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BEGIN:VEVENT
SUMMARY:William Beckner (University of Texas at Austin)
DTSTART:20200720T130000Z
DTEND:20200720T140000Z
DTSTAMP:20260314T084004Z
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:20200720T140000Z
DTEND:20200720T150000Z
DTSTAMP:20260314T084004Z
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:20200727T130000Z
DTEND:20200727T140000Z
DTSTAMP:20260314T084004Z
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:20201109T140000Z
DTEND:20201109T150000Z
DTSTAMP:20260314T084004Z
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:20200803T130000Z
DTEND:20200803T140000Z
DTSTAMP:20260314T084004Z
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:20200817T140000Z
DTEND:20200817T150000Z
DTSTAMP:20260314T084004Z
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:20200810T140000Z
DTEND:20200810T150000Z
DTSTAMP:20260314T084004Z
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.\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:20200824T143000Z
DTEND:20200824T153000Z
DTSTAMP:20260314T084004Z
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:20200831T140000Z
DTEND:20200831T150000Z
DTSTAMP:20260314T084004Z
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:20201116T140000Z
DTEND:20201116T150000Z
DTSTAMP:20260314T084004Z
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:20200907T130000Z
DTEND:20200907T140000Z
DTSTAMP:20260314T084004Z
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:20200803T140000Z
DTEND:20200803T150000Z
DTSTAMP:20260314T084004Z
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:20200921T130000Z
DTEND:20200921T140000Z
DTSTAMP:20260314T084004Z
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:20201026T140000Z
DTEND:20201026T150000Z
DTSTAMP:20260314T084004Z
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:20201005T140000Z
DTEND:20201005T150000Z
DTSTAMP:20260314T084004Z
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:20200914T130000Z
DTEND:20200914T140000Z
DTSTAMP:20260314T084004Z
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:20200928T130000Z
DTEND:20200928T140000Z
DTSTAMP:20260314T084004Z
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:20201102T150000Z
DTEND:20201102T160000Z
DTSTAMP:20260314T084004Z
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:20201012T130000Z
DTEND:20201012T140000Z
DTSTAMP:20260314T084004Z
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:20201019T140000Z
DTEND:20201019T150000Z
DTSTAMP:20260314T084004Z
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:20201214T140000Z
DTEND:20201214T150000Z
DTSTAMP:20260314T084004Z
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:20201207T140000Z
DTEND:20201207T150000Z
DTSTAMP:20260314T084004Z
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:20201130T140000Z
DTEND:20201130T150000Z
DTSTAMP:20260314T084004Z
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:20201214T150000Z
DTEND:20201214T160000Z
DTSTAMP:20260314T084004Z
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:20210118T140000Z
DTEND:20210118T160000Z
DTSTAMP:20260314T084004Z
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:20210125T150000Z
DTEND:20210125T160000Z
DTSTAMP:20260314T084004Z
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:20210111T140000Z
DTEND:20210111T150000Z
DTSTAMP:20260314T084004Z
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:20210215T140000Z
DTEND:20210215T150000Z
DTSTAMP:20260314T084004Z
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:20201109T140000Z
DTEND:20201109T150000Z
DTSTAMP:20260314T084004Z
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:20210208T140000Z
DTEND:20210208T150000Z
DTSTAMP:20260314T084004Z
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:20210222T140000Z
DTEND:20210222T150000Z
DTSTAMP:20260314T084004Z
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:20210301T140000Z
DTEND:20210301T150000Z
DTSTAMP:20260314T084004Z
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:20210308T140000Z
DTEND:20210308T150000Z
DTSTAMP:20260314T084004Z
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:20210329T130000Z
DTEND:20210329T140000Z
DTSTAMP:20260314T084004Z
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:20210426T140000Z
DTEND:20210426T150000Z
DTSTAMP:20260314T084004Z
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:20210315T140000Z
DTEND:20210315T150000Z
DTSTAMP:20260314T084004Z
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:20210419T130000Z
DTEND:20210419T140000Z
DTSTAMP:20260314T084004Z
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:20210412T130000Z
DTEND:20210412T150000Z
DTSTAMP:20260314T084004Z
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:20210322T140000Z
DTEND:20210322T150000Z
DTSTAMP:20260314T084004Z
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:20210201T140000Z
DTEND:20210201T150000Z
DTSTAMP:20260314T084004Z
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:20210503T140000Z
DTEND:20210503T150000Z
DTSTAMP:20260314T084004Z
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:20210510T140000Z
DTEND:20210510T150000Z
DTSTAMP:20260314T084004Z
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:20210517T140000Z
DTEND:20210517T150000Z
DTSTAMP:20260314T084004Z
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:20210531T140000Z
DTEND:20210531T150000Z
DTSTAMP:20260314T084004Z
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:20210524T130000Z
DTEND:20210524T140000Z
DTSTAMP:20260314T084004Z
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:20210607T140000Z
DTEND:20210607T150000Z
DTSTAMP:20260314T084004Z
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:20210614T140000Z
DTEND:20210614T150000Z
DTSTAMP:20260314T084004Z
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:20210628T130000Z
DTEND:20210628T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/49
DESCRIPTION:Title: Free boundaries in segregation problems\nby Susanna Terracin
i (Universitá di Torino) as part of Geometric and functional inequalities
and applications\n\n\nAbstract\nWe first consider classes of variational
problems for densities that repel each other at distance. Examples are giv
en by the minimizers of Dirichlet functional or the Rayleigh quotient\n\\[
\n D({\\bf u}) = \\sum_{i=1}^k \\int_{\\Omega} |\\nabla u_i|^2 \\quad \\t
ext{or} \\quad R({\\bf u}) = \\sum_{i=1}^k \\frac{\\int_{\\Omega} |\\nabl
a u_i|^2}{\\int_{\\Omega} u_i^2}\n\\]\nover the class of $H^1(\\Omega\,\\R
^k)$ functions attaining some boundary conditions on $\\partial \\Omega$\,
and subjected to the constraint \n\\[\n \\operatorname{dist} (\\{u_i > 0
\\}\, \\{u_j > 0\\}) \\ge 1 \\qquad \\forall i \\neq j.\n\\]\n\n\nAs seco
nd class of problems\, we consider energy minimizers of Dirichlet energies
with different metrics\n\\[\n D({\\bf u}) = \\sum_{i=1}^k \\int_{\\Omega
} \\langle A_i\\nabla u_i\, \\nabla u_i\\rangle\n\\]\nwith constraint\n\\[
\n u_i(x)\\cdot u_j(x)=0\, \\qquad \\forall x\\in \\Omega\\\;\, \\forall i
\\neq j.\n\\]\n\nFor these problems\, we investigate the optimal regulari
ty of the solutions\, prove a free-boundary extremality condition\, and de
rive some preliminary results characterising the emerging free boundary.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Moser (University of Bath)
DTSTART:20210621T130000Z
DTEND:20210621T140000Z
DTSTAMP:20260314T084004Z
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:20210405T140000Z
DTEND:20210405T150000Z
DTSTAMP:20260314T084004Z
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:20210705T130000Z
DTEND:20210705T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/52
DESCRIPTION:Title: Liouville theorems for semilinear biharmonic equations and inequ
alities\nby Lorenzo D'Ambrosio (Universita di Bari) as part of Geometr
ic and functional inequalities and applications\n\n\nAbstract\nWe study no
nexistence results for a coercive semilinear biharmonic equation on the wh
ole $R^N$. The analysis is made for general solutions without any assumpti
on on their sign nor on their behaviour at infinity. A relevant role is pl
ayed by some extensions of the Hardy-Rellich inequalities for general func
tions (not necessarily compactly supported).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART:20210913T140000Z
DTEND:20210913T150000Z
DTSTAMP:20260314T084004Z
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\n\nAbstract\nWe study the regulari
zation effect of the inhomogeneous Boltzmann equation without cutoff. We o
btain a priori estimates for all derivatives of the solution depending onl
y on bounds of its hydrodynamic quantities: mass density\, energy density
and entropy density. As a consequence\, a classical solution to the equati
on may fail to exist after a certain time T only if at least one of these
hydrodynamic quantities blows up. Our analysis applies to the case of mode
rately soft and hard potentials. We use methods that originated in the stu
dy of nonlocal 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/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshikazu Giga (University of Tokyo)
DTSTART:20210927T130000Z
DTEND:20210927T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/54
DESCRIPTION:Title: On the Helmholtz decomposition of BMO spaces of vector fields\nby Yoshikazu Giga (University of Tokyo) as part of Geometric and functi
onal inequalities and applications\n\n\nAbstract\nThe Helmholtz decomposit
ion of vector fields is a fundamental tool for analysis of vector fields e
specially to analyze the Navier-Stokes equations in a domain. It gives a u
nique decomposition of a (tangential) vector field defined in a domain of
an Euclidean space (or a riemannian maniford) into a sum of a gradient fie
ld and a solenoidal field with supplemental condition like a boundary cond
ition.It is well-known that such decomposition gives an orthogonal decomp
osition of the space of L^2 vector fields in an arbitrary domain and known
as the Weyl decomposition. It is also well-studied that in various domain
s including the half space\, smooth bounded and exterior domain\, it gives
a topological direct sum decomposition of the space of L^p vector fields
for 1 < p < ∞. The extension to the case p=∞ (or p=1) is impossible
because otherwise it would imply the boundedness of the Riesz type operato
r in L^∞ (or L^1) which is absurd.\n In this talk\, we extend the Hemlh
oltz decomposition in a space of vector fields with bounded mean oscillati
ons (BMO) when the domain of vector field is a smooth bounded domain in an
Euclidean space. There are several possible definitions of\na BMO space o
f vector fields. However\, to have a topological direct sum decomposition\
, it turns out that components of normal and tangential to the boundary s
hould be handled separately.\n This decomposition problem is equivalent t
o solve the Poisson equation with the divergence of the original vector fi
eld v as a data with the Neumann data with the normal trace of v. The desi
red gradient field is the gradient of the solution of this Poisson equatio
n. To solve this problem we construct a kind of volume potential so that t
he problem is reduced to the Neumann problem for the Laplace equation. Unf
ortunately\, taking usual Newton potential causes a problem to estimate ne
cessary norm so we construct another volume potential based on normal coor
dinate.We need a trace theorem to control L^∞ norm of the normal trace.
