundamental tool that helps one study endpo
int estimates for numerous operators near L1. In this talk\, we will discu
ss an extension of the decomposition to a particular operator valued setti
ng where noncommutativity makes its appearance. Noncommutativity will allo
w us to get rid of the -usually necessary- UMD property of the Banach spac
e where functions take values. Based on joint work with L. Cadilhac and J.
Parcet.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Dosidis (Charles University)
DTSTART:20210215T170000Z
DTEND:20210215T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/50
DESCRIPTION:Title: The uncentered spherical maximal function and Nikodym sets\nby
George Dosidis (Charles University) as part of HA-GMT-PDE Seminar\n\n\nAb
stract\nStein's spherical maximal function is an analogue of the Hardy-Lit
tlewood maximal function\, where the averages are taken over spheres inste
ad of balls. While the uncentered Hardy-Littlewood maximal function is bou
nded on Lp for all p>1 and pointwise equivalent to its centered counterpar
t\, the corresponding uncentered spherical maximal function is not as well
-behaved.\n\nWe provide multidimensional versions of the Kakeya\, Nikodym\
,and Besicovitch constructions associated with spheres. These yield counte
rexamples indicating that maximal operators given by translations of spher
ical averages are unbounded on Lp for all finite p.\n\nHowever\, for lower
-dimensional sets of translations\, we obtain Lp boundedness for the assoc
iated maximally translated spherical averages for a certain range of p tha
t\ndepends on the Minkowski dimension of the set of translations. This is
joint work with A. Chang and J. Kim.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blair Davey (Montana State University)
DTSTART:20210222T170000Z
DTEND:20210222T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/51
DESCRIPTION:Title: A quantification of the Besicovitch projection theorem and its gen
eralizations\nby Blair Davey (Montana State University) as part of HA-
GMT-PDE Seminar\n\n\nAbstract\nThe Besicovitch projection theorem asserts
that if a subset E of the plane has finite length in the sense of Hausdorf
f and is purely unrectifiable (so its intersection with any Lipschitz grap
h has zero length)\, then almost every linear projection of E to a line wi
ll have zero measure. As a consequence\, the probability that a randomly d
ropped line intersects such a set E is equal to zero. This shows us that
the Besicovitch projection theorem is connected to the classical Buffon ne
edle problem. Motivated by the so-called Buffon circle problem\, we explo
re what happens when lines are replaced by more general curves. This lead
s us to discuss generalized Besicovitch theorems and the ways in which we
can quantify such results by building upon the work of Tao\, Volberg\, and
others. This talk covers joint work with Laura Cladek and Krystal Taylor
.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polona Durcik (Chapman University)
DTSTART:20210301T170000Z
DTEND:20210301T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/52
DESCRIPTION:Title: Multilinear singular and oscillatory integrals and applications\nby Polona Durcik (Chapman University) as part of HA-GMT-PDE Seminar\n\n
\nAbstract\nWe give an overview of some recent results in the area of mult
ilinear singular and oscillatory integrals. We discuss their connection wi
th certain questions about point configurations in subsets of the Euclidea
n space and convergence of some ergodic averages. Based on joint works wit
h Michael Christ\, Vjekoslav Kovac\, and Joris Roos.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Ghinassi (University of Washington)
DTSTART:20210308T170000Z
DTEND:20210308T175000Z
DTSTAMP:20260404T094940Z
UID:anpdews/53
DESCRIPTION:Title: On the regularity of singular sets of minimizers for the Mumford-S
hah energy\nby Silvia Ghinassi (University of Washington) as part of H
A-GMT-PDE Seminar\n\n\nAbstract\nThe Mumford-Shah functional was introduce
d by Mumford and Shah in 1989 as a variational model for image reconstruct
ion. The most important regularity problem is the famous Mumford-Shah conj
ecture\, which states that (in 2 dimensions) the closure of the jump set c
an be described as the union of a locally finite collection of injective $
C^1$ arcs that can meet only at the endpoints\, in which case they have to
form triple junctions. If a point is an endpoint of one (and only one) of
such arcs\, it is called cracktip. In this talk\, I plan to survey some o
lder results concerning the regularity of Mumford-Shah minimizers and thei
r singular sets\, and discuss more recent developments (the talk is based
