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BEGIN:VEVENT
SUMMARY:Edriss S. Titi (University of Cambridge)
DTSTART:20200414T140000Z
DTEND:20200414T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/1
DESCRIPTION:Title: Mathematical analysis of atmospheric models with moisture\n
by Edriss S. Titi (University of Cambridge) as part of One World PDE semin
ar\n\n\nAbstract\nIn this talk I will present some recent results concerni
ng the global regularity of the three-dimensional Primitive Equations of o
ceanic and atmospheric dynamics with various anisotropic viscosity and tur
bulence mixing diffusion. However\, in the non-viscous (inviscid) case it
can be shown that there is a one-parameter family of initial data for whic
h the corresponding smooth solutions of the inviscid Primitive Equations d
evelop finite-time singularities (blowup).\n\nCapitalizing on the above re
sults\, one is able to provide rigorous justification for the derivation o
f the Primitive Equations of planetary scale oceanic dynamics from the thr
ee-dimensional Navier-Stokes equations\, for vanishing small values of the
aspect ratio of the depth to horizontal width.\n\nIn addition\, we will a
lso show the global well-posedeness of the coupled three-dimensional visco
us Primitive Equations with a micro-physics phase change moisture model fo
r cloud formation.\n\nFurthermore\, we will also consider the singular lim
it behavior of a tropical atmospheric model with moisture\, as \\(ε → 0
\\)\, where \\(ε >0\\) is a moisture phase transition small convective ad
justment relaxation time parameter.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART:20200414T150000Z
DTEND:20200414T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/2
DESCRIPTION:Title: Gross–Pitaeskii\, Kadomtsev–Petviashvili\, and Adler–Mose
r\nby Juncheng Wei (University of British Columbia) as part of One Wor
ld PDE seminar\n\n\nAbstract\nI will discuss the traveling wave solutions
to Gross–Pitaeskii equation with speed \\(c\\). I will show how Adler–
Moser polynomial and lump solutions of KP-I are connected as the speed var
ies from zero to sound speed. Key results proved are nondegeneracy of Adle
r–Moser\, and lump of KP-I.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Germain (Courant Institute)
DTSTART:20200421T140000Z
DTEND:20200421T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/3
DESCRIPTION:Title: On the derivation of the kinetic wave equation\nby Pierre G
ermain (Courant Institute) as part of One World PDE seminar\n\n\nAbstract\
nI will present recent work\, in collaboration with Charles Collot\, on th
e derivation of the kinetic wave equation. This equation is believed to de
scribe (weakly) nonlinear dispersive equations in a turbulent regime – i
t is very similar to the Boltzmann equation\, with particles replaced by p
honons\, or linear waves. Until recently\, little was known rigorously on
the derivation of the kinetic wave equation from nonlinear dispersive mode
ls. We show that the kinetic wave equation provides the correct descriptio
n on long time scales\, almost up to the expected kinetic time scale. The
proof combines ideas from random PDEs\, harmonic analysis\, and graph theo
ry (through Feynman graphs).\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tarek Elgindi (UC San Diego)
DTSTART:20200421T150000Z
DTEND:20200421T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/4
DESCRIPTION:Title: Singularity formation in incompressible fluids\nby Tarek El
gindi (UC San Diego) as part of One World PDE seminar\n\n\nAbstract\nI wil
l discuss various recent results and ideas related to the problem of finit
e-time singularity for solutions to the incompressible Euler equation.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Bonforte (Universidad Autónoma de Madrid)
DTSTART:20200428T140000Z
DTEND:20200428T150000Z
DTSTAMP:20260404T110825Z
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 homogen
eous Dirichlet problem for the Fast Diffusion Equation \\(u_t=Δ u^m\\)\,
posed in a smooth bounded domain \\(Ω⊂ \\mathbb{R}^N\\)\, in the expone
nt range \\(m_s=(N-2)_+/(N+2)0\\)\, and also that they approac