This is of independent interest. Finally\,we solve the Neumann problem wit
h L^∞ data in a necessary space. The Helmholtz decomposition for BMO v
ector fields is previously known only in the whole Euclidean space or the
half space so this seems to be the first result for a domain with a curved
boundary. This is a joint work with my student Z.Gu (University of Tokyo)
.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jill Pipher (Brown University)
DTSTART:20210920T140000Z
DTEND:20210920T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/55
DESCRIPTION:Title: Boundary value problems for p-elliptic operators\nby Jill Pi
pher (Brown University) as part of Geometric and functional inequalities a
nd applications\n\n\nAbstract\nWe give some background about the regularit
y of solutions to real and complex elliptic operators\, motivating a new a
lgebraic condition (p-ellipticity). We introduce this condition in order t
o solve new boundary value problems for operators with complex coefficient
s. Results with M. Dindos\, and with M. Dindos and J. Li\, are discussed.\
n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sundaram Thangavelu (INDIAN INSTITUTE OF SCIENCE)
DTSTART:20211004T130000Z
DTEND:20211004T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/56
DESCRIPTION:Title: On the extension problem for the sublaplacian on the Heisenberg
group\nby Sundaram Thangavelu (INDIAN INSTITUTE OF SCIENCE) as part of
Geometric and functional inequalities and applications\n\n\nAbstract\nIn
this talk we plan to describe some results on the extension problem associ
ated to the sublaplacian $ \\mathcal{L} $ on the Heisenberg group $ \\H^n
.$ The Dirichlet to Neumann map induced by this problem leads to conformal
ly invariant fractional powers of $ \\mathcal{L}.$ We use the results to p
rove a version of Hardy's inequality for such fractional powers. These res
ults are based on my joint work with Luz Roncal.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Grillo (Politecnico di Milano)
DTSTART:20211011T130000Z
DTEND:20211011T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/57
DESCRIPTION:Title: Nonlinear characterizations of stochastic completeness\nby G
abriele Grillo (Politecnico di Milano) as part of Geometric and functional
inequalities and applications\n\n\nAbstract\nA manifold is said to be sto
chastically complete if the free heat semigroup preserves probability. It
is well-known that this property is equivalent to nonexistence of nonnegat
ive\, bounded solutions to certain (linear) elliptic problems\, and to uni
queness of solutions to the heat equation corresponding to bounded initial
data. We prove that stochastic completeness is also equivalent to similar
properties for certain nonlinear elliptic and parabolic problems. This fa
ct\, and the known analytic-geometric characterizations of stochastic comp
leteness\, allow to give new explicit criteria for existence/nonexistence
of solutions to certain nonlinear elliptic equations on manifolds\, and fo
r uniqueness/nonuniqueness of solutions to certain nonlinear diffusions on
manifolds.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART:20211025T140000Z
DTEND:20211025T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/58
DESCRIPTION:Title: Mean-Value Inequalities for Convex Domains\nby Stefan Steine
rberger (University of Washington) as part of Geometric and functional ine
qualities and applications\n\n\nAbstract\nThe Mean Value Theorem implies t
hat the average value of a subharmonic\nfunction in a disk can be bounded
from above by the average value on the boundary. \nWhat happens if we rep
lace the disk by another domain? Maybe surprisingly\, the problem \nhas a
relatively clean answer -- we discuss a whole range of mean value inequal
ities for \nconvex domains in IR^n. The extremal domain remains a mystery
for most of them. \nThe techniques are an amusing mixture of classical po
tential theory\, complex analysis\,\na little bit of elliptic PDEs and\, s
urprisingly\, the theory of solids from the 1850s.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Manfredi (University of Pittsburgh)
DTSTART:20211129T140000Z
DTEND:20211129T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/62
DESCRIPTION:Title: NATURAL $p$-MEANS FOR THE $p$-LAPLACIAN IN EUCLIDEAN SPACE AND
THE HEISENBERG GROUP\nby Juan Manfredi (University of Pittsburgh) as p
art of Geometric and functional inequalities and applications\n\n\nAbstrac
t\nWe consider semi-discrete approximations to $p$-harmonic functions base
d on the natural\n$p$-means of Ishiwata\, Magnanini\, and Wadade in 2017 (
CVPDE 2017)\, who proved their local convergence. In the Euclidean case we
prove uniform convergence in bounded Lipschitz domains. We also consider
adapted semi-discrete approximations in the Heisenberg group $\\mathbb{H}$
and prove uniform convergence in bounded $C^{1\,1}$-domains.\n\nThis talk
is based in joint work with András Domokos and Diego Ricciotti (Sacramen
to)\nand Bianca Stroffolini (Naples)\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guofang Wang (University of Freiburg)
DTSTART:20211101T140000Z
DTEND:20211101T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/63
DESCRIPTION:Title: Geometric inequalities in the hyperbolic space and their applica
tions.\nby Guofang Wang (University of Freiburg) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nWe will talk a
bout Alexandrov-Fenchel type inequalities in the hyperbolic space and thei
r applications in a higher order mass of asymptotically hyperbolic manifol
ds. The talk is based on a series of work joint with Yuxin Ge\, Jie Wu and
Chao Xia\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Yang (Princeton University)
DTSTART:20220207T150000Z
DTEND:20220207T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/64
DESCRIPTION:Title: Sturm comparison for Jacobi vector fields and applications\n
by Paul Yang (Princeton University) as part of Geometric and functional in
equalities and applications\n\n\nAbstract\nFor CR manifolds of real dimens
ion three\, we study the Jacobi field equation. Under the condition that t
he torsion be parallel\, we obtain comparison results against a family of
homogeneous CR structures. As application\, we describe the singularities
of contact forms on the the homogeneous structures with finite total Q-pri
me curvature. This is ongoing joint work with Sagun Chanillo.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Chen (University of California at Berkeley)
DTSTART:20211108T150000Z
DTEND:20211108T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/65
DESCRIPTION:Title: Integral curvature pinching and sphere theorems via the Ricci fl
ow\nby Eric Chen (University of California at Berkeley) as part of Geo
metric and functional inequalities and applications\n\n\nAbstract\nI will
discuss how uniform Sobolev inequalities obtained from the monotonicity of
Perelman's W-functional can be used to prove curvature pinching theorems
on Riemannian manifolds. These are based on scale-invariant integral norm
s and generalize some earlier pointwise and supercritical integral pinchin
g statements. This is joint work with Guofang Wei and Rugang Ye.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qing Han (University of Notre Dame)
DTSTART:20211206T150000Z
DTEND:20211206T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/67
DESCRIPTION:Title: A Concise Boundary Regularity for the Loewner-Nirenberg Problem<
/a>\nby Qing Han (University of Notre Dame) as part of Geometric and funct
ional inequalities and applications\n\n\nAbstract\nLoewner and Nirenberg d
iscussed complete metrics conformal to the Euclidean metric and with a con
stant scalar curvature in bounded domains in the Euclidean space. The conf
ormal factors blow up on boundary. The asymptotic behaviors of the conform
al factors near boundary are known in smooth and sufficiently smooth domai
ns. In this talk\, we introduce the logarithm of the distance to boundary
as an additional independent self-variable and establish a concise boundar
y regularity.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jyotshana Prajapat (University of Mumbai)
DTSTART:20211122T140000Z
DTEND:20211122T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/68
DESCRIPTION:Title: Geodetically convex sets in Heisenberg group $H^n$\nby Jyots
hana Prajapat (University of Mumbai) as part of Geometric and functional i
nequalities and applications\n\n\nAbstract\nA classification of geodetical
ly convex subsets of Heisenberg group of homogeneous dimension 4 was prov
ed by Monti-Rickly. We extend their result to a higher dimension Heisenb
erg group. This is ongoing work with my PhD student Anoop Varghese.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert McCann (University of Toronto)
DTSTART:20211220T150000Z
DTEND:20211220T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/69
DESCRIPTION:Title: Inscribed radius bounds for lower Ricci bounded metric measure s
paces with mean convex boundary\nby Robert McCann (University of Toron
to) as part of Geometric and functional inequalities and applications\n\n\
nAbstract\nConsider an essentially nonbranching metric measure space with
the measure contraction property of Ohta and Sturm. We prove a sharp upper
bound on the inscribed radius of any subset whose boundary has a suitably
signed lower bound on its generalized mean curvature. This provides a non
smooth analog of results dating back to Kasue (1983) and subsequent author
s. We prove a stability statement concerning such bounds and --- in the Ri
emannian curvature-dimension (RCD) setting --- characterize the cases of e
quality. This represents joint work with Annegret Burtscher\, Christian Ke
tterer and Eric Woolgar.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vitali Kapovitch (University of Toronto)
DTSTART:20220131T140000Z
DTEND:20220131T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/70
DESCRIPTION:Title: Mixed curvature almost flat manifolds\nby Vitali Kapovitch (
University of Toronto) as part of Geometric and functional inequalities an
d applications\n\n\nAbstract\nA celebrated theorem of Gromov says that giv
en $n>1$ there is an $\\epsilon(n)>0$ such that if a closed Riemannian man
ifold $M^n$ satisfies $-\\epsilon < sec_M < \\epsilon\, diam(M) < 1$ then
$M$ is diffeomorphic to an infranilmanifold. I will show that the lower se
ctional curvature bound in Gromov’s theorem can be weakened to the lower
Bakry-Emery Ricci curvature bound. I will also discuss the relation of th
is result to the study of manifolds with Ricci curvature bounded below.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Vega (Basque Center for Applied Mathematics)
DTSTART:20220124T150000Z
DTEND:20220124T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/71
DESCRIPTION:Title: New Conservation Laws and Energy Cascade for 1d Cubic NLS\nb
y Luis Vega (Basque Center for Applied Mathematics) as part of Geometric a
nd functional inequalities and applications\n\n\nAbstract\nI’ll present
some recent results concerning the IVP of 1d cubic NLS at the critical le
vel of regularity. I’ll also exhibit a cascade of energy for the 1D Schr
ödinger map which is related to NLS through the so called Hasimoto transf
ormation. For higher regularity these two equations are completely integra
ble systems and therefore no cascade of energy is possible.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (University of Oxford)
DTSTART:20220509T130000Z
DTEND:20220509T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/72
DESCRIPTION:Title: Optimal transport and quantitative geometric inequalities\nb
y Andrea Mondino (University of Oxford) as part of Geometric and functiona
l inequalities and applications\n\n\nAbstract\nThe goal of the talk is to
discuss a quantitative version of the Levy-Gromov isoperimetric inequality
(joint with Cavalletti and Maggi) as well as a quantitative form of Obata
's rigidity theorem (joint with Cavalletti and Semola). Given a closed Rie
mannian manifold with strictly positive Ricci tensor\, one estimates the m
easure of the symmetric difference of a set with a metric ball with the de
ficit in the Levy-Gromov inequality. The results are obtained via a quanti
tative analysis based on the localisation method via L1-optimal transport.
