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BEGIN:VEVENT
SUMMARY:Edriss S. Titi (University of Cambridge)
DTSTART:20200414T140000Z
DTEND:20200414T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/1
DESCRIPTION:Title: Mathematical analysis of atmospheric models with moisture\nby Edri
ss S. Titi (University of Cambridge) as part of One World PDE seminar\n\n\
nAbstract\nIn this talk I will present some recent results concerning the
global regularity of the three-dimensional Primitive Equations of oceanic
and atmospheric dynamics with various anisotropic viscosity and turbulence
mixing diffusion. However\, in the non-viscous (inviscid) case it can be
shown that there is a one-parameter family of initial data for which the c
orresponding smooth solutions of the inviscid Primitive Equations develop
finite-time singularities (blowup).\n\nCapitalizing on the above results\,
one is able to provide rigorous justification for the derivation of the P
rimitive Equations of planetary scale oceanic dynamics from the three-dime
nsional Navier-Stokes equations\, for vanishing small values of the aspect
ratio of the depth to horizontal width.\n\nIn addition\, we will also sho
w the global well-posedeness of the coupled three-dimensional viscous Prim
itive Equations with a micro-physics phase change moisture model for cloud
formation.\n\nFurthermore\, we will also consider the singular limit beha
vior of a tropical atmospheric model with moisture\, as \\(ε → 0\\)\, w
here \\(ε >0\\) is a moisture phase transition small convective adjustmen
t relaxation time parameter.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART:20200414T150000Z
DTEND:20200414T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/2
DESCRIPTION:Title: Gross–Pitaeskii\, Kadomtsev–Petviashvili\, and Adler–Moser\n
by Juncheng Wei (University of British Columbia) as part of One World PDE
seminar\n\n\nAbstract\nI will discuss the traveling wave solutions to Gros
s–Pitaeskii equation with speed \\(c\\). I will show how Adler–Moser p
olynomial and lump solutions of KP-I are connected as the speed varies fro
m zero to sound speed. Key results proved are nondegeneracy of Adler–Mos
er\, and lump of KP-I.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Germain (Courant Institute)
DTSTART:20200421T140000Z
DTEND:20200421T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/3
DESCRIPTION:Title: On the derivation of the kinetic wave equation\nby Pierre Germain
(Courant Institute) as part of One World PDE seminar\n\n\nAbstract\nI will
present recent work\, in collaboration with Charles Collot\, on the deriv
ation of the kinetic wave equation. This equation is believed to describe
(weakly) nonlinear dispersive equations in a turbulent regime – it is ve
ry similar to the Boltzmann equation\, with particles replaced by phonons\
, or linear waves. Until recently\, little was known rigorously on the der
ivation of the kinetic wave equation from nonlinear dispersive models. We
show that the kinetic wave equation provides the correct description on lo
ng time scales\, almost up to the expected kinetic time scale. The proof c
ombines ideas from random PDEs\, harmonic analysis\, and graph theory (thr
ough Feynman graphs).\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tarek Elgindi (UC San Diego)
DTSTART:20200421T150000Z
DTEND:20200421T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/4
DESCRIPTION:Title: Singularity formation in incompressible fluids\nby Tarek Elgindi (
UC San Diego) as part of One World PDE seminar\n\n\nAbstract\nI will discu
ss various recent results and ideas related to the problem of finite-time
singularity for solutions to the incompressible Euler equation.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Bonforte (Universidad Autónoma de Madrid)
DTSTART:20200428T140000Z
DTEND:20200428T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/5
DESCRIPTION:Title: Sharp extinction rates for fast diffusion equations on generic bounded
domains\nby Matteo Bonforte (Universidad Autónoma de Madrid) as part
of One World PDE seminar\n\n\nAbstract\nWe investigate the homogeneous Di
richlet problem for the Fast Diffusion Equation \\(u_t=Δ u^m\\)\, posed i
n a smooth bounded domain \\(Ω⊂ \\mathbb{R}^N\\)\, in the exponent rang
e \\(m_s=(N-2)_+/(N+2)0\\)\, and also that they approach a sep
arate variable solution \\(u(t\,x)∼ (T-t)^{1/(1-m)}S(x)\\)\, as \\(t→
