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BEGIN:VEVENT
SUMMARY:William Beckner (University of Texas at Austin)
DTSTART;VALUE=DATE-TIME:20200720T130000Z
DTEND;VALUE=DATE-TIME:20200720T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/1
DESCRIPTION:Title: Symmetry in Fourier Analysis – Heisenberg to Stein-Weiss\nb
y William Beckner (University of Texas at Austin) as part of Geometric and
functional inequalities and applications\n\n\nAbstract\nEmbedded symmetry
within the Heisenberg group is used to couple geometric insight and analy
tic calculation to obtain a new sharp Stein-Weiss inequality with mixed ho
mogeneity on the line of duality. SL(2\,R) invariance and Riesz potentials
define a natural bridge for encoded information that connects distinct ge
ometric structures. Insight for Stein-Weiss integrals is gained from vorte
x dynamics\, embedding on hyperbolic space\, and conformal geometry. The i
ntrinsic character of the Heisenberg group makes it the natural playing fi
eld on which to explore the laws of symmetry and the interplay between ana
lysis and geometry on a manifold.\n\nZoom link: https://brown.zoom.us/j/91
683612862\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Malchiodi (Scuola Normale Superiore)
DTSTART;VALUE=DATE-TIME:20200720T140000Z
DTEND;VALUE=DATE-TIME:20200720T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/2
DESCRIPTION:Title: On the Sobolev quotient in sub-Riemannian geometry\nby Andrea
Malchiodi (Scuola Normale Superiore) as part of Geometric and functional
inequalities and applications\n\n\nAbstract\nWe consider three-dimensional
CR manifolds\, which are modelled on the Heisenberg group.\nWe introduce
a natural concept of “mass” and prove its positivity under the conditi
on that\nthe scalar curvature is positive and in relation to their (holomo
rphic) embeddability properties.\nWe apply this result to the CR Yamabe pr
oblem\, and we discuss extremality of Sobolev-type\nquotients\, giving som
e counterexamples for “Rossi spheres”.\nThis is joint work with J.H.Ch
eng and P.Yang.\n\nZoom link: https://brown.zoom.us/j/91683612862\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Cabre (ICREA and UPC (Barcelona))
DTSTART;VALUE=DATE-TIME:20200727T130000Z
DTEND;VALUE=DATE-TIME:20200727T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/3
DESCRIPTION:Title: Stable solutions to semilinear elliptic equations are smooth up t
o dimension 9\nby Xavier Cabre (ICREA and UPC (Barcelona)) as part of
Geometric and functional inequalities and applications\n\n\nAbstract\nThe
regularity of stable solutions to semilinear elliptic PDEs has been studie
d since the 1970's. In dimensions 10 and higher\, there exist singular sta
ble energy solutions. In this talk I will describe a recent work in collab
oration with Figalli\, Ros-Oton\, and Serra\, where we prove that stable s
olutions are smooth up to the optimal dimension 9. This answers to an open
problem posed by Brezis in the mid-nineties concerning the regularity of
extremal solutions to Gelfand-type problems.\n\nZoom link: https://brown.z
oom.us/j/91683612862\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jerison (MIT)
DTSTART;VALUE=DATE-TIME:20201109T140000Z
DTEND;VALUE=DATE-TIME:20201109T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/4
DESCRIPTION:Title: Rescheduled to Spring Semester 2021\nby David Jerison (MIT) a
s part of Geometric and functional inequalities and applications\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiming Zhao (MIT)
DTSTART;VALUE=DATE-TIME:20200803T130000Z
DTEND;VALUE=DATE-TIME:20200803T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/5
DESCRIPTION:Title: Reconstruction of convex bodies via Gauss map\nby Yiming Zhao
(MIT) as part of Geometric and functional inequalities and applications\n
\n\nAbstract\nIn this talk\, we will discuss the Gauss image problem\, a p
roblem that reconstructs the shape of a convex body using partial data reg
arding its Gauss map. In the smooth category\, this problem reduces to a M
onge-Ampere type equation on the sphere. But\, we will use a variational a
rgument that works with generic convex bodies. This is joint work with Ká
roly Böröczky\, Erwin Lutwak\, Deane Yang\, and Gaoyong Zhang.\n\nZoom l
ink: https://brown.zoom.us/j/91683612862\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20200817T140000Z
DTEND;VALUE=DATE-TIME:20200817T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/6
DESCRIPTION:Title: Rigidity Results for Allen-Cahn Equation\nby Juncheng Wei (Un
iversity of British Columbia) as part of Geometric and functional inequali
ties and applications\n\n\nAbstract\nI will discuss two recent rigidity re
sults for Allen-Cahn: the first is Half Space Theorem which states that if
the nodal set lies above a half space then it must be one-dimensional. Th
e second result is the stability of Cabre-Terra saddle solutions in R^8\,
R^{10} and R^{12}.\n\nZoom link: https://brown.zoom.us/j/91683612862\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fengbo Hang (New York University)
DTSTART;VALUE=DATE-TIME:20200810T140000Z
DTEND;VALUE=DATE-TIME:20200810T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/7
DESCRIPTION:Title: Concentration compactness principle in critical dimensions revisi
ted\nby Fengbo Hang (New York University) as part of Geometric and fun
ctional inequalities and applications\n\n\nAbstract\nConcentration compact
ness principle for functions in $W^{1\,n}_0$ on a\nn-dimensional domain wa
s introduced by Lions in 1985 with the\nMoser-Trudinger inequality in mind
. We will discuss some further\nrefinements after Cerny-Cianchi-Hencl's im
provement in 2013. These\nrefinements unifiy the approach for n=2 and n>2
cases and work for higher\norder or fractional order Sobolev spaces as wel
l. They are motivated by\nand closely related to the recent derivation of
Aubin's Moser-Trudinger\ninequality for functions with vanishing higher or
der moments on the\nstandard 2-sphere (one may see\nhttp://math.sjtu.edu.c
n/conference/2020p&g/videos/20200707_FengboHang_M1.html\nfor that part).\n
\nZoom link: https://brown.zoom.us/j/91683612862\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert Frank (CalTech)
DTSTART;VALUE=DATE-TIME:20200824T143000Z
DTEND;VALUE=DATE-TIME:20200824T153000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/8
DESCRIPTION:Title: REVERSE HARDY–LITTLEWOOD–SOBOLEV INEQUALITIES\nby Rupert