h 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 suitabl
e elliptic 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. Start
ing from this result\, we investigate the fine asymptotic behaviour and pr
ove sharp rates of convergence for the relative error. The proof is based
on an entropy method relying on a (improved) weighted Poincaré inequality
\, that we show to be true on generic bounded domains. Another essential a
spect of the method is the new concept of “almost orthogonality”\, whi
ch can be thought as a nonlinear analogous of the classical orthogonality
condition needed to obtain improved Poincaré inequalities and sharp conve
rgence rates for linear flows. This is a joint work with Alessio Figalli (
ETH Zürich\, CH).\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margaret Beck (Boston University)
DTSTART:20200505T140000Z
DTEND:20200505T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/6
DESCRIPTION:Title: Spectral stability\, the Maslov index\, and spatial dynamics\nby Margaret Beck (Boston University) as part of One World PDE seminar\n
\n\nAbstract\nUnderstanding the spectral stability of solutions to partial
differential equations is an important step in predicting long-time dynam
ics. Recently\, it has been shown that a topological invariant known as th
e Maslov Index can play an important role in determining spectral stabilit
y for systems that have a symplectic structure. In this talk\, the notions
of spectral stability and the Maslov Index will be introduced and an over
view of recent results will be given. If time permits\, the perspective of
spatial dynamics will be discussed\, as well has how these recent develop
ments have led to a notion of spatial dynamics in multiple space dimension
s.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mingione (Università di Parma)
DTSTART:20200512T140000Z
DTEND:20200512T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/7
DESCRIPTION:Title: A soup of Lipschitz estimates\nby Giuseppe Mingione (Univer
sità di Parma) as part of One World PDE seminar\n\n\nAbstract\nI am going
to give a review of Lipschitz estimates for nonlinear elliptic problems\,
with special emphasis on non-uniformly elliptic ones.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Topping (University of Warwick)
DTSTART:20200512T150000Z
DTEND:20200512T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/8
DESCRIPTION:Title: Gradient flows for the harmonic map energy\nby Peter Toppin
g (University of Warwick) as part of One World PDE seminar\n\n\nAbstract\n
In 1964\, Eells and Sampson introduced the harmonic map flow\, thus starti
ng the field of geometric flows. Their idea was essentially to consider th
e \\(L^2\\) gradient flow of the harmonic map energy\, i.e. the Dirichlet
energy\, but instead of considering real-valued functions (which would giv
e the heat equation) they considered more general maps\, for example takin
g values into a sphere or a more general Riemannian manifold.\n\nThe criti
cal domain dimension for this nonlinear PDE is two. In 1985 Struwe initiat
ed an analysis of the blow-up behaviour of the flow in this dimension\, an
d described it in terms of the notion of bubbling in the spirit of Sacks-U
hlenbeck.\n\nAfter giving a brief overview of this story I will describe a
different gradient flow for the harmonic map energy that I introduced wit
h Melanie 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 a
llow not only the map to evolve\, but also the domain metric. This changes
the purpose of the flow from finding harmonic maps to finding minimal sur
faces\, as I will explain. From a PDE perspective it introduces a selectio
n of new blow-up behaviours that are reminiscent of bubbling and yet throw
up completely new phenomena and possibilities. I will survey some of what
has been found over the past few years\, including hopefully our most rec
ent work joint with Rupflin and Kohout\, and mention some open problems.\n
\nI will not be assuming great geometry prerequisites. I will\, however\,
explain some of the elegant classical geometry that opens up this subject
to those coming from a nonlinear PDE background.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Malchiodi (Scuola Normale Superiore)