T^-\\)\, where \\(S\\) belongs to the set of solutions to a suitable ellip
tic problem and depends on the initial datum \\(u_0\\). It has been shown
recently that \\(v(x\,t) = u(t\,x)\\\,(T-t)^{-1/(1-m)}\\) tends to \\(S(x)
\\) as \\(t→ T^-\\)\, uniformly in the relative error norm. Starting fro
m this result\, we investigate the fine asymptotic behaviour and prove sha
rp rates of convergence for the relative error. The proof is based on an e
ntropy method relying on a (improved) weighted Poincaré inequality\, that
we show to be true on generic bounded domains. Another essential aspect o
f the method is the new concept of “almost orthogonality”\, which can
be thought as a nonlinear analogous of the classical orthogonality conditi
on needed to obtain improved Poincaré inequalities and sharp convergence
rates for linear flows. This is a joint work with Alessio Figalli (ETH Zü
rich\, CH).\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margaret Beck (Boston University)
DTSTART:20200505T140000Z
DTEND:20200505T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/6
DESCRIPTION:Title: Spectral stability\, the Maslov index\, and spatial dynamics\nby M
argaret Beck (Boston University) as part of One World PDE seminar\n\n\nAbs
tract\nUnderstanding the spectral stability of solutions to partial differ
ential equations is an important step in predicting long-time dynamics. Re
cently\, it has been shown that a topological invariant known as the Maslo
v Index can play an important role in determining spectral stability for s
ystems that have a symplectic structure. In this talk\, the notions of spe
ctral stability and the Maslov Index will be introduced and an overview of
recent results will be given. If time permits\, the perspective of spatia
l dynamics will be discussed\, as well has how these recent developments h
ave led to a notion of spatial dynamics in multiple space dimensions.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mingione (Università di Parma)
DTSTART:20200512T140000Z
DTEND:20200512T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/7
DESCRIPTION:Title: A soup of Lipschitz estimates\nby Giuseppe Mingione (Università d
i Parma) as part of One World PDE seminar\n\n\nAbstract\nI am going to giv
e a review of Lipschitz estimates for nonlinear elliptic problems\, with s
pecial emphasis on non-uniformly elliptic ones.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Topping (University of Warwick)
DTSTART:20200512T150000Z
DTEND:20200512T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/8
DESCRIPTION:Title: Gradient flows for the harmonic map energy\nby Peter Topping (Univ
ersity of Warwick) as part of One World PDE seminar\n\n\nAbstract\nIn 1964
\, Eells and Sampson introduced the harmonic map flow\, thus starting the
field of geometric flows. Their idea was essentially to consider the \\(L^
2\\) gradient flow of the harmonic map energy\, i.e. the Dirichlet energy\
, but instead of considering real-valued functions (which would give the h
eat equation) they considered more general maps\, for example taking value
s into a sphere or a more general Riemannian manifold.\n\nThe critical dom
ain dimension for this nonlinear PDE is two. In 1985 Struwe initiated an a
nalysis of the blow-up behaviour of the flow in this dimension\, and descr
ibed it in terms of the notion of bubbling in the spirit of Sacks-Uhlenbec
k.\n\nAfter giving a brief overview of this story I will describe a differ
ent gradient flow for the harmonic map energy that I introduced with Melan
ie Rupflin\, coinciding with the harmonic map flow on \\(S^2\\) and a flow
introduced on the torus \\(T^2\\) by Ding-Li-Liu. In our flow we allow no
t only the map to evolve\, but also the domain metric. This changes the pu
rpose of the flow from finding harmonic maps to finding minimal surfaces\,
as I will explain. From a PDE perspective it introduces a selection of ne
w blow-up behaviours that are reminiscent of bubbling and yet throw up com
pletely new phenomena and possibilities. I will survey some of what has be
en found over the past few years\, including hopefully our most recent wor
k joint with Rupflin and Kohout\, and mention some open problems.\n\nI wil
l not be assuming great geometry prerequisites. I will\, however\, explain
some of the elegant classical geometry that opens up this subject to thos
e coming from a nonlinear PDE background.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Malchiodi (Scuola Normale Superiore)