Frank (CalTech) as part of Geometric and functional inequalities and appli
cations\n\n\nAbstract\nWe are interested in a new family of reverse Hardy
–Littlewood–Sobolev inequalities which involve a power law kernel with
positive exponent and a Lebesgue exponent <1. We characterize the range o
f parameters for which the inequality holds and present results about the
existence of optimizers. A striking open question is the possibility of co
ncentration of a minimizing sequence.\n\nThis talk is based on joint work
with J. Carrillo\, M. Delgadino\, J. Dolbeault and F. Hoffmann.\n\nPlease
note the special time of this talk. \nFor Zoom link for each talk (future
links will not be posted here)\, please send an email to the organizers at
geometricinequalitiesandpdes@gmail.com\nZoom link: https://brown.zoom.us/
j/94525179475\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pengfei Guan (McGill University)
DTSTART;VALUE=DATE-TIME:20200831T140000Z
DTEND;VALUE=DATE-TIME:20200831T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/9
DESCRIPTION:Title: A mean curvature type flow and isoperimetric problem in warped pr
oduct spaces\nby Pengfei Guan (McGill University) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nWe will discu
ss a mean curvature type flow with the goal to solve isoperimetric problem
. The flow is induced from the variational properties associated to confor
mal Killing fields. Such flow was first introduced in space forms in a pre
vious joint work with Junfang Li\, where we provided a flow approach to th
e classical isoperimetric inequality in space form. Later\, jointly with J
unfang Li and Mu-Tao Wang\, we considered the similar flow in warped produ
ct spaces with general base. Under some natural conditions\, the flow pres
erves the volume of the bounded domain enclosed by a graphical hypersurfac
e\, and monotonically decreases the hypersurface area. Furthermore\, the r
egularity and convergence of the flow can be established\, thereby the iso
perimetric problem in warped product spaces can be solved. The flow serves
as an interesting way to achieve the optimal solution to the isoperimetri
c problem.\n\nZoom link: https://brown.zoom.us/j/99054390401\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Hebey (Université de Cergy-Pontoise)
DTSTART;VALUE=DATE-TIME:20201116T140000Z
DTEND;VALUE=DATE-TIME:20201116T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/10
DESCRIPTION:Title: Schrödinger-Proca constructions in the closed setting\nby E
mmanuel Hebey (Université de Cergy-Pontoise) as part of Geometric and fun
ctional inequalities and applications\n\n\nAbstract\nWe discuss Schröding
er-Proca constructions in the context of closed manifolds leading \nto the
Bopp-Podolsky-Schrödinger-Proca and the Schrödinger-Poisson-Proca syste
ms.\nThe goal is to present an introduction to these equations (how we bui
ld them\, what do \nthey represent) and then to present the result we got
on these systems about the \nconvergence of (BPSP) to (SPP) as the Bopp-Po
dolsky parameter goes to zero.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Wang (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20200907T130000Z
DTEND;VALUE=DATE-TIME:20200907T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/11
DESCRIPTION:Title: Rigidity of local minimizers of the $\\sigma_k$ functional\n
by Yi Wang (Johns Hopkins University) as part of Geometric and functional
inequalities and applications\n\n\nAbstract\nIn this talk\, I will present
a result on the rigidity of local minimizers of the functional $\\int \\s
igma_2+ \\oint H_2$ among all conformally flat metrics in the Euclidean (n
+ 1)-ball. We prove the metric is flat up to a conformal transformation i
n some (noncritical) dimensions. We also prove the analogous result in the
critical dimension n + 1 = 4. The main method is Frank-Lieb’s rearrange
ment-free argument. If minimizers exist\, this implies a fully nonlinear s
harp Sobolev trace inequality. I will also discuss a nonsharp Sobolev trac
e inequality. This is joint work with Jeffrey Case.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongmeng Xi (NYU)
DTSTART;VALUE=DATE-TIME:20200803T140000Z
DTEND;VALUE=DATE-TIME:20200803T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/12
DESCRIPTION:Title: An isoperimetric type inequality via a modified Steiner symmetri
zation scheme\nby Dongmeng Xi (NYU) as part of Geometric and functiona
l inequalities and applications\n\n\nAbstract\nWe establish an affine isop
erimetric inequality using a symmetrization scheme that involves a total o
f 2n elaborately chosen Steiner symmetrizations at a time. The necessity o
f this scheme\, as opposed to the usual Steiner symmetrization\, will be d
emonstrated with an example. This is a joint work with Dr. Yiming Zhao.\n\
nZoom link: https://brown.zoom.us/j/91683612862\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phan Thành Nam (LMU Munich)
DTSTART;VALUE=DATE-TIME:20200921T130000Z
DTEND;VALUE=DATE-TIME:20200921T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/13
DESCRIPTION:Title: Lieb-Thirring inequality with optimal constant and gradient erro
r term\nby Phan Thành Nam (LMU Munich) as part of Geometric and funct
ional inequalities and applications\n\n\nAbstract\nIn 1975\, Lieb and Thir
ring conjectured that the kinetic energy of fermions is not smaller than i
ts Thomas-Fermi (semiclassical) approximation\, at least in three or highe
r dimensions. I will discuss a rigorous lower bound with the sharp semicla
ssical constant and a gradient error term which is normally of lower order
in applications. The proof is based on a microlocal analysis and a vari
ant of the Berezin-Li-Yau inequality. This approach can be extended to der
ive an improved Lieb-Thirring inequality for interacting systems\, where t
he Gagliardo-Nirenberg constant appears in the strong coupling limit.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Minicozzi (MIT)
DTSTART;VALUE=DATE-TIME:20201026T140000Z
DTEND;VALUE=DATE-TIME:20201026T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/14
DESCRIPTION:Title: Mean curvature flow in high codimension\nby William Minicozz
i (MIT) as part of Geometric and functional inequalities and applications\
n\n\nAbstract\nMean curvature flow (MCF) is a geometric heat equation wher
e a\nsubmanifold evolves to minimize its area. A central problem is to\nu
nderstand the singularities that form and what these imply for the\nflow.