For simplicity of presentation\, the talk will present the results in cas
e of smooth Riemannian manifolds with Ricci Curvature bounded below\; more
over it will not require previous knowledge of optimal transport theory.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhan Li (University of Minnesota)
DTSTART:20211213T150000Z
DTEND:20211213T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/73
DESCRIPTION:Title: Comparison between the Green function and smooth distances\n
by Linhan Li (University of Minnesota) as part of Geometric and functional
inequalities and applications\n\n\nAbstract\nIn the upper half-space\, th
e distance function to the boundary is a positive solution to Laplace's eq
uation that vanishes on the boundary\, which can be interpreted as the Gre
en function with pole at infinity for the Laplacian. We are interested in
understanding the exact relations between the behavior of the Green functi
on\, the structure of the underlying operator\, and the geometry of the do
main. In joint work with G. David and S. Mayboroda\, we obtain a precise a
nd quantitative control of the proximity of the Green function and the dis
tance function on the upper half-space by the oscillation of the coefficie
nts of the operator. The class of the operators that we consider is of the
nature of the best possible for the Green function to behave like a dista
nce function. More recently\, together with J. Feneuil and S. Mayboroda\,
we obtain analogous results for domains with uniformly rectifiable boundar
ies.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaodan Zhou (Okinawa Institute of Science and Technology)
DTSTART:20220221T140000Z
DTEND:20220221T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/74
DESCRIPTION:Title: Quasiconvex envelope in the Heisenberg group\nby Xiaodan Zho
u (Okinawa Institute of Science and Technology) as part of Geometric and f
unctional inequalities and applications\n\n\nAbstract\nVarious notions of
convexity of sets and functions in the Heisenberg group have been studied
in the past two decades. In this talk\, we focus on the horizontally quasi
convex ($h$-quasiconvex) functions in the Heisenberg group. Inspired by th
e first-order characterization and construction of quasiconvex envelope by
Barron\, Goebel and Jensen in the Euclidean space\, we obtain a PDE appro
ach to construct the $h$-quasiconvex envelope for a given function $f$ in
the Heisenberg group. In particular\, we show the uniqueness and existence
of viscosity solutions to a non-local Hamilton-Jacobi equation and iterat
e the equation to obtain the $h$-quasiconvex envelope. Relations between $
h$-convex hull of a set and the $h$-quasiconvex envelopes are also investi
gated. This is joint work with Antoni Kijowski (OIST) and Qing Liu (Fukuok
a University/OIST).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Song (Rutgers University)
DTSTART:20220214T150000Z
DTEND:20220214T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/75
DESCRIPTION:Title: Positivity conditions for complex Hessian equations\nby Jian
Song (Rutgers University) as part of Geometric and functional inequalitie
s and applications\n\n\nAbstract\nIn this talk\, we will discuss the relat
ion between complex Hessian equation and positivity of algebraic numerical
conditions. In particular\, we will prove a Naki-Moishezon criterion for
Donaldson's J-equation.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enno Lenzmann (University of Basel)
DTSTART:20220228T140000Z
DTEND:20220228T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/76
DESCRIPTION:Title: Symmetry and symmetry-breaking for solutions of PDEs via Fourier
methods\nby Enno Lenzmann (University of Basel) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nIn this talk\,
I will review recent results on symmetry and symmetry-breaking for optimi
zing solutions of a general class of nonlinear elliptic PDEs. On one hand\
, I will discuss a novel approach to prove symmetry by using the so-called
Fourier rearrangements\, which can be applied to PDEs of arbitrary order
(where classical method such as the moving plane method or the Polya-Szeg
ö principle fail short). On the other hand\, I will discuss recent result
s on symmetry-breaking for optimizers by using Fourier methods and the Ste
in-Tomas inequality. This talk is based on joint work with Tobias Weth and
Jeremy Sok.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolyn Gordon (Dartmouth College)
DTSTART:20220328T130000Z
DTEND:20220328T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/77
DESCRIPTION:Title: Inverse spectral problems on compact Riemannian orbifolds\nb
y Carolyn Gordon (Dartmouth College) as part of Geometric and functional i
nequalities and applications\n\n\nAbstract\nOrbifolds are a generalization
of manifolds in which various types of singularities may occur. After r
eviewing the notion of Riemannian orbifolds and their Hodge Laplacians\, w
e will address the question: Does the spectrum of the Hodge Laplacian on p
-forms detect the presence of singularities? This question remains open in
the case of the Laplace-Beltrami operator (i.e.\, the case p=0)\, althoug
h many partial results are known. We will show that the spectra of the Hod
ge Laplacians on functions and 1-forms together suffice to distinguish man
ifolds from orbifolds with sufficiently large singular set. In particular
\, these spectra always distinguish low-dimensional orbifolds (dimension a
t most 3) with singularities from smooth manifolds. We also obtain weaker
affirmative results for the spectrum on 1-forms alone and show via counte
rexamples that some of these results are sharp.\n\n(This is based on recen
t joint work with Katie Gittins\, Magda Khalile\, Ingrid Membrillo Solis\,
Mary Sandoval\, and Elizabeth Stanhope and work in progress with the same
co-authors along with Juan Pablo Rossetti.) \n\nTime permitting\, we will
also make a few remarks concerning the Steklov spectrum on Riemannian orb
ifolds with boundary. The Steklov spectrum is the spectrum of the Dirich
let-to-Neumann operator\, which maps Dirichlet boundary values of harmonic
functions to their Neumann boundary values.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jérôme Vétois (McGill University)
DTSTART:20220307T140000Z
DTEND:20220307T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/78
DESCRIPTION:Title: Stability and instability results for sign-changing solutions to
second-order critical elliptic equations\nby Jérôme Vétois (McGill
University) as part of Geometric and functional inequalities and applicat
ions\n\n\nAbstract\nIn this talk\, we will consider a question of stabilit
y (i.e. compactness of solutions to perturbed equations) for sign-changing
solutions to second-order critical elliptic equations on a closed Riemann
ian manifold. I will present a stability result obtained in the case of di
mensions greater than or equal to 7. I will then discuss the optimality of
this result by constructing counterexamples in every dimension. This is a
joint work with Bruno Premoselli (Université Libre de Bruxelles\, Belgiu
m).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Loss (Georgia Institute of Technology)
DTSTART:20220404T130000Z
DTEND:20220404T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/79
DESCRIPTION:Title: Which magnetic fields support a zero mode?\nby Michael Loss
(Georgia Institute of Technology) as part of Geometric and functional ineq
ualities and applications\n\n\nAbstract\nI present some results concerning
the size of magnetic fields that support zero modes for the three dimensi
onal Dirac equation and related problems for spinor equations. The critica
l quantity\, is the $3/2$ norm of the magnetic field $B$. The point is tha
t the spinor structure enters the analysis in a crucial way. This is joint
work with Rupert Frank at LMU Munich.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fritz Gesztesy (Baylor University)
DTSTART:20220516T140000Z
DTEND:20220516T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/80
DESCRIPTION:Title: Continuity properties of the spectral shift function for massles
s Dirac operators and an application to the Witten index\nby Fritz Ges
ztesy (Baylor University) as part of Geometric and functional inequalities
and applications\n\n\nAbstract\nWe report on recent results regarding the
limiting absorption principle for multi-dimensional\, massless Dirac-type
operators (implying absence of singularly continuous spectrum) and contin
uity properties of the associated spectral shift function.\n\nWe will moti
vate our interest in this circle of ideas by briefly describing the connec
tion to the notion of the Witten index for a certain class of non-Fredholm
operators.\n\nThis is based on various joint work with A. Carey\, J. Kaad
\, G. Levitina\, R. Nichols\, D. Potapov\, F. Sukochev\, and D. Zanin.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Carlen (Rutgers University)
DTSTART:20220411T130000Z
DTEND:20220411T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/83
DESCRIPTION:Title: Some trace inequalities related to quantum entropy\nby Eric
Carlen (Rutgers University) as part of Geometric and functional inequaliti
es and applications\n\n\nAbstract\nMany inequalities for trace functional
are formulated as concavity/convexity theorems. These generally have an eq
uivalent monotonicity version asserting monotonicity of the functional und
er some class of completely positive maps. The monotonicty formulation has
advantages: (1) Often this has a direct physical interpretation. (2) Ofte
n a direct proof of the monotonicity version is simpler than a direct proo
f of the concavity/convexity version\, and the later is always recovered u
sing a simple partial trace argument. (3) Often the monotonicty theorem ho
lds for a broader class of maps\, not\, necessarily completely positive\,
and is thus a strictly stronger result. We discus significant examples\,