on joint work with Camillo De Lellis and Matteo Focardi).\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean McCurdy (Carnegie Mellon University)
DTSTART:20210315T160000Z
DTEND:20210315T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/54
DESCRIPTION:Title: The Analysts' Traveling Salesman Problem in Banach spaces\nby
Sean McCurdy (Carnegie Mellon University) as part of HA-GMT-PDE Seminar\n\
n\nAbstract\nThis talk discusses recent work (joint with Matthew Badger\,
UCONN) on generalizations of the Analysts' Traveling Salesman Theorem to u
niformly smooth and uniformly convex Banach spaces (e.g.\, l_p spaces). I
n 1990\, motivated by problems in Singular Integral Operators\, Peter Jone
s posed and solved his celebrated Analysts' Traveling Salesman Problem: na
mely\, to characterize all subsets of rectifiable curves in the plane. Si
nce then\, many authors have contributed\, proving similar results in Eucl
idean spaces\, Hilbert Spaces\, Carnot groups\, for 1-rectifiable measures
\, etc. This talk will give a broad overview of some of these results and
their core ideas. In the end\, we will discuss the challenges in Banach
spaces and what generalizations hold there. This talk will include lots o
f pictures and examples.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurel Ohm (Courant Institute)
DTSTART:20210322T160000Z
DTEND:20210322T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/55
DESCRIPTION:Title: Mathematical foundations of slender body theory\nby Laurel Ohm
(Courant Institute) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nMarch 22
\, Monday\, 11:00am-11:50am (CDT) - Laurel Ohm (Courant Institute\, New Yo
rk) Zoom link. https://umn.zoom.us/j/97214138395\nTitle. Mathematical fou
ndations of slender body theory \nAbstract. Slender body theory (SBT) fac
ilitates computational simulations of thin filaments in a 3D viscous fluid
by approximating the hydrodynamic effect of each fiber as the flow due to
a line force density along a 1D curve. Despite the popularity of SBT in c
omputational models\, there had been no rigorous analysis of the error in
using SBT to approximate the interaction of a thin fiber with fluid. In th
is talk\, we develop a PDE framework for analyzing the error introduced by
this approximation. In particular\, given a 1D force along the fiber cent
erline\, we define a notion of `true' solution to the full 3D slender body
problem and obtain an error estimate for SBT in terms of the fiber radius
. This places slender body theory on firm theoretical footing. In addition
\, we perform a complete spectral analysis of the slender body PDE in a si
mple geometric setting\, which sheds light on the use of SBT in approximat
ing the `slender body inverse problem\,' where we instead specify the fibe
r velocity and solve for the 1D force density. Finally\, we make some comp
arisons to the method of regularized Stokeslets and offer thoughts on impr
ovements to SBT.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Neumayer (Northwestern University)
DTSTART:20210329T160000Z
DTEND:20210329T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/56
DESCRIPTION:Title: Quantitative stability for minimizing Yamabe metrics\nby Robin
Neumayer (Northwestern University) as part of HA-GMT-PDE Seminar\n\n\nAbs
tract\nThe Yamabe problem asks whether\, given a closed Riemannian manifol
d\, one can find a conformal metric of constant scalar curvature (CSC). An
affirmative answer was given by Schoen in 1984\, following contributions
from Yamabe\, Trudinger\, and Aubin\, by establishing the existence of a f
unction that minimizes the so-called Yamabe energy functional\; the minimi
zing function corresponds to the conformal factor of the CSC metric.\n\n\n
We address the quantitative stability of minimizing Yamabe metrics. On any
closed Riemannian manifold we show—in a quantitative sense—that if a
function nearly minimizes the Yamabe energy\, then the corresponding confo
rmal metric is close to a CSC metric. Generically\, this closeness is cont
rolled quadratically by the Yamabe energy deficit. However\, we construct
an example demonstrating that this quadratic estimate is false in the gene
ral. This is joint work with Max Engelstein and Luca Spolaor.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariana Smit Vega Garcia (Western Washington University)
DTSTART:20210405T160000Z
DTEND:20210405T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/57
DESCRIPTION:Title: Almost minimizers for obstacle problems\nby Mariana Smit Vega
Garcia (Western Washington University) as part of HA-GMT-PDE Seminar\n\n\n
Abstract\nIn the applied sciences one is often confronted with free bounda