DTSTART:20200519T140000Z
DTEND:20200519T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/9
DESCRIPTION:Title: On critical points of the Moser-Trudinger functional\nby Andrea Ma
lchiodi (Scuola Normale Superiore) as part of One World PDE seminar\n\n\nA
bstract\nSince the fundamental work by Trudinger from 1967 it is known tha
t in two dimensions Sobolev functions in $W^{1\,2}$ satisfy embedding prop
erties of exponential type. In 1971 Moser then obtained a sharp form of th
e embedding\, controlling the integrability of $F(u) := ∫ \\exp(u^2)$ in
terms of the Sobolev norm of $u$.\n\nOn a closed Riemannian surface\, $F(
u)$ is unbounded above for $\\|u\\|_{W^{1\,2}} > 4\\pi$. We are however ab
le to find critical points of $F$ constrained to any sphere $\\{ \\|u\\|_{
W^{1\,2}} = \\beta \\}$\, with $\\beta > 0$ arbitrary. The proof combines
min-max theory\, a monotonicity argument by Struwe\, blow-up analysis and
compactness estimates. This is joint work with F. De Marchis\, O. Druet\,
L. Martinazzi and P. D. Thizy.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Maggi (UT Austin)
DTSTART:20200519T150000Z
DTEND:20200519T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/10
DESCRIPTION:Title: A model for soap films based on capillarity theory\nby Francesco
Maggi (UT Austin) as part of One World PDE seminar\n\n\nAbstract\nSoap fil
ms are modeled\, rather than as surfaces with zero mean curvature\, as reg
ions with small volume satisfying a spanning condition of homotopic type.
We discuss qualitative properties of such soap films\, and their convergen
ce towards minimal surfaces\, when the volume goes to zero. This is a join
t work with Antonello Scardicchio (ICTP)\, Darren King (UT Austin) and Sal
vatore Stuvard (UT Austin).\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Merle (Université de Cergy-Pontoise)
DTSTART:20200526T140000Z
DTEND:20200526T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/11
DESCRIPTION:Title: On the implosion of a three dimensional compressible fluid\nby Fr
ank Merle (Université de Cergy-Pontoise) as part of One World PDE seminar
\n\n\nAbstract\nWe consider the compressible three dimensional Navier Stok
es and Euler equations. In a suitable regime of barotropic laws\, we const
ruct a set of finite energy smooth initial data for which the correspondin
g solutions to both equations implode (with infinite density) at a later t
ime at a point\, and completely describe the associated formation of singu
larity.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ovidiu Savin (Columbia University)
DTSTART:20200526T150000Z
DTEND:20200526T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/12
DESCRIPTION:Title: Free boundary regularity for the 3 membranes problem\nby Ovidiu S
avin (Columbia University) as part of One World PDE seminar\n\n\nAbstract\
nFor a positive integer \\(N\\)\, the \\(N\\)-membranes problem describes
the equilibrium position of \\(N\\) ordered elastic membranes subject to f
orcing and boundary conditions. If the heights of the membranes are descri
bed by real functions \\(u_1\, u_2\,…\,u_N\\)\, then the problem can be
understood as a system of \\(N-1\\) coupled obstacle problems with interac
ting free boundaries which can cross each other. When \\(N=2\\) there is o
nly one free boundary and the problem is equivalent to the classical obsta
cle problem. In my first lecture I will review some of the regularity theo
ry for the standard obstacle problem\, and in my second lecture I will dis
cuss some recent work in collaboration with Hui Yu about the case when \\(
N=3\\) and there are two interacting free boundaries.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Gursky (University of Notre Dame)
DTSTART:20200505T150000Z
DTEND:20200505T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/13
DESCRIPTION:Title: Singular solutions to some PDEs arising in conformal geometry\nby
Matthew Gursky (University of Notre Dame) as part of One World PDE semina
r\n\n\nAbstract\nI will describe some aspects of the k-Yamabe problem\, a
fully nonlinear version of the Yamabe problem\, emphasizing the negative c
ase. I will begin with a quick overview of the regularity theory in the
‘positive’ case\, and contrast this with how little is known in the ne
gative case. (This is a remarkable difference with the classical Yamabe pr