DTSTART:20200519T140000Z
DTEND:20200519T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/9
DESCRIPTION:Title: On critical points of the Moser-Trudinger functional\nby An
drea Malchiodi (Scuola Normale Superiore) as part of One World PDE seminar
\n\n\nAbstract\nSince the fundamental work by Trudinger from 1967 it is kn
own that in two dimensions Sobolev functions in $W^{1\,2}$ satisfy embeddi
ng properties of exponential type. In 1971 Moser then obtained a sharp for
m of the embedding\, controlling the integrability of $F(u) := ∫ \\exp(u
^2)$ in terms of the Sobolev norm of $u$.\n\nOn a closed Riemannian surfac
e\, $F(u)$ is unbounded above for $\\|u\\|_{W^{1\,2}} > 4\\pi$. We are how
ever able to find critical points of $F$ constrained to any sphere $\\{ \\
|u\\|_{W^{1\,2}} = \\beta \\}$\, with $\\beta > 0$ arbitrary. The proof co
mbines min-max theory\, a monotonicity argument by Struwe\, blow-up analys
is and compactness estimates. This is joint work with F. De Marchis\, O. D
ruet\, L. Martinazzi and P. D. Thizy.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Maggi (UT Austin)
DTSTART:20200519T150000Z
DTEND:20200519T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/10
DESCRIPTION:Title: A model for soap films based on capillarity theory\nby Fra
ncesco Maggi (UT Austin) as part of One World PDE seminar\n\n\nAbstract\nS
oap films are modeled\, rather than as surfaces with zero mean curvature\,
as regions with small volume satisfying a spanning condition of homotopic
type. We discuss qualitative properties of such soap films\, and their co
nvergence towards minimal surfaces\, when the volume goes to zero. This is
a joint work with Antonello Scardicchio (ICTP)\, Darren King (UT Austin)
and Salvatore Stuvard (UT Austin).\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Merle (Université de Cergy-Pontoise)
DTSTART:20200526T140000Z
DTEND:20200526T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/11
DESCRIPTION:Title: On the implosion of a three dimensional compressible fluid
\nby Frank Merle (Université de Cergy-Pontoise) as part of One World PDE
seminar\n\n\nAbstract\nWe consider the compressible three dimensional Navi
er Stokes and Euler equations. In a suitable regime of barotropic laws\, w
e construct a set of finite energy smooth initial data for which the corre
sponding solutions to both equations implode (with infinite density) at a
later time at a point\, and completely describe the associated formation o
f singularity.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ovidiu Savin (Columbia University)
DTSTART:20200526T150000Z
DTEND:20200526T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/12
DESCRIPTION:Title: Free boundary regularity for the 3 membranes problem\nby O
vidiu Savin (Columbia University) as part of One World PDE seminar\n\n\nAb
stract\nFor a positive integer \\(N\\)\, the \\(N\\)-membranes problem des
cribes the equilibrium position of \\(N\\) ordered elastic membranes subje
ct to forcing and boundary conditions. If the heights of the membranes are
described 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
interacting free boundaries which can cross each other. When \\(N=2\\) the
re is only one free boundary and the problem is equivalent to the classica
l obstacle problem. In my first lecture I will review some of the regulari
ty theory for the standard obstacle problem\, and in my second lecture I w
ill discuss some recent work in collaboration with Hui Yu about the case w
hen \\(N=3\\) and there are two interacting free boundaries.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Gursky (University of Notre Dame)
DTSTART:20200505T150000Z
DTEND:20200505T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/13
DESCRIPTION:Title: Singular solutions to some PDEs arising in conformal geometry<
/a>\nby Matthew Gursky (University of Notre Dame) as part of One World PDE
seminar\n\n\nAbstract\nI will describe some aspects of the k-Yamabe probl
em\, a fully nonlinear version of the Yamabe problem\, emphasizing the neg
ative case. I will begin with a quick overview of the regularity theory in