I will talk about joint work with Toby Colding on higher\ncodimension MCF
\, where the flow becomes a complicated system of\nequations and much less
is known.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Saloff-Coste (Cornell University)
DTSTART;VALUE=DATE-TIME:20201005T140000Z
DTEND;VALUE=DATE-TIME:20201005T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/15
DESCRIPTION:Title: Heat kernel on manifolds with finitely many ends\nby Laurent
Saloff-Coste (Cornell University) as part of Geometric and functional ine
qualities and applications\n\n\nAbstract\nFor over twenty years A. Grigor'
yan and the speaker have studied heat kernel estimates on manifolds with a
finite number of nice ends.\nDespite these efforts\, question remains. In
this talk\, after giving an overview of what the problem is and what we k
now\, the main difficulty will be explained and recent progresses involvin
g joint work with Grigor'yan and Ishiwata will be explained. They provide
results concerning Poincaré inequality in large central balls on such man
ifold.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Dolbeault (Université Paris-Dauphine)
DTSTART;VALUE=DATE-TIME:20200914T130000Z
DTEND;VALUE=DATE-TIME:20200914T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/16
DESCRIPTION:Title: Stability in Gagliardo-Nirenberg inequalities\nby Jean Dolbe
ault (Université Paris-Dauphine) as part of Geometric and functional ineq
ualities and applications\n\n\nAbstract\nOptimal constants and optimal fun
ctions are known in some functional inequalities. The next question is the
stability issue: is the difference of the two terms controlling a distanc
e to the set of optimal functions ? A famous example is provided by Sobole
v's inequalities: in 1991\, G. Bianchi and H. Egnell proved that the diffe
rence of the two terms is bounded from below by a distance to the manifold
of the Aubin-Talenti functions. They argued by contradiction and gave a v
ery elegant although not constructive proof. Since then\, estimating the s
tability constant and giving a constructive proof has been a challenge. \n
\nThis lecture will focus mostly on subcritical inequalities\, for which e
xplicit constants can be provided. The main tool is based on entropy metho
ds and nonlinear flows. Proving stability amounts to establish\, under som
e constraints\, a version of the entropy - entropy production inequality w
ith an improved constant. In simple cases\, for instance on the sphere\, r
ather explicit results have been obtained by the « carré du champ » met
hod introduced by D. Bakry and M. Emery. In the Euclidean space\, results
based on constructive regularity estimates for the solutions of the nonlin
ear flow and corresponding to a joint research project with Matteo Bonfort
e\, Bruno Nazaret\, and Nikita Simonov will be presented.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jungang Li (Brown University)
DTSTART;VALUE=DATE-TIME:20200928T130000Z
DTEND;VALUE=DATE-TIME:20200928T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/17
DESCRIPTION:Title: Higher order Brezis-Nirenberg problems on hyperbolic spaces\
nby Jungang Li (Brown University) as part of Geometric and functional ineq
ualities and applications\n\n\nAbstract\nThe Brezis-Nirenberg problem cons
iders elliptic equations whose nonlinearity is associated with critical So
bolev exponents. In this talk we will discuss a recent progress on higher
order Brezis-Nirenberg problem on hyperbolic spaces. The existence of solu
tions relates closely to the study of higher order sharp Hardy-Sobolev-Maz
'ya inequalities\, which is due to G. Lu and Q. Yang. On the other hand\,
we obtain a nonexistence result on star-shaped domains. In addition\, with
the help of Green's function estimates\, we apply moving plane method to
establish the symmetry of positive solutions. This is a joint work with Gu
ozhen Lu and Qiaohua Yang.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Flynn (University of Connecticut)
DTSTART;VALUE=DATE-TIME:20201102T150000Z
DTEND;VALUE=DATE-TIME:20201102T160000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/18
DESCRIPTION:Title: Sharp Caffarelli-Kohn-Nirenberg Inequalities for Grushin Vector
Fields and Iwasawa Groups.\nby Joshua Flynn (University of Connecticut
) as part of Geometric and functional inequalities and applications\n\n\nA
bstract\nSharp Caffarelli-Kohn-Nirenberg inequalities are established for
the Grushin vector fields and for Iwasawa groups (i.e.\, the boundary grou
p of a real rank one noncompact symmetric space). For all but one paramete
r case\, this is done by introducing a generalized Kelvin transform which
is shown to be an isometry of certain weighted Sobolev spaces. For the exc
eptional parameter case\, the best constant is found for the Grushin vecto
r fields by introducing Grushin cylindrical coordinates and studying the t
ransformed Euler-Lagrange equation.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Cazacu (University of Bucharest)
DTSTART;VALUE=DATE-TIME:20201012T130000Z
DTEND;VALUE=DATE-TIME:20201012T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/19
DESCRIPTION:Title: Optimal constants in Hardy and Hardy-Rellich type inequalities<
/a>\nby Cristian Cazacu (University of Bucharest) as part of Geometric and
functional inequalities and applications\n\n\nAbstract\nIn this talk we d
iscuss Hardy and Hardy-Rellich type inequalities\, so important in establi
shing useful properties for differential operators with singular potential
s and their PDEs. We recall some well-known and recent results and present
some new extensions. We analyze singular potentials with one or various s