oblem\, in which the negative case is easy). At the end of the talk I will
discuss some ongoing work with M. Musso on constructing solutions with is
olated singularities.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria del Mar Gonzalez (Universidad Autónoma de Madrid)
DTSTART:20200407T140000Z
DTEND:20200407T145000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/14
DESCRIPTION:Title: A free boundary problem for the half-Laplacian\, the Steklov eigenval
ue and higher order generalizations\nby Maria del Mar Gonzalez (Univer
sidad Autónoma de Madrid) as part of One World PDE seminar\n\n\nAbstract\
nA free boundary problem for the half-Laplacian\, the Steklov eigenvalue a
nd higher order generalizations\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Antonio Carrillo (University of Oxford)
DTSTART:20200407T150000Z
DTEND:20200407T155000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/15
DESCRIPTION:Title: Nonlinear Aggregation-Diffusion Equations: Stationary States\, Functi
onal inequalities & Stabilization\nby José Antonio Carrillo (Universi
ty of Oxford) as part of One World PDE seminar\n\n\nAbstract\nNonlinear Ag
gregation-Diffusion Equations: Stationary States\, Functional inequalities
& Stabilization\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mónica Clapp (Universidad Nacional Autónoma de México)
DTSTART:20200428T150000Z
DTEND:20200428T155000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/16
DESCRIPTION:Title: Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounde
d Domains\nby Mónica Clapp (Universidad Nacional Autónoma de México
) as part of One World PDE seminar\n\n\nAbstract\nWe investigate the homog
eneous Dirichlet problem for the Fast Diffusion Equation \\(u_t=Δ u^m\\)\
, posed in a smooth bounded domain \\(Ω⊂ \\mathbb{R}^N\\)\, in the expo
nent range \\(m_s=(N-2)_+/(N+2)0\\)\, and also that they appro
ach a separate variable solution \\(u(t\,x)∼ (T-t)^{1/(1-m)}S(x)\\)\, as
\\(t→ T^-\\)\, where \\(S\\) belongs to the set of solutions to a suita
ble elliptic problem and depends on the initial datum \\(u_0\\). It has be
en shown recently that \\(v(x\,t) = u(t\,x)\\\,(T-t)^{-1/(1-m)}\\) tends t
o \\(S(x)\\) as \\(t→ T^-\\)\, uniformly in the relative error norm. Sta
rting from this result\, we investigate the fine asymptotic behaviour and
prove sharp rates of convergence for the relative error. The proof is base
d on an entropy method relying on a (improved) weighted Poincaré inequali
ty\, that we show to be true on generic bounded domains. Another essential
aspect of the method is the new concept of “almost orthogonality”\, w
hich can be thought as a nonlinear analogous of the classical orthogonalit
y condition needed to obtain improved Poincaré inequalities and sharp con
vergence rates for linear flows. This is a joint work with Alessio Figalli
(ETH Zürich\, CH).\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART:20200602T140000Z
DTEND:20200602T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/17
DESCRIPTION:Title: Regularity estimates for the Boltzmann equation without cutoff\nb
y Luis Silvestre (University of Chicago) as part of One World PDE seminar\
n\n\nAbstract\nWe study the regularization effect of the inhomogeneous Bol
tzmann equation without cutoff. We obtain a priori estimates for all deriv
atives of the solution depending only on bounds of the hydrodynamic quanti
ties: mass density\, energy density and entropy density. As a consequence\
, a classical solution to the equation may fail to exists after certain ti
me \\(T\\) only if at least one of these hydrodynamic quantities blows up.
Our analysis applies to the case of moderately soft and hard potentials.
We use methods that originated in the study of nonlocal elliptic equations
: a weak Harnack inequality in the style of De Giorgi\, and a Schauder-typ
e estimate.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert L. Frank (California Institute of Technology)
DTSTART:20200602T150000Z
DTEND:20200602T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/18
DESCRIPTION:Title: A ‘liquid-solid’ phase transition in a simple model for swarming<
/a>\nby Rupert L. Frank (California Institute of Technology) as part of On
e World PDE seminar\n\n\nAbstract\nWe consider a non-local optimization pr
oblem\, which is motivated by a simple model for swarming and other self-a
ssembly/aggregation models\, and prove the existence of different phases.