the ‘positive’ case\, and contrast this with how little is known in t
he negative case. (This is a remarkable difference with the classical Yama
be problem\, 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 wi
th isolated singularities.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria del Mar Gonzalez (Universidad Autónoma de Madrid)
DTSTART:20200407T140000Z
DTEND:20200407T145000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/14
DESCRIPTION:Title: A free boundary problem for the half-Laplacian\, the Steklov e
igenvalue and higher order generalizations\nby Maria del Mar Gonzalez
(Universidad Autónoma de Madrid) as part of One World PDE seminar\n\n\nAb
stract\nA free boundary problem for the half-Laplacian\, the Steklov eigen
value and higher order generalizations\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Antonio Carrillo (University of Oxford)
DTSTART:20200407T150000Z
DTEND:20200407T155000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/15
DESCRIPTION:Title: Nonlinear Aggregation-Diffusion Equations: Stationary States\,
Functional inequalities & Stabilization\nby José Antonio Carrillo (U
niversity of Oxford) as part of One World PDE seminar\n\n\nAbstract\nNonli
near Aggregation-Diffusion Equations: Stationary States\, Functional inequ
alities & Stabilization\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mónica Clapp (Universidad Nacional Autónoma de México)
DTSTART:20200428T150000Z
DTEND:20200428T155000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/16
DESCRIPTION:Title: Sharp Extinction Rates for Fast Diffusion Equations on Generic
Bounded Domains\nby Mónica Clapp (Universidad Nacional Autónoma de
México) as part of One World PDE seminar\n\n\nAbstract\nWe investigate th
e homogeneous Dirichlet problem for the Fast Diffusion Equation \\(u_t=Δ
u^m\\)\, posed in a smooth bounded domain \\(Ω⊂ \\mathbb{R}^N\\)\, in t
he exponent range \\(m_s=(N-2)_+/(N+2)0\\)\, and also that the
y approach 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 suitable elliptic 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 no
rm. Starting from this result\, we investigate the fine asymptotic behavio
ur and prove sharp rates of convergence for the relative error. The proof
is based on an entropy method relying on a (improved) weighted Poincaré i
nequality\, that we show to be true on generic bounded domains. Another es
sential aspect of the method is the new concept of “almost orthogonality
”\, which can be thought as a nonlinear analogous of the classical ortho
gonality condition needed to obtain improved Poincaré inequalities and sh
arp convergence rates for linear flows. This is a joint work with Alessio
Figalli (ETH Zürich\, CH).\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART:20200602T140000Z
DTEND:20200602T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/17
DESCRIPTION:Title: Regularity estimates for the Boltzmann equation without cutoff
\nby Luis Silvestre (University of Chicago) as part of One World PDE s
eminar\n\n\nAbstract\nWe study the regularization effect of the inhomogene
ous Boltzmann equation without cutoff. We obtain a priori estimates for al
l derivatives of the solution depending only on bounds of the hydrodynamic
quantities: mass density\, energy density and entropy density. As a conse
quence\, a classical solution to the equation may fail to exists after cer
tain time \\(T\\) only if at least one of these hydrodynamic quantities bl
ows up. Our analysis applies to the case of moderately soft and hard poten
tials. We use methods that originated in the study of nonlocal elliptic eq
uations: a weak Harnack inequality in the style of De Giorgi\, and a Schau
der-type estimate.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert L. Frank (California Institute of Technology)
DTSTART:20200602T150000Z
DTEND:20200602T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/18
DESCRIPTION:Title: A ‘liquid-solid’ phase transition in a simple model for sw
arming\nby Rupert L. Frank (California Institute of Technology) as par
t of One World PDE seminar\n\n\nAbstract\nWe consider a non-local optimiza
tion problem\, which is motivated by a simple model for swarming and other