some coming from recent joint work with Alexander Mueller-Hermes.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaping Wang (University of Minnesota)
DTSTART:20220418T140000Z
DTEND:20220418T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/84
DESCRIPTION:Title: Spectrum of complete manifolds\nby Jiaping Wang (University
of Minnesota) as part of Geometric and functional inequalities and applica
tions\n\n\nAbstract\nSpectrum of Laplacian is an important set of geometri
c invariants. The talk\, largely based on\njoint work with Peter Li and Ov
idiu Munteanu\, concerns its structure and size on complete manifolds unde
r various curvature conditions. The focus is on sharp estimates of the bot
tom spectrum in terms of either Ricci or scalar curvature lower bound.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galia Dafni (Concordia University)
DTSTART:20220523T140000Z
DTEND:20220523T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/85
DESCRIPTION:Title: Locally uniform domains and extension of nonhomogeneous BMO spac
es\nby Galia Dafni (Concordia University) as part of Geometric and fun
ctional inequalities and applications\n\n\nAbstract\nIn joint work with Al
maz Butaev (Cincinnati)\, we study local versions of uniform domains\, whi
ch can be identified with the epsilon-delta domains used by Jones to exten
d Sobolev spaces. We show that a domain is locally uniform if and only if
it is an extension domain for the nonhomogeneous (also known as "local") s
pace of functions of bounded mean oscillation introduced by Goldberg\, and
denoted by bmo. We also prove analogous results for functions of vanishi
ng mean oscillation.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Stancu (Concordia University)
DTSTART:20220425T130000Z
DTEND:20220425T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/86
DESCRIPTION:Title: On the fundamental gap of convex sets in hyperbolic space\nb
y Alina Stancu (Concordia University) as part of Geometric and functional
inequalities and applications\n\n\nAbstract\nThe difference between the fi
rst two eigenvalues of the Dirichlet Laplacian on convex sets of R^n and\,
respectively S^n\, satisfies the same strictly positive lower bound depen
ding on the diameter of the domain. In work with collaborators\, we have f
ound that the gap of the hyperbolic space on convex sets behaves strikingl
y different even if a stronger notion of convexity is employed. This is ve
ry interesting as many other features of first two eigenvalues behave in t
he same way on all three spaces of constant sectional curvature.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pei-Yong Wang (Wayne State University)
DTSTART:20220502T140000Z
DTEND:20220502T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/88
DESCRIPTION:Title: A Bifurcation Phenomenon Of The Perturbed Two-Phase Transition P
roblem\nby Pei-Yong Wang (Wayne State University) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nThis talk pre
sents a joint work with F. Charro\, A. Haj Ali\, M. Raihen\, and\nM. Torre
s on a bifurcation phenomenon in a two-phase\, singularly perturbed\, free
\nboundary problem of phase transition. We show that the uniqueness of the
solution\nfor the two-phase problem breaks down as the boundary data decr
eases through\na threshold value. For boundary values below the threshold\
, there are at least\nthree solutions\, namely\, the harmonic solution whi
ch is treated as a trivial solution\nin the absence of a free boundary\, a
nontrivial minimizer of the functional under\nconsideration\, and a third
solution of the mountain-pass type. We classify these\nsolutions accordin
g to the stability through evolution. The evolution with initial\ndata nea
r a stable solution\, such as the trivial harmonic solution or a minimizer
of\nthe functional\, converges to the stable solution. On the other hand\
, the evolution\ndeviates away from a non-minimal solution of the free bou
ndary problem.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bianca Stroffolini (Universit`a degli Studi di NAPOLI ”Federico
II”)
DTSTART:20220919T140000Z
DTEND:20220919T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/89
DESCRIPTION:Title: Taylor formula and regularity properties for degenerate Kolmogor
ov equations with Dini continuous coefficients\nby Bianca Stroffolini
(Universit`a degli Studi di NAPOLI ”Federico II”) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nWe study the
regularity properties of the second order linear operator in $\\mathbb{R}^
{N+1}$:\n\\[\n\\mathscr{L}u:= \\sum_{j\,k=1}^{m} a_{jk} \\partial^{2}_{x_j
x_k} u + \\sum_{j\,k=1}^N b_{jk} x_k \\partial_{x_j} u - \\partial_t u\,\
n\\]\nwhere $A = (a_{jk})_{j\,k=1\,\\ldots m}$\, $B = (b_{jk})_{j\,k=1\,\\
ldots N}$ are real valued matrices with constant coefficients\, with $A$ s
ymmetric and strictly positive. We prove that\, if the operator $\\mathscr
{L}$ satisfies Hörmander's hypoellipticity condition\, and $f$ is a Dini
continuous function\, then the second order derivatives of the solution $u
$ to the equation $\\mathscr{L}u = f$ are Dini continuous functions as wel
l. We also consider the case of Dini continuous coefficients $a_{jk}$'s. A
key step in our proof is a Taylor formula for classical solutions to $\\m
athscr{L}u=f$ that we establish under minimal regularity assumptions on $u
$.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mimi Dai (University of Illinois at Chicago)
DTSTART:20221003T140000Z
DTEND:20221003T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/91
DESCRIPTION:Title: Navier-Stokes equation: determining wavenumber\, Kolmogorov’s
dissipation number\, and Kraichnan’s number\nby Mimi Dai (University
of Illinois at Chicago) as part of Geometric and functional inequalities
and applications\n\n\nAbstract\nWe show the existence of determining waven
umber for the Naiver-Stokes equation in both 3D and 2D. Estimates on the d
etermining wavenumber are established in term of the phenomenological Kolm
ogorov’s dissipation number (3D) and Kraichnan’s number (2D). The resu
lts rigorously justify the criticality of Kolmogorov’s dissipation numbe
r and Kraichnan’s number.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias König (Goethe-Universität Frankfurt)
DTSTART:20221010T140000Z
DTEND:20221010T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/92
DESCRIPTION:Title: Multibubble blow-up analysis for the Brezis-Nirenberg problem in
three dimensions\nby Tobias König (Goethe-Universität Frankfurt) as
part of Geometric and functional inequalities and applications\n\n\nAbstr
act\nIn this talk\, I will present a recent result about blow-up asymptoti
cs in the three-dimensional Brezis-Nirenberg problem. More precisely\, fo
r a smooth bounded domain $\\Omega \\subset \\R^3$ and smooth functions $a
$ and $V$\, consider a sequence of positive solutions $u_\\epsilon$ to $-\
\Delta u_\\epsilon + (a+\\epsilon V) u_\\epsilon = u_\\epsilon^5$ on $\\Om
ega$ with zero Dirichlet boundary conditions\, which blows up as $\\epsilo
n \\to 0$. We derive the sharp blow-up rate and characterize the location
of concentration points in the general case of multiple blow-up\, thereby
obtaining a complete picture of blow-up phenomena in the framework of the
Brezis-Peletier conjecture in dimension $N=3$. I will also indicate a fort
hcoming new result parallel to this one for dimension $N \\geq 4$.\n\nThis
is joint work with Paul Laurain (IMJ-PRG Paris and ENS Paris).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianxiong Wang (University of Connecticut)
DTSTART:20221017T140000Z
DTEND:20221017T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/93
DESCRIPTION:Title: Symmetry of solutions to higher and fractional order semilinear
equations on hyperbolic spaces\nby Jianxiong Wang (University of Conne
cticut) as part of Geometric and functional inequalities and applications\
n\n\nAbstract\nWe show that nontrivial solutions to higher and fractional
order equations with certain nonlinearity are radially symmetric and nonin
creasing on geodesic balls in the hyperbolic space $\\mathbb{H}^n$ as well
as on the entire space $\\mathbb{H}^n$ . Applying Helgason-Fourier analys
is techniques on $\\mathbb{H}^n$ \, we developed a moving plane approach f
or integral equations on $\\mathbb{H}^n$. We also established the symmetry
to solutions of certain equations with singular terms on Euclidean spaces
. Moreover\, we obtained symmetry to solutions of some semilinear equation
s involving fractional order derivatives.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Flynn (Centre de Recherches Mathématiques)
DTSTART:20221024T140000Z
DTEND:20221024T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/94
DESCRIPTION:Title: Sharp Uncertainty Principles for Physical Vector Fields and Seco
nd Order Derivatives\nby Joshua Flynn (Centre de Recherches Mathémati
ques) as part of Geometric and functional inequalities and applications\n\
n\nAbstract\nThe Heisenberg uncertainty principle is a fundamental result
in quantum mechanics. Related inequalities are the hydrogen and Hardy unce
rtainty principles and all three belong to the family of geometric inequal
ities known as the Caffarelli-Kohn-Nirenberg inequalities. In this talk\,
we present our recent results pertaining to uncertainty principles and CKN
inequalities with a particular focus on higher order derivatives and vect
or-valued cases. Presented works were done jointly with G. Lu\, N. Lam and
C. Cazacu.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Kristaly (Babes-Bolyai University)
DTSTART:20221031T140000Z
DTEND:20221031T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/95
DESCRIPTION:Title: Lord Rayleigh’s conjecture for clamped plates in curved spaces
\nby Alexandru Kristaly (Babes-Bolyai University) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nThis talk is
focused on the vibrating clamped plate problem\, initially formulated by L
ord Rayleigh in 1877\, and solved by M. Ashbaugh & R. Benguria (Duke Math.