In particular\, we show that in the large mass regime the ground state den
sity profile is the characteristic function of a round ball. An essential
ingredient in our proof is a strict rearrangement inequality with a quanti
tative error estimate. We formulate several open problems which might be a
menable to PDE techniques.\n\nThe talk is based on joint work with E. Lieb
.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nader Masmoudi (Courant Institute & NYU Abu-Dhabi)
DTSTART:20200609T140000Z
DTEND:20200609T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/19
DESCRIPTION:Title: Recent advances in nonlinear inviscid damping\nby Nader Masmoudi
(Courant Institute & NYU Abu-Dhabi) as part of One World PDE seminar\n\n\n
Abstract\nWe will review some recent results dealing with inviscid damping
. These results include the optimality of the Gevrey regularity required t
o get the damping as well as the generalization to more general monotone f
lows.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julio D. Rossi (Universidad de Buenos Aires)
DTSTART:20200609T150000Z
DTEND:20200609T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/20
DESCRIPTION:Title: Coupling and mixing local and nonlocal equations\nby Julio D. Ros
si (Universidad de Buenos Aires) as part of One World PDE seminar\n\n\nAbs
tract\nIn this talk we present a simple way of coupling a local and a nonl
ocal evolution equation in such a way that the usual properties (like exis
tence and uniqueness of solutions\, conservation of the total mass\, etc)
are satisfied. Moreover\, we study the limit as we homogenize this setting
mixing the regions in which local and nonlocal operators act.\n\n(Based o
n joint works with A. Garriz (Madrid) and F. Quiros (Madrid) and with M. C
apanna (L’Aquila))\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Niethammer (Universität Bonn)
DTSTART:20200616T140000Z
DTEND:20200616T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/21
DESCRIPTION:Title: Oscillatory and peak solutions in coagulation-fragmentation equations
a\nby Barbara Niethammer (Universität Bonn) as part of One World PD
E seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fanghua Lin (Courant Institute)
DTSTART:20200616T150000Z
DTEND:20200616T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/22
DESCRIPTION:Title: Several questions related to homogenization\nby Fanghua Lin (Cour
ant Institute) as part of One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sun-Yung Alice Chang (Princeton University)
DTSTART:20200623T140000Z
DTEND:20200623T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/23
DESCRIPTION:Title: On Moser–Trudinger–Onofri inequalty under constraints\nby Sun
-Yung Alice Chang (Princeton University) as part of One World PDE seminar\
n\n\nAbstract\nA classical result of Aubin states that the constant in Mos
er–Trudinger–Onofri inequality on the 2-sphere \\(S^2\\) can be improv
ed for functions with zero first order moments of the area element. In a j
oint work with Fengbo Hang\, we generalize Aubin’s inequality to higher
order moments case. These new inequalities bear similarity to a sequence o
f Lebedev–Milin type inequalities on the unit circle \\(S^1\\) coming fr
om the work of Grenander–Szego on Toeplitz determinants (as pointed out
by Widom). I will also report some joint work with Changfeng Gui still in
progress\, where we made attempt to formulate the analogue on \\(S^2\\) of
the second inequality in Szego’s limit theorem.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joaquim Serra (ETH Zurich)
DTSTART:20200623T150000Z
DTEND:20200623T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/24
DESCRIPTION:Title: The singular set in the Stephan problem\nby Joaquim Serra (ETH Zu
rich) as part of One World PDE seminar\n\n\nAbstract\nThe classical Stepha
n problem\, first introduced in 1831 by Lamé and Clapeyron\, aims to desc
ribe the evolution of the temperature in a block of ice (initially at zero
degrees centigrade) that is melting to water. The Baiochi-Duvait transfor
mation reduces it to the parabolic obstacle problem\, easier to treat in m
any aspects. It is known since the celebrated work of Caffarelli that the
interface between ice and water (the so-called free boundary) is smooth ou
tside of a closed set of the spacetime\, which is called the singular set.