ingularities. The tools of our proofs are mainly based on the method of su
persolutions\, proper transformations and spherical harmonics decompositio
n. We also focus on the best constants and the existence/nonexistence of m
inimizers in the energy space. This presentation is partially supported b
y CNCS-UEFISCDI Grant No. PN-III-P1-1.1-TE-2016-2233.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiuyi Zhu (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20201019T140000Z
DTEND;VALUE=DATE-TIME:20201019T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/20
DESCRIPTION:Title: The bounds of nodal sets of eigenfunctions\nby Jiuyi Zhu (Lo
uisiana State University) as part of Geometric and functional inequalities
and applications\n\n\nAbstract\nMotivated by Yau's conjecture\, the study
of the measure of nodal sets (Zero level sets) for eigenfunctions is inte
resting. We investigate the measure of nodal sets for Steklov\, Dirichlet
and Neumann eigenfunctions in the domain and on the boundary of the domai
n. For Dirichlet or Neumann eigenfunctions in the analytic domains\, we s
how some sharp upper bounds of nodal sets which touch the boundary. We w
ill also discuss some upper bounds of nodal sets for eigenfunctions of ge
neral eigenvalue problems. Furthermore\, some sharp doubling inequalities
and vanishing order are obtained. Part of the talk is based on joint wor
k with Fanghua Lin.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Almut Burchard (University of Toronto)
DTSTART;VALUE=DATE-TIME:20201214T140000Z
DTEND;VALUE=DATE-TIME:20201214T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/21
DESCRIPTION:Title: Rearrangement inequalities on spaces of bounded mean oscillation
\nby Almut Burchard (University of Toronto) as part of Geometric and f
unctional inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanna Citti (University of Bologna)
DTSTART;VALUE=DATE-TIME:20201207T140000Z
DTEND;VALUE=DATE-TIME:20201207T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/22
DESCRIPTION:Title: Degree preserving variational formulas for submanifolds\nby
Giovanna Citti (University of Bologna) as part of Geometric and functional
inequalities and applications\n\n\nAbstract\nI present a joint work with
M. Ritoré and G. Giovannardi related to an area functional for \nsubmanif
olds of fixed degree immersed in a graded manifold. The expression of this
area functional \nstrictly depends on the degree of the manifold\, so tha
t\, while computing the first variation\, \nwe need to keep fixed its degr
ee. We will show that there are isolated surfaces\, \nfor which this type
of degree preserving variations do not exist: they can be considered \nhi
gher dimensional extension of the subriemannian abnormal geodesics.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annalisa Baldi (University of Bologna)
DTSTART;VALUE=DATE-TIME:20201130T140000Z
DTEND;VALUE=DATE-TIME:20201130T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/23
DESCRIPTION:Title: Poincaré and Sobolev inequalities for differential forms in Euc
lidean spaces and Heisenberg groups\nby Annalisa Baldi (University of
Bologna) as part of Geometric and functional inequalities and applications
\n\n\nAbstract\nIn this talk I present some recent results obtained in col
laboration with B. Franchi and P. Pansu about Poincaré and Sobolev inequa
lities for differential forms in Heisenberg groups (some results are new a
lso for Euclidean spaces). For L^p\, p>1\, the estimates are consequence o
f singular integral estimates. In the limiting case L^1\, the singular i
ntegral estimates are replaced with inequalities which go back to Bourgain
-Brezis and Lanzani-Stein in Euclidean spaces\, and to Chanillo-Van Schaft
ingen and Baldi-Franchi-Pansu in Heisenberg groups. Also the case p=Q (Q i
s the homogeneous dimension of the Heisenberg group ) is considered.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20201214T150000Z
DTEND;VALUE=DATE-TIME:20201214T160000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/24
DESCRIPTION:Title: Fourier restriction to degenerate hypersurfaces\nby Betsy St
ovall (University of Wisconsin-Madison) as part of Geometric and functiona
l inequalities and applications\n\n\nAbstract\nIn this talk\, we will desc
ribe various open questions and recent progress on the Fourier restriction
problem associated to hypersurfaces with varying or vanishing curvature.\
n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Gursky (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20210118T140000Z
DTEND;VALUE=DATE-TIME:20210118T160000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/25
DESCRIPTION:Title: Extremal Eigenvalues of the conformal laplacian\nby Matthew
Gursky (University of Notre Dame) as part of Geometric and functional ineq
ualities and applications\n\n\nAbstract\nI will report on joint work with
Samuel Perez-Ayala in which we consider the problem of extremizing eigenva
lues of the conformal laplacian in a fixed conformal class. This generali
zes the problem of extremizing the eigenvalues of the laplacian on a compa
ct surface. I will explain the connection of this problem to the existenc
e of harmonic maps\, and to nodal solutions of the Yamabe problem (first n
oticed by Ammann-Humbert).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhen-Qing Chen (University of Washington)
DTSTART;VALUE=DATE-TIME:20210125T150000Z
DTEND;VALUE=DATE-TIME:20210125T160000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/26
DESCRIPTION:Title: Stability of Elliptic Harnack Inequality\nby Zhen-Qing Chen