J.\, 1995) and N. Nadirashvili (ARMA\, 1995) in 2 and 3 dimensional eucli
dean spaces. We consider the same problem on both negatively and positivel
y curved spaces\, and provide various answers depending on the curvature\,
dimension and the width/size of the clamped plate.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaolong Han (California State University)
DTSTART:20221107T150000Z
DTEND:20221107T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/96
DESCRIPTION:Title: Fractal uncertainty principle for discrete Fourier transform and
random Cantor sets\nby Xiaolong Han (California State University) as
part of Geometric and functional inequalities and applications\n\n\nAbstra
ct\nThe Fourier uncertainty principle describes a fundamental phenomenon t
hat a function and its Fourier transform cannot simultaneously localize. D
yatlov and his collaborators (Zahl\, Bourgain\, Jin\, Nonnenmacher) recent
ly introduced a concept of Fractal Uncertainty Principle (FUP). It is a ma
thematical formulation concerning the limit of localization of a function
and its Fourier transform on sets with certain fractal structure. \n\nThe
FUP has quickly become an emerging topic in Fourier analysis and also has
important applications to other fields such as wave decay in obstacle scat
tering. In this talk\, we consider the discrete Fourier transform and the
fractal sets are given by discrete Cantor sets. We present the FUP in this
discrete setting with a much more favorable estimate than the one known b
efore\, when the Cantor sets are constructed by a random procedure. This i
s a joint work with Suresh Eswarathasan.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Reiter (University of Technology at Chemnitz)
DTSTART:20221114T150000Z
DTEND:20221114T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/97
DESCRIPTION:Title: Elasticity models with self-contact\nby Philipp Reiter (Univ
ersity of Technology at Chemnitz) as part of Geometric and functional ineq
ualities and applications\n\n\nAbstract\nMaintaining the topology of objec
ts undergoing deformations is a crucial\naspect of elasticity models. In t
his talk we consider two different\nsettings in which impermeability is im
plemented via regularization by a\nsuitable nonlocal functional.\n\nThe be
havior of long slender objects may be characterized by the classic\nKirchh
off model of elastic rods. Phenomena like supercoiling which play an\nesse
ntial role in molecular biology can only be observed if\nself-penetrations
are precluded. This can be achieved by adding a\nself-repulsive functiona
l such as the tangent-point energy. We discuss the\ndiscretization of this
approach and present some numerical simulations.\n\nIn case of elastic so
lids whose shape is described by the image of a\nreference domain under a
deformation map\, self-interpenetrations can be\nruled out by claiming glo
bal invertibility. Given a suitable stored energy\ndensity\, the latter is
ensured by the Ciarlet–Nečas condition which\,\nhowever\, is difficult
to handle numerically in an efficient way. This\nmotivates approximating
the latter by adding a self-repulsive functional\nwhich formally correspon
ds to a suitable Sobolev–Slobodeckiĭ seminorm of\nthe inverse deformati
on.\n\nThis is joint work with Sören Bartels (Freiburg) and Stefan Kröme
r\n(Prague).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Falocchi (Politecnico di Milano)
DTSTART:20221121T150000Z
DTEND:20221121T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/100
DESCRIPTION:Title: Some results on the 3D Stokes eigenvalue problem under Navier b
oundary conditions\nby Alessio Falocchi (Politecnico di Milano) as par
t of Geometric and functional inequalities and applications\n\n\nAbstract\
nWe study the Stokes eigenvalue problem under Navier boundary conditions i
n $C^{1\,1}$-domains $\\Omega\\subset \\mathbb{R}^3$. Differently from the
Dirichlet boundary conditions\, zero may be the least eigenvalue. We full
y characterize the domains where this happens\, showing the related validi
ty/failure of a suitable Poincar\\'{e}-type inequality.\n\nAs application
we prove regularity results for the solution of the evolution Navier-Stok
es equations under Navier boundary conditions in a class of merely {\\em L
ipschitz domains} of physical interest\, that we call {\\em sectors}.\n\nT
his is a joint work with Filippo Gazzola\, Politecnico di Milano.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schlein (University of Zurich)
DTSTART:20230306T150000Z
DTEND:20230306T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/101
DESCRIPTION:Title: Gross-Pitaevskii and Bogoliubov theory for trapped Bose-Einstei
n condensates.\nby Benjamin Schlein (University of Zurich) as part of
Geometric and functional inequalities and applications\n\n\nAbstract\nWe c
onsider a quantum system consisting of N bosons (particles described by a
permutation symmetric wave function) trapped in a volume of order one and
interacting through a short range potential\, with scattering length of t
he order 1/N (this is known as the Gross-Pitaevskii regime). First\, we wi
ll show how non-linear Gross-Pitaevskii theory describes\, to leading orde
r\, the ground state energy of the gas and the time-evolution resulting fr
om a change of the external fields. In the second part of the talk\, I wil
l then explain how Bogoliubov theory predicts the next order corrections.\
n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk (Spring Break)
DTSTART:20230313T130000Z
DTEND:20230313T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/103
DESCRIPTION:by No Talk (Spring Break) as part of Geometric and functional
inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Damien Thizy (University of Lyon 1 (Claude Bernard))
DTSTART:20230410T140000Z
DTEND:20230410T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/104
DESCRIPTION:Title: Large blow-up sets for Q-curvature equations.\nby Pierre-Da
mien Thizy (University of Lyon 1 (Claude Bernard)) as part of Geometric an
d functional inequalities and applications\n\n\nAbstract\nOn a bounded dom
ain of the Euclidean space $\\mathbb{R}^{2m}$\, $m>1$\, Adimurthi\, Robert
and Struwe pointed out that\, even assuming a volume bound $\\int e^{2mu}
dx \\leq C$\, some blow-up solutions for prescribed Q-curvature equations
$(-\\Delta)^m u= Q e^{2m u}$ without boundary conditions may blow-up not
only at points\, but also on the zero set of some nonpositive nontrivial p
olyharmonic function. This is in striking contrast with the two dimensiona
l case ($m=1$). During this talk\, starting from a work in progress with A
li Hyder and Luca Martinazzi\, we will discuss the construction of such so
lutions which involves (possible generalizations of) the Walsh-Lebesgue th
eorem and some issues about elliptic problems with measure data.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deping Ye (Memorial University of Newfoundland)
DTSTART:20230123T150000Z
DTEND:20230123T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/105
DESCRIPTION:Title: The $L_p$ surface area measure and related Minkowski problem fo
r log-concave functions\nby Deping Ye (Memorial University of Newfound
land) as part of Geometric and functional inequalities and applications\n\
n\nAbstract\nThe Minkowski type problems for convex bodies are fundamental
\nin convex geometry\, and have found many important connections and\nappl
ications in analysis\, partial differential equations\, etc. It is\nwell-k
nown that the log-concave functions behave rather similar to\nconvex bodie
s in many aspects\, for example the famous Prékopa–Leindler\ninequality
to the (dimension free) Brunn-Minkowski inequality.\n\nIn this talk\, I w
ill present an $L_p$ theory for the log-concave\nfunctions\, which is anal
ogous to the $L_p$ Brunn-Minkowski theory of\nconvex bodies. In particular
\, I will explain how to define the $L_p$ sum\nof log-concave functions\,
present a variational formula related to the\n$L_p$ addition\, and talk ab
out the corresponding $L_p$ Minkowski\nproblems as well as their solutions
.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Strauss (Brown University)
DTSTART:20230227T150000Z
DTEND:20230227T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/106
DESCRIPTION:Title: Instability of Water Waves (even small ones)\nby Walter Str
auss (Brown University) as part of Geometric and functional inequalities a
nd applications\n\n\nAbstract\nAfter a gentle introduction on water waves\
, I will present an exposition of joint work with Huy Quang Nguyen. We pro
ve rigorously that the classical (small-amplitude irrotational steady peri
odic) water waves are unstable with respect to long-wave perturbations. T
hat is\, the perturbations grow exponentially in time. This instability w
as first observed heuristically more than half a century ago by Benjamin a
nd Feir. However\, a rigorous proof was never found except in the case of
finite depth. We provide a completely different and self-contained proof o
f both the finite and infinite depth cases that retains the physical varia
bles. The proof reduces to an analysis of the spectrum of an explicit ope
rator. The growth is obtained by means of a Liapunov-Schmidt reduction th
at more or less reduces the analysis to four dimensions.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonard Gross (Cornell University)
DTSTART:20230911T140000Z
DTEND:20230911T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/107
DESCRIPTION:Title: Invariance of intrinsic hypercontractivity under perturbation o
f Schrodinger operators.\nby Leonard Gross (Cornell University) as par
t of Geometric and functional inequalities and applications\n\n\nAbstract\
nA Schrodinger operator that is bounded below and has a unique\npositive g
round state can be transformed into a Dirichlet form operator\nby the grou
nd state transformation. If the resulting Dirichlet form\noperator is hype
rcontractive\, Davies and Simon call the Schrodinger\noperator ``intrinsic
ally hypercontractive”. I will show that if one adds a\nsuitable potenti
al onto an intrinsically hypercontractive Schrodinger\noperator it remains
intrinsically hypercontractive. All bounds are dimension independent. I w