\n\nIn the talk\, I will introduce a forthcoming joint work with A. Figall
i and X. Ros-Oton on the size and regularity of this singular set.\n\nIn t
hree spatial dimensions we prove that the singular set splits into two pie
ces. The first is a set of parabolic dimension 1 (hence it is small). The
second piece satisfies that its spatial projection can be covered by count
able unions of \\(C^\\infty\\) surfaces and its projection onto the time a
xis has dimension zero!\n\nIn particular\, we show that the free boundary
of the Stefan problem in three spatial dimensions will be a smooth surface
outside of a set of times of dimension at most 1/2.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanyan Li (Rutgers University)
DTSTART:20200630T140000Z
DTEND:20200630T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/25
DESCRIPTION:Title: Some recent works on conformally invariant fully nonlinear elliptic e
quations\nby Yanyan Li (Rutgers University) as part of One World PDE s
eminar\n\n\nAbstract\nThe following problem was raised by Nirenberg: Which
function on the standard 2-sphere is the Gauss curvature of a metric conf
ormally equivalent to the standard metric. Naturally one may ask a similar
question in the higher dimensional case\, namely\, which function on the
standard \\(n\\)-sphere is the scalar curvature of a metric conformally eq
uivalent to the standard metric.\n\nAn analogous question can be asked for
the \\(\\sigma_k\\) curvature instead of the scalar curvature\, and we ca
ll it the \\(\\sigma_k\\)-Nirenberg problem. We will present some results
on the existence and compactness of solutions of the \\(\\sigma_k\\)-Niren
berg problem for \\(n≥ 3\\) and \\(k≥ n/2\\). The results for \\(n=4\\
) and \\(k=2\\) were established by Alice Chang\, Zheng-Chao Han and Paul
Yang in 2011. We will also present some recent results on the \\(σ_k\\)-L
oewner–Nirenberg problem. These results are from a couple of joint works
with Maria del Mar Gonzalez\, Luc Nguyen\, Bo Wang\, and Jingang Xiong.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gustav Holzegel (Imperial College London)
DTSTART:20200630T150000Z
DTEND:20200630T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/26
DESCRIPTION:Title: The non-linear stability of the Schwarzschild family of black holes\nby Gustav Holzegel (Imperial College London) as part of One World PDE
seminar\n\n\nAbstract\nI will discuss recent work with M. Dafermos\, I. Ro
dnianski and M. Taylor proving the full finite codimension asymptotic stab
ility of the Schwarzschild family of black holes in the exterior of the bl
ack hole region. The proof is expressed entirely in physical space and bas
ed on our previous understanding of linear stability of the Schwarzschild
family in a double null gauge.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Dolbeault (CEREMADE\, Université Paris-Dauphine)
DTSTART:20200707T140000Z
DTEND:20200707T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/27
DESCRIPTION:Title: Stability in Gagliardo-Nirenberg inequalities\nby Jean Dolbeault
(CEREMADE\, Université Paris-Dauphine) as part of One World PDE seminar\n
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:André Neves (University of Chicago)
DTSTART:20200707T150000Z
DTEND:20200707T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/28
DESCRIPTION:Title: Counting minimal surfaces in negatively curved 3-manifolds\nby An
dré Neves (University of Chicago) as part of One World PDE seminar\n\n\nA
bstract\nI will survey some of the recent progress regarding existence of
minimal hypersurfaces and then I will talk about my joint work with Calega
ri and Marques where we asymptotically count minimal surfaces in negativel
y curved manifolds.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helena J. Nussenzveig Lopes (Universidade Federal do Rio de Janeir
o)
DTSTART:20200714T140000Z
DTEND:20200714T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/29
DESCRIPTION:Title: Analysis of incompressible flows with helical symmetry\nby Helena
J. Nussenzveig Lopes (Universidade Federal do Rio de Janeiro) as part of
One World PDE seminar\n\n\nAbstract\nThe analysis of incompressible flows
under different symmetry reductions is an ongoing topic of research. While
flows with translational symmetry – 2D flows – and axisymmetric flows
have a broad associated literature\, helically symmetric flows have attra
cted less mathematical attention.\n\nHelically symmetric flows are those i
nvariant under simultaneous rotation and translation with respect to a fix
ed axis. These flows arise in real world applications such as the flow gen
erated by a rotating blade. From the point of view of mathematical analysi
s\, flows with helical symmetry lie between 2D flows and axisymmetric flow
s. The purpose of the talk is to illustrate this observation\, discussing
both existence theorems and vanishing viscosity results for helically symm
etric fluid flow\, and establishing comparisons with 2D and axisymmetric c
ases.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gigliola Staffilani (MIT)
DTSTART:20200714T150000Z
DTEND:20200714T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/30
DESCRIPTION:Title: The Schrodinger equations as inspiration of beautiful mathematics