(University of Washington) as part of Geometric and functional inequalitie
s and applications\n\n\nAbstract\nHarnack inequality\, if it holds\, is a
useful tool in analysis and probability theory.\nIn this talk\, I will dis
cuss scale invariant elliptic Harnack inequality for general diffusions\,
or equivalently\, for general differential operators on metric measure spa
ces\, and show that it is stable under form-comparable perturbations for s
trongly local Dirichlet forms on complete locally compact separable metri
c spaces that satisfy metric doubling property. \nBased on Joint work with
Martin Barlow and Mathav Murugan.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Carron (University of Nantes)
DTSTART;VALUE=DATE-TIME:20210111T140000Z
DTEND;VALUE=DATE-TIME:20210111T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/27
DESCRIPTION:Title: Euclidean heat kernel rigidity\nby Gilles Carron (University
of Nantes) as part of Geometric and functional inequalities and applicati
ons\n\n\nAbstract\nThis is joint work with David Tewodrose (Bruxelles). I
will explain that a metric measure space with Euclidean heat kernel are E
uclidean. An almost rigidity result comes then for free\, and this can be
used to give another proof of Colding's almost rigidity for complete mani
fold with non negative Ricci curvature and almost Euclidean growth.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yehuda Pinchover (Technion -Israel Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210215T140000Z
DTEND;VALUE=DATE-TIME:20210215T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/28
DESCRIPTION:Title: On families of optimal Hardy-weights for linear second-order ell
iptic operators.\nby Yehuda Pinchover (Technion -Israel Institute of T
echnology) as part of Geometric and functional inequalities and applicatio
ns\n\n\nAbstract\nWe construct families of optimal Hardy-weights for a sub
critical linear second-order elliptic operator using a one-dimensional red
uction. More precisely\, we first characterize all optimal Hardy-weights
with respect to one-dimensional subcritical Sturm-Liouville operators on $
(a\,b)$\, $\\infty \\leq a < b \\leq \\infty$\, and then apply this re
sult to obtain families of optimal Hardy inequalities for general linear s
econd-order elliptic operators in higher dimensions. This is a joint work
with Idan Versano.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ling Xiao (University of Connecticut)
DTSTART;VALUE=DATE-TIME:20201109T140000Z
DTEND;VALUE=DATE-TIME:20201109T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/29
DESCRIPTION:Title: Entire spacelike constant $\\sigma_{n-1}$ curvature in Minkowski
space\nby Ling Xiao (University of Connecticut) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nWe prove that\
, in the Minkowski space\, if a spacelike\, (n − 1)-convex hypersurface
M with constant $\\sigma_{n−1}$ curvature has bounded principal curvatur
es\, then M is convex. Moreover\, if M is not strictly convex\, after an R
^{n\,1} rigid motion\, M splits as a product $M^{n−1}\\times R.$ We also
construct nontrivial examples of strictly convex\, spacelike hypersurface
M with constant $\\sigma_{n−1}$ curvature and bounded principal curvatu
res. This is a joint work with Changyu Ren and Zhizhang Wang.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Dindos (The University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210208T140000Z
DTEND;VALUE=DATE-TIME:20210208T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/30
DESCRIPTION:Title: On p-ellipticity and connections to solvability of elliptic comp
lex valued PDEs\nby Martin Dindos (The University of Edinburgh) as par
t of Geometric and functional inequalities and applications\n\n\nAbstract\
nThe notion of an elliptic partial differential equation (PDE)\ngoes back
at least to 1908\, when it appeared in a paper J. Hadamard. In\nthis talk
we present a recently discovered structural condition\, called\n$p$-ellip
ticity\, which generalizes classical ellipticity. It was\nco-discovered i
ndependently by Carbonaro and Dragicevic on one hand\, and\nPipher and mys
elf on the other\, and plays a fundamental role in many\nseemingly mutuall
y unrelated aspects of the $L^p$ theory of elliptic\ncomplex-valued PDE.
So far\, $p$-ellipticity has proven to be the key\ncondition for:\n\n(i) c
onvexity of power functions (Bellman functions)\n(ii) dimension-free bilin
ear embeddings\,\n(iii) $L^p$-contractivity and boundedness of semigroups
$(P_t^A)_{t>0}$\nassociated with elliptic operators\,\n(iv) holomorphic fu
nctional calculus\,\n(v) multilinear analysis\,\n(vi) regularity theory of
elliptic PDE with complex coefficients.\n\nDuring the talk\, I will descr
ibe my contribution to this development\, in\nparticular to (vi).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saikat Mazumdar (Indian Institute of Technology Bombay)
DTSTART;VALUE=DATE-TIME:20210222T140000Z
DTEND;VALUE=DATE-TIME:20210222T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/31
DESCRIPTION:Title: EXISTENCE RESULTS FOR THE HIGHER-ORDER $Q$-CURVATURE EQUATION\nby Saikat Mazumdar (Indian Institute of Technology Bombay) as part of
Geometric and functional inequalities and applications\n\n\nAbstract\nIn t
his talk\, we will obtain some existence results for the $Q$-curvature equ
ation\nof arbitrary $2k$-th order\, where $k \\geq 1$ is an integer\, on a
compact Riemannian\nmanifold of dimension $n \\geq 2k + 1$. This amounts
to solving a nonlinear elliptic\nPDE involving the powers of Laplacian cal
led the GJMS operator. The difficulty\nin determining the explicit form of