ries\, which arise when the solution to a problem consists of a pair: a fu
nction u (often satisfying a partial differential equation)\, and a set wh
ere this function has a specific behavior. Two central issues in the study
of free boundary problems are: \n\n(1) What is the optimal regularity of
the solution u? \n\n(2) How smooth is the free boundary? \n\nThe study of
the classical obstacle problem - one of the most renowned free boundary pr
oblems - began in the ’60s with the pioneering works of G. Stampacchia\,
H. Lewy\, and J. L. Lions. During the past decades\, it has led to beauti
ful developments\, and its study still presents very interesting and chall
enging questions. In contrast to the classical obstacle problem\, which ar
ises from a minimization problem (as many other PDEs do)\, minimizing prob
lems with noise lead to the notion of almost minimizers. In this talk\, I
will introduce obstacle type problems and overview recent developments in
almost minimizers for the thin obstacle problem\, illustrating techniques
that can be used to tackle questions (1) and (2) in various settings. This
is joint work with Seongmin Jeon and Arshak Petrosyan.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cruz Prisuelos-Arribas (Universidad de Alcalá)
DTSTART:20210412T160000Z
DTEND:20210412T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/58
DESCRIPTION:Title: Vertical square functions and other operators associated with an e
lliptic operator\nby Cruz Prisuelos-Arribas (Universidad de Alcalá) a
s part of HA-GMT-PDE Seminar\n\n\nAbstract\nAlthough\, in general\, vertic
al and conical square functions are equivalent operators just in $L^2$\, i
n this talk we show that\, when this square functions are defined through
the heat or Poisson semigroup that arise from an elliptic operator\, there
exist open intervals of p's containing 2 where the equivalence holds in $
L^p$. As a consequence we obtain new boundedness results for some square f
unctions. We also show how similar ideas lead us to improve the known rang
e where a non-tangential maximal function associated with the Poisson semi
group is bounded.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moritz Egert (Université Paris-Sud (Orsay))
DTSTART:20210419T160000Z
DTEND:20210419T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/59
DESCRIPTION:Title: Boundary value problems for elliptic systems with block structure<
/a>\nby Moritz Egert (Université Paris-Sud (Orsay)) as part of HA-GMT-PDE
Seminar\n\n\nAbstract\nI’ll consider a very simple elliptic PDE in the
upper half-space: divergence form\, transversally independent coefficients
and no mixed transversal-tangential derivatives. In this case\, the Diric
hlet problem can formally be solved via a Poisson semigroup\, but there mi
ght not be a heat semigroup. The construction is rigorous for L2 data. For
other data classes X (Lebesgue\, Hardy\, Sobolev\, Besov\,…) the questi
on\, whether the corresponding Dirichlet problem is well-posed\, is insepa
rably tied to the question\, whether there is a compatible Poisson semigro
up on X. \n\n\nOn a "semigroup space" the infinitesimal generator has (alm
ost?) every operator theoretic property that one can dream of and these ca
n be used to prove well-posedness. But it turns out that there are genuine
ly more "well-posedness spaces" than "semigroup spaces". For example\, up
to boundary dimension n=4 there is a well-posed BMO-Dirichlet problem\, wh
ose unique solution has no reason to keep its tangential regularity in the
interior of the domain. \n\n\nI’ll give an introduction to the general
theme and discuss some new results\, all based on a recent monograph joint
ly written with Pascal Auscher.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murat Akman (University of Essex)
DTSTART:20210428T160000Z
DTEND:20210428T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/60
DESCRIPTION:Title: A Minkowski-type problem for measure associated to A-harmonic PDEs
\nby Murat Akman (University of Essex) as part of HA-GMT-PDE Seminar\n
\n\nAbstract\nThe classical Minkowski problem consists in finding a convex
polyhedron from data consisting of normals to their faces and their surfa
ce areas. In the smooth case\, the corresponding problem for convex bodies
is to find the convex body given the Gauss curvature of its boundary\, as
a function of the unit normal. The proof consists of three parts: existen
ce\, uniqueness\, and regularity. \n\n\nIn this talk\, we study a Minkowsk
i problem for certain measure associated with a compact convex set E with
nonempty interior and its A-harmonic capacitary function in the complement
of E. Here A-harmonic PDE is a non-linear elliptic PDE whose structure is