ill show how to use this theorem in two examples.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Visan (University of California at Los Angeles)
DTSTART:20230220T150000Z
DTEND:20230220T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/108
DESCRIPTION:Title: The derivative nonlinear Schrodinger equation\nby Monica Vi
san (University of California at Los Angeles) as part of Geometric and fun
ctional inequalities and applications\n\n\nAbstract\nI will discuss the de
rivative nonlinear Schrodinger equation\, how some inherent instabilities
have hindered the study of this equation\, and how we were able to demonst
rate global well-posedness in the natural scale-invariant space. This is j
oint work with Ben Harrop-Griffiths\, Rowan Killip\, and Maria Ntekoume.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rowan Killip (University of California at Los Angles)
DTSTART:20230320T140000Z
DTEND:20230320T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/109
DESCRIPTION:Title: From Optics to the Deift Conjecture\nby Rowan Killip (Unive
rsity of California at Los Angles) as part of Geometric and functional ine
qualities and applications\n\n\nAbstract\nAfter providing a mathematical b
ackground for some curious\noptical experiments in the 19th century\, we w
ill then describe how\nthese ideas inform our understanding of the Deift c
onjecture for the\nKorteweg--de Vries equation. Specifically\, they allow
us to show that the\nevolution of almost-periodic initial data need not r
emain almost\nperiodic. This is joint work with Andreia Chapouto and Moni
ca Visan.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Cingolani (Università degli Studi di Bari Aldo Moro)
DTSTART:20230508T140000Z
DTEND:20230508T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/111
DESCRIPTION:Title: On the planar Schrödinger-Newton system\nby Silvia Cingola
ni (Università degli Studi di Bari Aldo Moro) as part of Geometric and fu
nctional inequalities and applications\n\n\nAbstract\nI present some exist
ence results for nonlocal interaction energy functionals\nin two dimension
. I also characterize critical rates for some inequalities with\nlogarithm
ic kernels. The seminar is based on joint papers with Tobias Weth\,\nGoeth
e-Universität Frankfurt (Germany).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20230327T130000Z
DTEND:20230327T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/112
DESCRIPTION:by No Talk as part of Geometric and functional inequalities an
d applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenchuan Tian (UC Santa Barbara)
DTSTART:20230130T150000Z
DTEND:20230130T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/113
DESCRIPTION:Title: On a family of integral operators on the ball\nby Wenchuan
Tian (UC Santa Barbara) as part of Geometric and functional inequalities a
nd applications\n\n\nAbstract\nIn this work\, we prove an extension inequa
lity in the hyperbolic space. The inequality involves the hyperbolic harm
onic extension of a function on the boundary and the Fefferman-Graham comp
actification of the hyperbolic metric. We offer an interpretation of the e
xtension inequality as a conformally invariant generalization of Carleman'
s inequality to higher dimensions. \nIn addition to that\, we classify all
the solutions to the Euler-Lagrange equation of the extension inequality.
The proof uses the moving sphere method and relies on the properties of t
he Fefferman-Graham compactification of the hyperbolic metric.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Roysdon (Brown University)
DTSTART:20230213T150000Z
DTEND:20230213T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/114
DESCRIPTION:Title: Intersection Functions\nby Michael Roysdon (Brown Universit
y) as part of Geometric and functional inequalities and applications\n\n\n
Abstract\nThe classical Busemann-Petty Problem from the 1950s asked the fo
llowing tomographic question:\n\nAssuming you have two origin-symmetric co
nvex bodies $K$ and $L$ in the $n$-dimensional Euclidean space satisfying
the following volume inequality:\n\n\n$$|K \\cap \\theta^{\\perp}| \\leq |
L \\cap \\theta^{\\perp}| for all \\theta \\in S^{n-1}\,$$\n\ndoes it foll
ow that $|K| \\leq |L|$? The answer is affirmative for $n \\leq 4$ and ne
gative whenever $n >5$. However\, if $K$ belongs to a certain class of co
nvex bodies\, the intersection bodies\, then the answer to the Busemann-Pe
tty problem is affirmative in all dimension. Several extensions of this r
esult have been shown in the case of measures on convex bodies\, and isomo
rphic results of the same type have been established. Moreover\, the isom
orphic Busemann-Petty problem is actually equivalent to the isomorphic sli
cing problem of Bourgain (1986)\, which remains open to this day. \n\nIn
this talk\, we will introduce the notion of an intersection function\, pro
vide a Fourier analytic characterization for such functions\, and show som
e versions of the Busemann-Petty problem in this setting. In particular\,
we will show that if you have a pair of continuous\, even\, integrable fu
nctions $f\,g \\colon \\R^n \\to \\R_+$ which satisfy $[Rf] \\leq [Rg]$\,
where $R$ denotes the Radon transform\, then one has that $|f|_{L^2} \\leq
|g|_{L^2}$ provided that the function $f$ is an intersection function. \
n\nThis is based on a joint work with Alexander Koldobsky and Artem Zvavit
ch\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Capogna (Smith College)
DTSTART:20230417T140000Z
DTEND:20230417T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/115
DESCRIPTION:Title: The Neumann problem and the fractional p-Laplacian in measure m
etric spaces\nby Luca Capogna (Smith College) as part of Geometric and
functional inequalities and applications\n\n\nAbstract\nIn this talk we w
ill report on some recent joint work with Josh Kline\, Riikka Korte\, Mari
e Snipes and Nages Shanmugalingam\, concerning the Neumann problem in PI s
paces\, and a new definition of fractional p-Laplacians in arbitrary doubl
ing measure metric space. Following ideas of Caffarelli and Silvestre in a
nd using recent progress in hyperbolic fillings\, we define fractional p-L
aplacians on any compact\, doubling metric measure space\, and prove exist
ence\, regularity\, Harnack inequality and stability for the correspondi
ng non-homogeneous non-local equation. These results\, in turn\, rest on t
he new existence\, global Hölder regularity and stability theorems that
we prove for the Neumann problem for p-Laplacians in bounded domains of m
easure metric spaces endowed with a doubling measure that supports a Poinc
aré inequality. Our work also includes as special cases many of the prev
ious results by other authors in the Euclidean\, Riemannian and Carnot gro
up settings. Unlike other recent contributions in the metric measure space
context\, our work does not rely on the assumption that the space support
s a Poincare inequality.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Qing (UC Santa Cruz)
DTSTART:20230501T140000Z
DTEND:20230501T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/116
DESCRIPTION:Title: Potential theory in conformal geometry\nby Jie Qing (UC San
ta Cruz) as part of Geometric and functional inequalities and applications
\n\n\nAbstract\nIn this talk we would like to report my recent joint work
with Shiguang Ma\non the application of the potential theory in conformal
geometry. We will mention\nmany interesting equations in conformal geometr
y and the potential-theoretic\napproach to study them. In particular\, we
present the recent work on the extensions\nof Huber type theorem in higher
dimensions under integral conditions of various\ncurvature. We will demon
strate main ideas via the outlines of a proof of Huber Theorem.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lu Wang (Yale University)
DTSTART:20231009T140000Z
DTEND:20231009T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/117
DESCRIPTION:Title: A mean curvature flow approach to density of minimal cones\
nby Lu Wang (Yale University) as part of Geometric and functional inequali
ties and applications\n\n\nAbstract\nMinimal cones are models for singular
ities in minimal submanifolds\, as well as stationary solutions to the mea
n curvature flow. In this talk\, I will explain how to utilize mean curvat
ure flow to yield near optimal estimates on density of topologically nontr
ivial minimal cones. This is joint with Jacob Bernstein.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María del Mar González (Universidad Autónoma de Madrid)
DTSTART:20230424T140000Z
DTEND:20230424T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/118
DESCRIPTION:Title: Spectral properties of Levy Fokker-Planck equations\nby Mar
ía del Mar González (Universidad Autónoma de Madrid) as part of Geo
metric and functional inequalities and applications\n\n\nAbstract\nWe stud
y the spectrum of a fractional Laplacian equation with drift in suitable w
eighted spaces. This operator arises when studying the fractional heat equ
ation in self-similar variables. We show\, in the radially symmetric case\
, compactness\, and then calculate the eigenfunctions in terms of Laguerre
polynomials. The proofs involve Mellin transform and complex analysis met
hods. This is joint work with H. Chan\, M. Fontelos and J. Wei.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Fonseca (Carnegie Mellon University)
DTSTART:20230925T151000Z
DTEND:20230925T161000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/119
DESCRIPTION:Title: From Phase Separation in Heterogeneous Media to Learning Traini
ng Schemes for Image Denoising\nby Irene Fonseca (Carnegie Mellon Univ
ersity) as part of Geometric and functional inequalities and applications\
n\n\nAbstract\nWhat do these two themes have in common? Both are treated v
ariationally\, both deal with\n\nenergies of different dimensionalities\,
and concepts of geometric measure theory prevail in both.\n\n\nPhase Se
paration in Heterogeneous Media: Modern technologies and biological sy
stems\, such as temperature-responsive polymers and lipid rafts\, take adv
antage of engineered inclusions\, or natural heterogeneities of the medium
\, to obtain novel composite materials with specific physical properties.