self-assembly/aggregation models\, and prove the existence of different p
hases. In particular\, we show that in the large mass regime the ground st
ate density profile is the characteristic function of a round ball. An ess
ential ingredient in our proof is a strict rearrangement inequality with a
quantitative error estimate. We formulate several open problems which mig
ht be amenable to PDE techniques.\n\nThe talk is based on joint work with
E. Lieb.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nader Masmoudi (Courant Institute & NYU Abu-Dhabi)
DTSTART:20200609T140000Z
DTEND:20200609T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/19
DESCRIPTION:Title: Recent advances in nonlinear inviscid damping\nby Nader Ma
smoudi (Courant Institute & NYU Abu-Dhabi) as part of One World PDE semina
r\n\n\nAbstract\nWe will review some recent results dealing with inviscid
damping. These results include the optimality of the Gevrey regularity req
uired to get the damping as well as the generalization to more general mon
otone flows.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julio D. Rossi (Universidad de Buenos Aires)
DTSTART:20200609T150000Z
DTEND:20200609T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/20
DESCRIPTION:Title: Coupling and mixing local and nonlocal equations\nby Julio
D. Rossi (Universidad de Buenos Aires) as part of One World PDE seminar\n
\n\nAbstract\nIn this talk we present a simple way of coupling a local and
a nonlocal evolution equation in such a way that the usual properties (li
ke existence 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 on joint works with A. Garriz (Madrid) and F. Quiros (Madrid) and wi
th M. Capanna (L’Aquila))\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Niethammer (Universität Bonn)
DTSTART:20200616T140000Z
DTEND:20200616T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/21
DESCRIPTION:Title: Oscillatory and peak solutions in coagulation-fragmentation eq
uations a\nby Barbara Niethammer (Universität Bonn) as part of One W
orld PDE seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fanghua Lin (Courant Institute)
DTSTART:20200616T150000Z
DTEND:20200616T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/22
DESCRIPTION:Title: Several questions related to homogenization\nby Fanghua Li
n (Courant Institute) as part of One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sun-Yung Alice Chang (Princeton University)
DTSTART:20200623T140000Z
DTEND:20200623T150000Z
DTSTAMP:20260404T110825Z
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 s
eminar\n\n\nAbstract\nA classical result of Aubin states that the constant
in Moser–Trudinger–Onofri inequality on the 2-sphere \\(S^2\\) can be
improved for functions with zero first order moments of the area element.
In a joint work with Fengbo Hang\, we generalize Aubin’s inequality to
higher order moments case. These new inequalities bear similarity to a seq
uence of Lebedev–Milin type inequalities on the unit circle \\(S^1\\) co
ming from the work of Grenander–Szego on Toeplitz determinants (as point
ed out by Widom). I will also report some joint work with Changfeng Gui st
ill 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://stable.researchseminars.org/talk/OneWorldPDE/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joaquim Serra (ETH Zurich)
DTSTART:20200623T150000Z
DTEND:20200623T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/24
DESCRIPTION:Title: The singular set in the Stephan problem\nby Joaquim Serra
(ETH Zurich) as part of One World PDE seminar\n\n\nAbstract\nThe classical
Stephan problem\, first introduced in 1831 by Lamé and Clapeyron\, aims
to describe the evolution of the temperature in a block of ice (initially
at zero degrees centigrade) that is melting to water. The Baiochi-Duvait t
ransformation reduces it to the parabolic obstacle problem\, easier to tre
at in many aspects. It is known since the celebrated work of Caffarelli th
at the interface between ice and water (the so-called free boundary) is sm
ooth outside of a closed set of the spacetime\, which is called the singul
ar set.\n\nIn the talk\, I will introduce a forthcoming joint work with A.