this GJMS operator together with a lack of\nmaximum principle complicates
the issues of existence.\nThis is a joint work with Jérôme Vétois (McG
ill University).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Del Pino (University of Bath)
DTSTART;VALUE=DATE-TIME:20210301T140000Z
DTEND;VALUE=DATE-TIME:20210301T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/33
DESCRIPTION:Title: Dynamics of concentrated vorticities in 2d and 3d Euler flows\nby Manuel Del Pino (University of Bath) as part of Geometric and functi
onal inequalities and applications\n\n\nAbstract\nA classical problem that
traces back to Helmholtz and Kirchoff is the understanding \nof the dynam
ics of solutions to the 2d and 3d Euler equations of an inviscid incompres
sible \nfluid\, when the vorticity of the solution is initially concentrat
ed near isolated points in 2d or \nvortex lines in 3d. We discuss some rec
ent result on existence and asymptotic behaviour of \nthese solutions. We
describe\, with precise asymptotics\, interacting vortices and travelling
helices. We rigorously establish the law of of motion of of "leapfroggin
g vortex rings"\, originally conjectured by Helmholtz in 1858. This is jo
int work with Juan Davila\, Monica Musso and Juncheng Wei.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrique Zuazua (Friedrich-Alexander-Universität)
DTSTART;VALUE=DATE-TIME:20210308T140000Z
DTEND;VALUE=DATE-TIME:20210308T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/34
DESCRIPTION:Title: UNILATERAL BOUNDS FOR NONLINEAR SEMIGROUPS AND TIME-INVERSION\nby Enrique Zuazua (Friedrich-Alexander-Universität) as part of Geometr
ic and functional inequalities and applications\n\n\nAbstract\nSome classi
cal nonlinear semigroups arising in mechanics induce unilateral bounds on
solutions. \nHamilton--Jacobi equations and 1-d scalar conservation laws
are classical examples of such nonlinear effects: solutions spontaneously
develop one-sided Lipschitz or semi-concavity conditions.\n\nWhen this occ
urs the range of the semigroup is unilaterally bounded by a threshold.\n\n
On the other hand\, in practical applications\, one is led to consider the
problem of time-inversion\, so to identify the initial sources that have
led to the observed dynamics at the final time.\n\nIn this lecture we shal
l discuss this problem answering to the following two questions: On one ha
nd\, to identify the range of the semigroup and\, given a target\, to char
acterize and reconstruct the ensemble of initial data leading to it.\n\nIl
lustrative numerical simulations will be presented\, and a complete geome
tric interpretation will also be provided.\n\nWe shall also present a numb
er of open problems arising in this area and the possible link with reinfo
rcement learning.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Street (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20210329T130000Z
DTEND;VALUE=DATE-TIME:20210329T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/35
DESCRIPTION:Title: Maximal Hypoellipticity\nby Brian Street (University of Wisc
onsin-Madison) as part of Geometric and functional inequalities and applic
ations\n\n\nAbstract\nIn 1974\, Folland and Stein introduced a generalizat
ion of ellipticity known as maximal hypoellipticity. This talk will be an
introduction to this concept and some of the ways it generalizes elliptic
ity.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Kenig (University of Chicago)
DTSTART;VALUE=DATE-TIME:20210426T140000Z
DTEND;VALUE=DATE-TIME:20210426T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/36
DESCRIPTION:Title: Wave maps into the sphere\nby Carlos Kenig (University of Ch
icago) as part of Geometric and functional inequalities and applications\n
\n\nAbstract\nWe will introduce wave maps\, an important geometric flow\,
and\ndiscuss\, for the case when the target is the sphere\, the asymptotic
\nbehavior near the ground state (without symmetry) and recent results in\
nthe general case (under co-rotational symmetry) in joint work with\nDuyc
kaerts\, Martel and Merle.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man Wah Wong (York University)
DTSTART;VALUE=DATE-TIME:20210315T140000Z
DTEND;VALUE=DATE-TIME:20210315T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/37
DESCRIPTION:Title: Spectral Theory and Number Theory of the Twisted Bi-Laplacian\nby Man Wah Wong (York University) as part of Geometric and functional i
nequalities and applications\n\n\nAbstract\nWe begin with the sub-Laplacia
n on the Heisenberg group and then the twisted Laplacian by taking its inv
erse Fourier transform with respect to the center of the group. The eigenv
alues and the eigenfunctions of the twisted Laplacian are computed explici
tly. Then we turn our attention to the product of the twisted Laplacian an
d its transpose\, thus obtaining a fourth order partial differential opera
tor dubbed the twisted bi-Laplacian. The connections between the spectral
analysis of the twisted bi-Laplacian and Dirichlet divisors\, the Riemann
zeta function and the Dixmier trace are explained.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanyan Li (Rutgers University)
DTSTART;VALUE=DATE-TIME:20210419T130000Z
DTEND;VALUE=DATE-TIME:20210419T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/38
DESCRIPTION:Title: Regular solutions of the stationary Navier-Stokes equations on h
igh dimensional Euclidean space\nby Yanyan Li (Rutgers University) as
part of Geometric and functional inequalities and applications\n\n\nAbstra
ct\nWe study the existence of regular solutions of the incompressible stat