To model such situations using a variational approach based on the gradien
t theory of phase transitions\, the potential and the wells may have to de
pend on the spatial position\, even in a discontinuous way\, and different
regimes should be considered.\n\n\nIn the critical case case where the sc
ale of the small heterogeneities is of the same order of the scale governi
ng the phase transition and the wells are fixed\, the interaction between
homogenization and the phase transitions process leads to an anisotropic i
nterfacial energy. The supercritical case for fixed wells is also addresse
d\, now leading to an isotropic interfacial energy. In the subcritical cas
e with moving wells\, where the heterogeneities of the material are of a l
arger scale than that of the diffuse interface between different phases\,
it is observed that there is no macroscopic phase separation and that ther
mal fluctuations play a role in the formation of nanodomains.\n\n\nThis is
joint work with Riccardo Cristoferi (Radboud University\, The Netherlands
) and Likhit Ganedi (Aachen University\, Germany)\, USA)\, based on previo
us results also obtained with Adrian Hagerty (USA) and Cristina Popovici (
USA).\n\n\n\nLearning Training Schemes for Image Denoising: Due to
their ability to handle discontinuous images while having a well-understoo
d behavior\, regularizations with total variation (TV) and total generaliz
ed variation (TGV) are some of the best known methods in image denoising.
However\, like other variational models including a fidelity term\, they c
rucially depend on the choice of their tuning parameters. A remedy is to c
hoose these automatically through multilevel approaches\, for example by o
ptimizing performance on noisy/clean image training pairs. Such methods wi
th space-dependent parameters which are piecewise constant on dyadic grids
are considered\, with the grid itself being part of the minimization. Exi
stence of minimizers for discontinuous parameters is established\, and it
is shown that box constraints for the values of the parameters lead to exi
stence of finite optimal partitions. Improved performance on some represen
tative test images when compared with constant optimized parameters is dem
onstrated.\n\n\n\nThis is joint work with Elisa Davoli (TU Wien\, Austria)
\, Jose Iglesias (U. Twente\, The Netherlands) and Rita Ferreira (KAUST\,
Saudi Arabia)\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malabika Pramanik (University of British Columbia)
DTSTART:20231204T150000Z
DTEND:20231204T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/120
DESCRIPTION:Title: Points and distances\nby Malabika Pramanik (University of B
ritish Columbia) as part of Geometric and functional inequalities and appl
ications\n\n\nAbstract\nThe Pythagorean theorem\, dating back to before 50
0 BC\, gives a\nformula for computing the Euclidean distance between two p
oints. It is\nsimply astounding that a concept so simple and classical has
continued to\nfascinate mathematicians over the ages\, and remains a tant
alizing source of\nopen problems to this day.\n\nGiven a set E\, its dista
nce set consists of numbers representing distances\nbetween points of E. I
f E is large\, how large is its distance set? How does\nthe structure of a
set influence the structure of distances in the set?\nSuch questions play
an important role in many areas of mathematics and\nbeyond. The talk will
mention a few research problems involving Euclidean\ndistances between po
ints and some landmark results associated with them.\n\nThe presentation i
s intended to be an introduction to a vibrant research\narea\; no advanced
mathematical background will be assumed.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donatella Danielli (Arizona State University)
DTSTART:20230918T140000Z
DTEND:20230918T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/121
DESCRIPTION:Title: Obstacle problems for fractional powers of the Laplacian\nb
y Donatella Danielli (Arizona State University) as part of Geometric and f
unctional inequalities and applications\n\n\nAbstract\nIn this talk we wil
l discuss two models of obstacle-type problems associated with the fractio
nal Laplacian $(−\\Delta)^s$ \, for $1 < s < 2$. Our goals are to establ
ish regularity properties of the solution and to describe the structure of
the free boundary. To this end\, we combine classical techniques from pot
ential theory and the calculus of variations with more modern methods\, su
ch as the localization of the operator and monotonicity formulas. This is
joint work with A. Haj Ali (Arizona State University)\, A. Petrosyan (Purd
ue University)\, and M. Talluri (University of Pisa).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (New York University)
DTSTART:20231002T140000Z
DTEND:20231002T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/122
DESCRIPTION:Title: Furstenberg sets estimate in the plane\nby Hong Wang (New Y
ork University) as part of Geometric and functional inequalities and appli
cations\n\n\nAbstract\nA $(s\,t)$-Furstenberg set is a set $E$ in the plan
e with the following property: there exists a $t$-dim family of lines such
that each line intersects $E$ in a $\\geq s$--dimensional set. An unpubli
shed conjecture of Furstenberg states that any $(s\,1)$-Furstenberg set ha
s dimensions at least $(3s+1)/2$. Furstenberg set problem can be viewed a
s a natural generalization of Davies's result that a Kakeya set in the pla
ne (a set that contains a line segment in any direction) has dimension 2.
\n\nWe will survey a sequence of results by Orponen\, Shmerkin\, and a re
cent result by Ren and myself that leads to the solution of Furstenberg se
ts conjecture in the plane: any $(s\,t)$-Furstenberg set has dimension at
least $\\min \\{s+t\, (3s+t)/2\, s+1\\}$.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Ni (UC San Diego)
DTSTART:20231023T140000Z
DTEND:20231023T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/123
DESCRIPTION:Title: Complex Monge-Ampère equations\, Grauert tube and estimate of
Betti numbers\nby Lei Ni (UC San Diego) as part of Geometric and funct
ional inequalities and applications\n\n\nAbstract\nIn this talk I shall ex
plain a geometric construction motivated by the study of complex Monge-Amp
ère equations\, namely the so-called Grauert tube\, and its application i
n obtaining an effective estimate on the Betti numbers of the loop space
of a compact Riemannian manifold whose sectional curvature is bounded from
below.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilhelm Schlag (Yale University)
DTSTART:20231120T150000Z
DTEND:20231120T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/124
DESCRIPTION:Title: On continuous time bubbling for the harmonic map heat flow in t
wo dimensions\nby Wilhelm Schlag (Yale University) as part of Geometri
c and functional inequalities and applications\n\n\nAbstract\nI will descr
ibe recent work with Jacek Jendrej (CNRS\, Paris Nord) and Andrew Lawrie (
MIT) on harmonic maps of finite energy from the plane to the two sphere\,
without making any symmetry assumptions. While it has been known since the
1990s that bubbling occurs along a carefully chosen sequence of times via
an elliptic Palais-Smale mechanism\, we show that this continues to hold
continuously in time. The key notion is that of the “minimal collision e
nergy” which appears in the soliton resolution result by Jendrej and Law
rie on critical equivariant wave maps.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihaela Ifrim (University of Wisconsin – Madison)
DTSTART:20240122T150000Z
DTEND:20240122T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/127
DESCRIPTION:Title: The small data global well-posedness conjecture for 1D defocusi
ng dispersive flows\nby Mihaela Ifrim (University of Wisconsin – Mad
ison) as part of Geometric and functional inequalities and applications\n\
n\nAbstract\nI will present a very recent conjecture which broadly asserts
that small data should yield global solutions for 1D defocusing dispersi
ve flows with cubic nonlinearities\, in both semilinear and quasilinear se
ttings. This conjecture was recently proved in several settings in joint w
ork with Daniel Tataru.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannick Sire (Johns Hopkins University)
DTSTART:20240205T150000Z
DTEND:20240205T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/128
DESCRIPTION:Title: Eigenvalue estimates and a conjecture of Yau\nby Yannick Si
re (Johns Hopkins University) as part of Geometric and functional inequali
ties and applications\n\n\nAbstract\nI will describe various upper and low
er bounds on the spectrum of the Laplace-Beltrami on Riemannian manifolds.
The upper bounds led to some important results in spectral geometry estab
lishing a link between the so-called conformal spectrum and branched minim
al immersions into Euclidean spheres. I will then move to describe a conje
cture by Yau on the first eigenvalue on minimal submanifolds of the sphere
\, which is known only for some examples. I will then present some recent
results where we improve quantitatively the best known lower bound (in th
e general case) of Choi and Wang of the mid 80’s. I will address some op
en problems and possible generalizations of our argument.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yumeng Ou (University of Pennsylvania)
DTSTART:20240129T150000Z
DTEND:20240129T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/129
DESCRIPTION:Title: New improvement to Falconer’s distance set conjecture in high
er dimensions\nby Yumeng Ou (University of Pennsylvania) as part of Ge
ometric and functional inequalities and applications\n\n\nAbstract\nFalcon
er’s distance set conjecture says that if a compact set in $\\mathbb{R}^
d$ has Hausdorff dimension larger than $d/2$\, then its distance set must
have positive measure. The conjecture is currently open in all dimensions.