Figalli and X. Ros-Oton on the size and regularity of this singular set.\
n\nIn three spatial dimensions we prove that the singular set splits into
two pieces. The first is a set of parabolic dimension 1 (hence it is small
). The second piece satisfies that its spatial projection can be covered b
y countable unions of \\(C^\\infty\\) surfaces and its projection onto the
time axis has dimension zero!\n\nIn particular\, we show that the free bo
undary 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://stable.researchseminars.org/talk/OneWorldPDE/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanyan Li (Rutgers University)
DTSTART:20200630T140000Z
DTEND:20200630T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/25
DESCRIPTION:Title: Some recent works on conformally invariant fully nonlinear ell
iptic equations\nby Yanyan Li (Rutgers University) as part of One Worl
d PDE seminar\n\n\nAbstract\nThe following problem was raised by Nirenberg
: Which function on the standard 2-sphere is the Gauss curvature of a metr
ic conformally 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 conform
ally equivalent to the standard metric.\n\nAn analogous question can be as
ked for the \\(\\sigma_k\\) curvature instead of the scalar curvature\, an
d we call it the \\(\\sigma_k\\)-Nirenberg problem. We will present some r
esults on the existence and compactness of solutions of the \\(\\sigma_k\\
)-Nirenberg problem for \\(n≥ 3\\) and \\(k≥ n/2\\). The results for \
\(n=4\\) and \\(k=2\\) were established by Alice Chang\, Zheng-Chao Han an
d Paul Yang in 2011. We will also present some recent results on the \\(σ
_k\\)-Loewner–Nirenberg problem. These results are from a couple of join
t works with Maria del Mar Gonzalez\, Luc Nguyen\, Bo Wang\, and Jingang X
iong.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gustav Holzegel (Imperial College London)
DTSTART:20200630T150000Z
DTEND:20200630T160000Z
DTSTAMP:20260404T110825Z
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 Wor
ld PDE seminar\n\n\nAbstract\nI will discuss recent work with M. Dafermos\
, I. Rodnianski and M. Taylor proving the full finite codimension asymptot
ic stability of the Schwarzschild family of black holes in the exterior of
the black hole region. The proof is expressed entirely in physical space
and based on our previous understanding of linear stability of the Schwarz
schild family in a double null gauge.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Dolbeault (CEREMADE\, Université Paris-Dauphine)
DTSTART:20200707T140000Z
DTEND:20200707T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/27
DESCRIPTION:Title: Stability in Gagliardo-Nirenberg inequalities\nby Jean Dol
beault (CEREMADE\, Université Paris-Dauphine) as part of One World PDE se
minar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:André Neves (University of Chicago)
DTSTART:20200707T150000Z
DTEND:20200707T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/28
DESCRIPTION:Title: Counting minimal surfaces in negatively curved 3-manifolds
\nby André Neves (University of Chicago) as part of One World PDE seminar
\n\n\nAbstract\nI will survey some of the recent progress regarding existe
nce of minimal hypersurfaces and then I will talk about my joint work with
Calegari and Marques where we asymptotically count minimal surfaces in ne
gatively curved manifolds.\n
LOCATION:https://stable.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:20260404T110825Z
UID:OneWorldPDE/29
DESCRIPTION:Title: Analysis of incompressible flows with helical symmetry\nby
Helena J. Nussenzveig Lopes (Universidade Federal do Rio de Janeiro) as p
art 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 axisymmetri
c flows have a broad associated literature\, helically symmetric flows hav
e attracted less mathematical attention.\n\nHelically symmetric flows are
those invariant under simultaneous rotation and translation with respect t
o a fixed axis. These flows arise in real world applications such as the f
low generated by a rotating blade. From the point of view of mathematical
analysis\, flows with helical symmetry lie between 2D flows and axisymmetr
ic flows. The purpose of the talk is to illustrate this observation\, disc
ussing both existence theorems and vanishing viscosity results for helical
ly symmetric fluid flow\, and establishing comparisons with 2D and axisymm
etric cases.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gigliola Staffilani (MIT)
DTSTART:20200714T150000Z
DTEND:20200714T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/30
DESCRIPTION:Title: The Schrodinger equations as inspiration of beautiful mathemat
ics\nby Gigliola Staffilani (MIT) as part of One World PDE seminar\n\n
\nAbstract\nIn the last two decades great progress has been made in the st
udy of dispersive and wave equations. Over the years the toolbox used in o
rder to attack highly nontrivial problems related to these equations has d