ionary Navier-Stokes equations in n-dimensional Euclidean space with a giv
en bounded external force of compact support. In dimensions $n\\le 5$\, th
e existence of such solutions was known. In this paper\, we extend it to d
imensions $n\\le 15$. This is a joint work with Zhuolun Yang.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spring Recess (No Talk)
DTSTART;VALUE=DATE-TIME:20210412T130000Z
DTEND;VALUE=DATE-TIME:20210412T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/39
DESCRIPTION:by Spring Recess (No Talk) as part of Geometric and functional
inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenxiong Chen (Yeshiva University)
DTSTART;VALUE=DATE-TIME:20210322T140000Z
DTEND;VALUE=DATE-TIME:20210322T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/40
DESCRIPTION:Title: Asymptotic radial symmetry\, monotonicity\, non-existence for so
lutions to fractional parabolic equations\nby Wenxiong Chen (Yeshiva U
niversity) as part of Geometric and functional inequalities and applicatio
ns\n\n\nAbstract\nIn this talk\, we will consider nonlinear parabolic frac
tional equations\n\nWe develop a systematical approach in applying an asym
ptotic method\nof moving planes to investigate qualitative properties of p
ositive solutions for\nfractional parabolic equations. To this end\, we de
rive a series of needed key\ningredients such as narrow region principles\
, and various asymptotic maximum and strong maximum principles for antisym
metric functions in both bounded and unbounded domains. Then we illustrate
how these new methods can be employed to obtain asymptotic radial symmetr
y and monotonicity\nof positive solutions in a unit ball and on the whole
space. Namely\, we show\nthat no matter what the initial data are\, the so
lutions will eventually approach to radially symmetric functions. We will
also consider the entire positive solutions on a half space\, in\nthe whol
e space\, and with indefinite nonlinearity. Monotonicity and nonexistence
of solutions are obtained. This is joint work with P. Wang\, Y. Niu\, Y. H
u and L. Wu.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunfeng Zhang (University of Connecticut)
DTSTART;VALUE=DATE-TIME:20210201T140000Z
DTEND;VALUE=DATE-TIME:20210201T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/41
DESCRIPTION:Title: Schr\\"odinger equations on compact globally symmetric spaces\nby Yunfeng Zhang (University of Connecticut) as part of Geometric and f
unctional inequalities and applications\n\n\nAbstract\nLet $M$ be a compac
t manifold of dimension $d$. Scale-invariant Strichartz estimates of the f
orm\n\n$$\\|e^{it\\Delta}f\\|_{L^p(I\\times M)}\\lesssim \\|f\\|_{H^{d/2-(
d+2)/p}(M)}$$\n\nhave only been proved for a few model cases of $M$\, most
of which are compact globally symmetric spaces.\n\nIn this talk\, we repo
rt that the above estimate holds true on an arbitrary compact globally sym
metric space $M$ equipped with the canonical Killing metric\, for all $p\\
geq 2+8/r$\, where $r$ denotes the rank of $M$. As an immediate applicatio
n\, we provide local well-posedness results for nonlinear Schr\\"odinger e
quations of polynomial nonlinearities of degree $\\beta\\geq 4$ on any com
pact globally symmetric space of large enough rank\, in all subcritical sp
aces.\n\nWe also discuss bilinear Strichartz estimates on compact globally
symmetric spaces\, and critical and subcritical local well-posedness resu
lts for the cubic nonlinearity.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jungang Li (Brown University)
DTSTART;VALUE=DATE-TIME:20210503T140000Z
DTEND;VALUE=DATE-TIME:20210503T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/42
DESCRIPTION:Title: Sharp critical and subcritical Moser-Trudinger inequalities on c
omplete and noncompact Riemannian manifolds\nby Jungang Li (Brown Univ
ersity) as part of Geometric and functional inequalities and applications\
n\n\nAbstract\nMoser-Trudinger inequality is the borderline case of the So
bolev inequality and has many applications in differential geometry. In th
is talk\, I will report a recent progress of critical and subcritical Mose
r-Trudinger inequalities on complete noncompact Riemannian manifolds. Clas
sical results depend heavily on the validity of some rearrangement inequal
ities\, which are unavailable on general manifolds. To overcome this diffi
culty\, we applied a rearrangement-free approach to obtain those inequalit
ies on manifolds\, together with their sharp constants. This is a joint wo
rk with Guozhen Lu.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Struwe (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20210510T140000Z
DTEND;VALUE=DATE-TIME:20210510T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/43
DESCRIPTION:Title: Normalized harmonic map flow\nby Michael Struwe (ETH Zürich
) as part of Geometric and functional inequalities and applications\n\n\nA
bstract\nFinding non-constant harmonic 3-spheres for a closed target manif
old N\nis a prototype of a super-critical variational problem. In fact\, t
he\ndirect method fails\, as the infimum of Dirichlet energy in any homoto
py\nclass of maps from the 3-sphere to any closed N is zero\; moreover\, t
he\nharmonic map heat flow may blow up in finite time\, and even the ident
ity\nmap from the 3-sphere to itself is not stable under this flow.\n\nTo
overcome these difficulties\, we propose the normalized harmonic map\nheat
flow as a new tool\, and we show that for this flow the identity map\nfro
m the 3-sphere to itself now\, indeed\, is stable\; moreover\, the flow\nc
onverges to a harmonic 3-sphere also when we perturb the target\ngeometry.