modelled on the p-Laplace equation. If \\mu_E denotes this measure\, the
n the Minkowski problem we consider in this setting is that\; for a given
finite Borel measure \\mu on S^(n-1)\, find necessary and sufficient condi
tions for which there exists E as above with \\mu_E =\\mu. We will discuss
the existence\, uniqueness\, and regularity of this problem in this setti
ng.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cole Jeznach (University of Minnesota)
DTSTART:20210510T160000Z
DTEND:20210510T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/61
DESCRIPTION:Title: Regularized Distances and Geometry of Measures\nby Cole Jeznac
h (University of Minnesota) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nI
will present joint work with Max Engelstein and Svitlana Mayboroda where
we generalize the notion of the regularized distance function \n$$\nD_{\\m
u\,\\alpha}(x)= \\left(\\int |x-y|^{d-\\alpha}\\\, d\\mu(y)\\right)^{1/\\a
lpha}\,\n$$\n \n\nto functions with more general integrands. We provide a
large class of integrands for which the corresponding distance functions c
ontain geometric information about $\\mu$. In particular\, we produce exam
ples that are in some sense far from the original kernel $|x-y|^{d-\\alpha
}$ but still characterize the geometry of $\\mu$ since they have nice sym
metries with respect to flat sets. In co-dimension 1\, these examples are
explicit\, but in higher co-dimensions\, our proof of existence of such ex
amples is non-constructive\, and thus we have no additional information ab
out their structure.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhan Li (University of Minnesota)
DTSTART:20210517T160000Z
DTEND:20210517T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/62
DESCRIPTION:Title: Carleson measure estimates for the Green function\nby Linhan L
i (University of Minnesota) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nW
e are interested in the relations between an elliptic operator on a domain
\, the geometry of the domain\, and the boundary behavior of the Green fun
ction. In joint work with Guy David and Svitlana Mayboroda\, we show that
if the coefficients of the operator satisfy a quadratic Carleson condition
\, then the Green function on the half-space is almost affine\, in the sen
se that the normalized difference between the Green function with a suffic
iently far away pole and a suitable affine function at every scale satisfi
es a Carleson measure estimate. We demonstrate with counterexamples that o
ur results are optimal\, in the sense that the class of the operators cons
idered are essentially the best possible.\n\nThis work is motivated mainly
by finding PDE characterizations of uniform rectifiable sets with higher
co-dimension. I’ll talk about this motivation and backgrounds\, our rece
nt results\, as well as possible directions in the future.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erisa Hasani (Florida Institute of Technology)
DTSTART:20210503T160000Z
DTEND:20210503T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/63
DESCRIPTION:Title: On the compactness threshold in the critical Kirchhoff equation\nby Erisa Hasani (Florida Institute of Technology) as part of HA-GMT-PDE
Seminar\n\n\nAbstract\nWe study a class of critical Kirchhoff problems wi
th a general nonlocal term. The main difficulty here is the absence of a c
losed-form formula for the compactness threshold. First we obtain a variat
ional characterization of this threshold level. Then we prove a series of
existence and multiplicity results based on this variational characterizat
ion.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART:20210525T160000Z
DTEND:20210525T165000Z
DTSTAMP:20260404T094940Z
UID:anpdews/64
DESCRIPTION:Title: Mean-Value Inequalities for Harmonic Functions\nby Stefan Stei
nerberger (University of Washington) as part of HA-GMT-PDE Seminar\n\n\nAb
stract\nThe mean-value theorem for harmonic functions says that we can bou
nd the integral of a harmonic function in a ball by the average value on t
he boundary (and\, in fact\, there is equality). What happens if we repla
ce the ball by a general convex or even non-convex set? As it turns out\,
this simple question has connections to classical potential theory\, prob
ability theory\, PDEs and even mechanics: one of the arising questions dat
es back to Saint Venant (1856). There are some fascinating new isoperimet
ric problems: for example\, the worst case convex domain in the plane seem
s to look a lot like the letter "D" but we cannot prove it. I will discuss
some recent results and many open problems.\n
LOCATION:https://stable.researchseminars.org/talk/anpdews/64/
END:VEVENT
END:VCALENDAR