eveloped to include a collection of techniques: Fourier and harmonic analy
sis\, analytic number theory\, math physics\, dynamical systems\, probabil
ity and symplectic geometry. In this talk I will introduce a variety of re
sults using as model problem the periodic 2D cubic nonlinear Schrodinger e
quation. I will start by giving a physical derivation of the equation from
a quantum many-particles system\, I will introduce periodic Strichartz es
timates along with some remarkable connections to analytic number theory\,
I will move on the concept of energy transfer and its connection to dynam
ical systems\, and I will end with some results\, such as the non-squeezin
g theorem\, that one can obtain once the equation is viewed in the frequen
cy space as an infinite dimension Hamiltonian system.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Kenig (University of Chicago)
DTSTART:20200901T140000Z
DTEND:20200901T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/31
DESCRIPTION:Title: Asymptotic simplification for solutions of the energy critical
nonlinear wave equation\nby Carlos Kenig (University of Chicago) as p
art of One World PDE seminar\n\n\nAbstract\nIn this lecture I will describ
e the progress made in the last 12 years\, in our understanding of the lon
g-time behavior of large solutions to the energy critical focusing nonline
ar wave equation. In the last part of the talk I will concentrate on recen
t progress (with Duyckaerts and Merle) on the asymptotic simplification fo
r large time\, into sums of modulated static solutions plus a linear term\
, in all odd dimensions\, in the radial case.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Ionescu (Princeton University)
DTSTART:20200901T150000Z
DTEND:20200901T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/32
DESCRIPTION:Title: On the nonlinear stability of shear flows and vortices\nby
Alexandru Ionescu (Princeton University) as part of One World PDE seminar
\n\n\nAbstract\nI will discuss some recent work (in collaboration with Hao
Jia) on the global asymptotic stability of shear flows and vortices among
solutions of the 2D Euler equations. More precisely\, we prove (1) global
asymptotic stability in a finite channel of general smooth monotonic shea
r flows that satisfy a suitable spectral condition\, and (2) global asympt
otic stability of point vortices in the plane.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Bressan (Pennsylvania State University)
DTSTART:20200908T140000Z
DTEND:20200908T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/33
DESCRIPTION:by Alberto Bressan (Pennsylvania State University) as part of
One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene M. Gamba (University of Texas at Austin)
DTSTART:20200908T150000Z
DTEND:20200908T160000Z
DTSTAMP:20260404T110825Z
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://stable.researchseminars.org/talk/OneWorldPDE/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Ball (Heriot-Watt University\, Edinburgh)
DTSTART:20200915T140000Z
DTEND:20200915T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/35
DESCRIPTION:Title: Axisymmetry of critical points of the Onsager functional for l
iquid crystals\nby John Ball (Heriot-Watt University\, Edinburgh) as p
art of One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gui-Qiang G. Chen (University of Oxford)
DTSTART:20200915T150000Z
DTEND:20200915T160000Z
DTSTAMP:20260404T110825Z
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://stable.researchseminars.org/talk/OneWorldPDE/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (Institute for Advanced Study)
DTSTART:20200922T140000Z
DTEND:20200922T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/37
DESCRIPTION:Title: Flows of vector fields: classical and modern\nby Camillo D
e Lellis (Institute for Advanced Study) as part of One World PDE seminar\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hatem Zaag (Université Sorbonne Paris Nord)
DTSTART:20200922T150000Z
DTEND:20200922T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/38
DESCRIPTION:Title: A stylized pyramid-shaped blow-up set for the 2d semilinear wa
ve equation\nby Hatem Zaag (Université Sorbonne Paris Nord) as part o
f One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Strauss (Brown University)
DTSTART:20200929T140000Z
DTEND:20200929T150000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/39
DESCRIPTION:by Walter Strauss (Brown University) as part of One World PDE
seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland)
DTSTART:20200929T150000Z
DTEND:20200929T160000Z
DTSTAMP:20260404T110825Z
UID:OneWorldPDE/40
DESCRIPTION:Title: Quantitative hypoelliptic regularity and the estimation of Lya
punov exponents and other long-time dynamical properties of stochastic dif
ferential equations\nby Jacob Bedrossian (University of Maryland) as p
art of One World PDE seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldPDE/40/
END:VEVENT
END:VCALENDAR