While our results are strongest in the perturbative setting\,\nwe also ou
tline a possible global theory.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20210517T140000Z
DTEND;VALUE=DATE-TIME:20210517T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/44
DESCRIPTION:by No talk as part of Geometric and functional inequalities an
d applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk (Memorial Day)
DTSTART;VALUE=DATE-TIME:20210531T140000Z
DTEND;VALUE=DATE-TIME:20210531T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/45
DESCRIPTION:by No Talk (Memorial Day) as part of Geometric and functional
inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaojun Huang (Rutgers University)
DTSTART;VALUE=DATE-TIME:20210524T130000Z
DTEND;VALUE=DATE-TIME:20210524T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/46
DESCRIPTION:Title: Revisit to a non-degeneracy property for extremal mappings\n
by Xiaojun Huang (Rutgers University) as part of Geometric and functional
inequalities and applications\n\n\nAbstract\nI will discuss a generalizati
on of my previous result on the localization of extremal maps near a stron
gly pseudo-convex point.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sun-Yung Alice Chang (Princeton University)
DTSTART;VALUE=DATE-TIME:20210607T140000Z
DTEND;VALUE=DATE-TIME:20210607T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/47
DESCRIPTION:Title: On bi-Lipschitz equivalence of a class of non-conformally flat s
pheres\nby Sun-Yung Alice Chang (Princeton University) as part of Geom
etric and functional inequalities and applications\n\n\nAbstract\nThis is
a report of some recent joint work with Eden Prywes and Paul Yang. The mai
n\nresult is a bi-Lipschitz equivalence of a class of metrics on 4-shpere
under curvature constraints. The proof involves two steps: first a constru
ction of quasiconformal maps between\ntwo conformally related metrics in a
positive Yamabe class\, followed by the step of applying\nthe Ricci flow
to establish the bi-Lipschitz equivalence from such a conformal class to t
he\nstandard conformal class on 4-sphere.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svitlana Mayboroda (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20210614T140000Z
DTEND;VALUE=DATE-TIME:20210614T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/48
DESCRIPTION:Title: Green Function vs. Geometry\nby Svitlana Mayboroda (Universi
ty of Minnesota) as part of Geometric and functional inequalities and appl
ications\n\n\nAbstract\nIn this talk we will discuss connections between t
he geometric and PDE properties of sets. The emphasis is on quantifiable\,
global results which yield true equivalence between the geometric and PDE
notions in very rough scenarios\, including domains and equations with si
ngularities and structural complexity. The main result establishes that in
all dimensions $d < n$\, a $d$-dimensional set in $\\mathbb{R}^n$ is regu
lar (rectifiable) if and only if the Green function for elliptic operators
is well approximated by affine functions (distance to the hyperplanes). T
o the best of our knowledge\, this is the first free boundary result of th
is type for lower dimensional sets and the first free boundary result in t
he classical case $d=n-1$ without restrictions on the coefficients of the
equation.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Terracini (Universitá di Torino)
DTSTART;VALUE=DATE-TIME:20210628T130000Z
DTEND;VALUE=DATE-TIME:20210628T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/49
DESCRIPTION:by Susanna Terracini (Universitá di Torino) as part of Geomet
ric and functional inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Moser (University of Bath)
DTSTART;VALUE=DATE-TIME:20210621T130000Z
DTEND;VALUE=DATE-TIME:20210621T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/50
DESCRIPTION:Title: The infinity-elastica problem\nby Roger Moser (University of
Bath) as part of Geometric and functional inequalities and applications\n
\n\nAbstract\nThe Euler elastica problem seeks to minimise the $L^2$-norm
of\nthe curvature of curves under certain boundary conditions. If we\nrepl
ace the $L^2$-norm with the $L^\\infty$-norm\, then we obtain a\nvariation
al problem with quite different properties. Nevertheless\, even\nthough th
e underlying functional is not differentiable\, it turns out\nthat the sol
utions of the problem can still be described by\ndifferential equations. A
n analysis of these equations then gives a\nclassification of the solution
s.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingzhi Tie (University of Georgia)
DTSTART;VALUE=DATE-TIME:20210405T140000Z
DTEND;VALUE=DATE-TIME:20210405T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/51
DESCRIPTION:Title: CR analogue of Yau’s Conjecture on pseudo harmonic functions o
f polynomial growth.\nby Jingzhi Tie (University of Georgia) as part o
f Geometric and functional inequalities and applications\n\n\nAbstract\nCh
eng and Yau derived the well-known gradient estimate for positive harmonic
functions and obtained the classical Liouville theorem\, which states tha
t any bounded harmonic function is constant in complete noncompact Riemann
ian manifolds with nonnegative Ricci curvature. I will talk about the CR a
nalogue of Yau’s conjecture. We need to derive the CR volume doubling pr
operty\, CR\\ Sobolev inequality\, and mean value inequality. Then we can
apply them to prove the CR analogue of Yau's conjecture on the space consi
sting of all pseudoharmonic functions of polynomial growth of degree at mo
st $d$ in a complete noncompact pseudohermitian $(2n+1)$-manifold. As a by
-product\, we obtain the CR analogue of volume growth estimate and Gromov
precompactness theorem.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo D'Ambrosio (Universita di Bari)
DTSTART;VALUE=DATE-TIME:20210705T130000Z
DTEND;VALUE=DATE-TIME:20210705T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/52
DESCRIPTION:by Lorenzo D'Ambrosio (Universita di Bari) as part of Geometri
c and functional inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART;VALUE=DATE-TIME:20210913T140000Z
DTEND;VALUE=DATE-TIME:20210913T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/53
DESCRIPTION:Title: Regularity estimates for the Boltzmann equation without cutoff\nby Luis Silvestre (University of Chicago) as part of Geometric and fun
ctional inequalities and applications\n\nInteractive livestream: https://b
rown.zoom.us/j/91683612862\n\nAbstract\nWe study the regularization effect
of the inhomogeneous Boltzmann equation without cutoff. We obtain a prior
i estimates for all derivatives of the solution depending only on bounds o
f its hydrodynamic quantities: mass density\, energy density and entropy d
ensity. As a consequence\, a classical solution to the equation may fail t
o exist after a certain time T only if at least one of these hydrodynamic
quantities blows up. Our analysis applies to the case of moderately soft a
nd hard potentials. We use methods that originated in the study of nonloca
l elliptic and parabolic equations: a weak Harnack inequality in the style
of De Giorgi\, and a Schauder-type estimate.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/53/
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshikazu Giga
DTSTART;VALUE=DATE-TIME:20210927T130000Z
DTEND;VALUE=DATE-TIME:20210927T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/54
DESCRIPTION:Title: University of Tokyo\nby Yoshikazu Giga as part of Geometric
and functional inequalities and applications\n\nInteractive livestream: ht
tps://brown.zoom.us/j/91683612862\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/54/
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jill Pipher (Brown University)
DTSTART;VALUE=DATE-TIME:20210920T140000Z
DTEND;VALUE=DATE-TIME:20210920T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T233441Z
UID:GeomInequAndPDEs/55
DESCRIPTION:by Jill Pipher (Brown University) as part of Geometric and fun
ctional inequalities and applications\n\nInteractive livestream: https://b
rown.zoom.us/j/91683612862\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/55/
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
END:VCALENDAR