\nby Gigliola Staffilani (MIT) as part of One World PDE seminar\n\n\nAbstr
act\nIn the last two decades great progress has been made in the study of
dispersive and wave equations. Over the years the toolbox used in order to
attack highly nontrivial problems related to these equations has develope
d to include a collection of techniques: Fourier and harmonic analysis\, a
nalytic number theory\, math physics\, dynamical systems\, probability and
symplectic geometry. In this talk I will introduce a variety of results u
sing as model problem the periodic 2D cubic nonlinear Schrodinger equation
. I will start by giving a physical derivation of the equation from a quan
tum many-particles system\, I will introduce periodic Strichartz estimates
along with some remarkable connections to analytic number theory\, I will
move on the concept of energy transfer and its connection to dynamical sy
stems\, and I will end with some results\, such as the non-squeezing theor
em\, that one can obtain once the equation is viewed in the frequency spac
e as an infinite dimension Hamiltonian system.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Kenig (University of Chicago)
DTSTART:20200901T140000Z
DTEND:20200901T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/31
DESCRIPTION:Title: Asymptotic simplification for solutions of the energy critical nonlin
ear wave equation\nby Carlos Kenig (University of Chicago) as part of
One World PDE seminar\n\n\nAbstract\nIn this lecture I will describe the p
rogress made in the last 12 years\, in our understanding of the long-time
behavior of large solutions to the energy critical focusing nonlinear wave
equation. In the last part of the talk I will concentrate on recent progr
ess (with Duyckaerts and Merle) on the asymptotic simplification for large
time\, into sums of modulated static solutions plus a linear term\, in al
l odd dimensions\, in the radial case.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Ionescu (Princeton University)
DTSTART:20200901T150000Z
DTEND:20200901T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/32
DESCRIPTION:Title: On the nonlinear stability of shear flows and vortices\nby Alexan
dru Ionescu (Princeton University) as part of One World PDE seminar\n\n\nA
bstract\nI will discuss some recent work (in collaboration with Hao Jia) o
n the global asymptotic stability of shear flows and vortices among soluti
ons of the 2D Euler equations. More precisely\, we prove (1) global asympt
otic stability in a finite channel of general smooth monotonic shear flows
that satisfy a suitable spectral condition\, and (2) global asymptotic st
ability of point vortices in the plane.\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Bressan (Pennsylvania State University)
DTSTART:20200908T140000Z
DTEND:20200908T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/33
DESCRIPTION:by Alberto Bressan (Pennsylvania State University) as part of
One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene M. Gamba (University of Texas at Austin)
DTSTART:20200908T150000Z
DTEND:20200908T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/34
DESCRIPTION:by Irene M. Gamba (University of Texas at Austin) as part of O
ne World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Ball (Heriot-Watt University\, Edinburgh)
DTSTART:20200915T140000Z
DTEND:20200915T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/35
DESCRIPTION:Title: Axisymmetry of critical points of the Onsager functional for liquid c
rystals\nby John Ball (Heriot-Watt University\, Edinburgh) as part of
One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gui-Qiang G. Chen (University of Oxford)
DTSTART:20200915T150000Z
DTEND:20200915T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/36
DESCRIPTION:by Gui-Qiang G. Chen (University of Oxford) as part of One Wor
ld PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (Institute for Advanced Study)
DTSTART:20200922T140000Z
DTEND:20200922T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/37
DESCRIPTION:Title: Flows of vector fields: classical and modern\nby Camillo De Lelli
s (Institute for Advanced Study) as part of One World PDE seminar\n\nAbstr
act: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hatem Zaag (Université Sorbonne Paris Nord)
DTSTART:20200922T150000Z
DTEND:20200922T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/38
DESCRIPTION:Title: A stylized pyramid-shaped blow-up set for the 2d semilinear wave equa
tion\nby Hatem Zaag (Université Sorbonne Paris Nord) as part of One W
orld PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Strauss (Brown University)
DTSTART:20200929T140000Z
DTEND:20200929T150000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/39
DESCRIPTION:by Walter Strauss (Brown University) as part of One World PDE
seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland)
DTSTART:20200929T150000Z
DTEND:20200929T160000Z
DTSTAMP:20260422T225719Z
UID:OneWorldPDE/40
DESCRIPTION:Title: Quantitative hypoelliptic regularity and the estimation of Lyapunov e
xponents and other long-time dynamical properties of stochastic differenti
al equations\nby Jacob Bedrossian (University of Maryland) as part of
One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldPDE/40/
END:VEVENT
END:VCALENDAR