In this talk\, I’ll discuss some recent progress towards it in dimensio
n three and higher\, which involves new techniques from the theory of radi
al projections and decoupling. This is based on joint works with Xiumin Du
\, Kevin Ren\, and Ruixiang Zhang.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Yu (University of California-Irvine)
DTSTART:20240212T150000Z
DTEND:20240212T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/130
DESCRIPTION:Title: Existence and nonexistence of effective burning velocity under
the curvature G-equation model\nby Yifeng Yu (University of California
-Irvine) as part of Geometric and functional inequalities and applications
\n\n\nAbstract\nG-equation is a well known level set model in turbulent co
mbustion\, and becomes an advective mean curvature type evolution equation
when the curvature effect is considered:\n$$\nG_t + \\left(1-d\\\, \\Div{
\\frac{DG}{|DG|}}\\right)_+|DG|+V(x)\\cdot DG=0.\n$$\n In this talk\, I wi
ll show the existence of effective burning velocity under the above curvat
ure G-equation model when $V$ is a two dimensional cellular flow\, which c
an be extended to more general two dimensional incompressible periodic flo
ws. Our proof combines PDE methods with a dynamical analysis of the Kohn-
Serfaty deterministic game characterization of the curvature G-equation ba
sed on the two dimensional structures. In three dimensions\, the effecti
ve burning velocity will cease to exist even for simple periodic shear flo
ws when the flow intensity surpasses a bifurcation value.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debdip Ganguly (Indian Institute of Technology)
DTSTART:20240219T150000Z
DTEND:20240219T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/131
DESCRIPTION:Title: Sharp Quantitative stability of Poincar\\'e-Sobolev inequality
in the hyperbolic space\nby Debdip Ganguly (Indian Institute of Techno
logy) as part of Geometric and functional inequalities and applications\n\
n\nAbstract\nThe talk is devoted to the sharp stability of\nPoincar\\'e-So
bolev inequalities in the hyperbolic space. To begin with\,\nI shall formu
late the question of the stability of the classical Sobolev\ninequality in
the Euclidean space and recall some of the seminal results\nof Bianchi-Eg
nelland Ciraolo\, Figalli and Maggi and many others. Then I\nshall deduce
the (sharp) quantitative gradient stability of the\nPoincar\\'e-Sobolev in
equalities in the hyperbolic space and the\ncorresponding Euler-Lagrange e
quation locally around a bubble (and\npossibly at a higher energy level!)
if time permits. This is joint work\nwith M.~Bhakta\, D~Karmakar\, and S.
~Mazumdar.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiqin Lu (UC Irvine)
DTSTART:20240226T150000Z
DTEND:20240226T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/132
DESCRIPTION:Title: The Spectrum of Laplacian on forms over open manifolds\nby
Zhiqin Lu (UC Irvine) as part of Geometric and functional inequalities and
applications\n\n\nAbstract\nWe computed the $L^p$ spectrum of Laplacians
on $k$-forms on hyperbolic spaces. Moreover\, we proved the $L^p$ boundedn
ess of certain resolvent of Laplacians by assuming the Ricci lower bound a
nd manifold volume growth. This generalized a result of M. Taylor\, in whi
ch bounded geometry of the manifold is assumed. This is a joint work of N.
Charalambous.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Maggi (UT Austin)
DTSTART:20240304T150000Z
DTEND:20240304T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/134
DESCRIPTION:Title: Plateau's laws for soap films\, the Allen--Cahn equation\, and
a hierarchy of Plateau-type problems\nby Francesco Maggi (UT Austin) a
s part of Geometric and functional inequalities and applications\n\n\nAbst
ract\nThe incompatibility between Plateau's laws and stable solutions to t
he Allen--Cahn equation is resolved by the formulation and analysis of a n
ew model for soap films as small volume regions with diffused interfaces.
As a result\, Plateau-type singularities are approximated by stable soluti
ons to free boundary problems for modified Allen--Cahn equations. Underlyi
ng our approach is the study of a hierarchy of Plateau problems that showc
ases the newly introduced diffused interface model at the top\, a soap fil
m capillarity model with sharp interfaces and bulk spanning at the interme
diate level\, and the classical Plateau model at the bottom. Central to ou
r analysis is a measure-theoretic revision of the topological notion of ho
motopic spanning that has been behind much recent progress on the classica
l Plateau problem.\n\nThis is joint work with Michael Novack (CMU Pittsbur
gh) and Daniel Restrepo (Johns Hopkins University).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaodong Wang (Michigan State University)
DTSTART:20240429T140000Z
DTEND:20240429T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/135
DESCRIPTION:Title: Geometric inequalities on asymptotically Poincaré-Einstein man
ifolds\nby Xiaodong Wang (Michigan State University) as part of Geomet
ric and functional inequalities and applications\n\n\nAbstract\nPoincaré-
Einstein manifolds are a class of noncompact Riemannian manifolds with a w
ell-defined boundary at infinity. They appear as the framework of AdS/CFT
correspondence in string theory and have been studied intensively. I will
discuss some recent results relating the Yamabe invariant of the boundary
and that of the interior. This is based on joint work with Zhixin Wang.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela De Silva (Columbia University)
DTSTART:20240415T140000Z
DTEND:20240415T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/136
DESCRIPTION:Title: An energy model for harmonic graphs with junctions\nby Dani
ela De Silva (Columbia University) as part of Geometric and functional ine
qualities and applications\n\n\nAbstract\nWe consider an energy model for
$N$ ordered elastic membranes subject to forcing and boundary conditions.
The heights of the membranes are described by real functions $u_1\, u_2\,.
..\,u_N$\, which minimize an energy functional involving the Dirichlet int
egral and a potential term depending on the cardinality of the set $\\{u_1
\,..\,u_N\\}$. The potential term corresponds to the physical situation wh
en consecutive membranes are glued to each other on their coincidence set.
\nThe problem can be understood as a system of $N-1$ coupled one-phase fre
e boundary problems with interacting free boundaries.\nI will review the k
nown results in the scalar case\, and discuss the free boundary regularity
when dealing with 3 or more membranes (joint with O. Savin).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tataru (UC Berkeley)
DTSTART:20240318T140000Z
DTEND:20240318T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/137
DESCRIPTION:Title: Free boundary problems for Euler type flows\nby Daniel Tata
ru (UC Berkeley) as part of Geometric and functional inequalities and appl
ications\n\n\nAbstract\nFree boundary problems are very interesting but al
so very challenging problems in fluid dynamics\, where the boundary of the
fluid is also freely moving along with the fluid flow. I will discuss t
wo such models\, governed by the compressible\, respectively the incompres
sible Euler equations. This is joint work with Mihaela Ifrim\, and in part
with Benjamin Pineau and Mitchell Taylor.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Tyson (UIUC and NSF)
DTSTART:20240506T140000Z
DTEND:20240506T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/139
DESCRIPTION:Title: Horizontal polar coordinates and H-type stability of step two C
arnot groups\nby Jeremy Tyson (UIUC and NSF) as part of Geometric and
functional inequalities and applications\n\n\nAbstract\nThe sub-Riemannian
Heisenberg group is foliated (a.e.) by a smooth family of horizontal curv
es equipped with a transversal `spherical’ measure\, with respect to whi
ch an analog of the classical Euclidean polar coordinate integration formu
la holds. Such `horizontal polar coordinates’ were first constructed by
Kor\\’anyi and Reimann (1987)\, who used them to compute explicit expres
sions for the conformal moduli of spherical ring domains with applications
to the regularity of quasiconformal mappings. We motivate the study of re
ctifiable polar coordinates in metric measure spaces\, and especially hori
zontal polar coordinates in sub-Riemannian Carnot groups\, via three osten
sibly different topics: (i) existence of coherent global fundamental solut
ions for the $p$-Laplace operators\, (ii) optimal H\\”older regularity o
f quasiconformal mappings\, and (iii) existence and uniqueness of limits a
t infinity for homogeneous Sobolev functions. Horizontal polar coordinates
exist in a restricted class of sub-Riemannian Carnot groups\, which inclu
des the Heisenberg-type groups. We discuss geometric and analytic conseque
nces of such integration formulas as well as examples and non-examples of
`polarizable’ Carnot groups. It is conjectured that the only polarizable
groups are the groups of Heisenberg type (H-type). We conclude with an ov
erview of some recent and ongoing work addressing this conjecture\, based
on the notion of the H-type deviation of a step two Carnot group.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Setti (UNIVERSITÀ DEGLI STUDI DELL'INSUBRIA)
DTSTART:20240408T140000Z
DTEND:20240408T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/140
DESCRIPTION:Title: ${\\bf L^{p}}$-parabolicity of Riemannian manifolds\nby Alb
erto Setti (UNIVERSITÀ DEGLI STUDI DELL'INSUBRIA) as part of Geometric an
d functional inequalities and applications\n\n\nAbstract\nUsing non-linear
$L^p$ capacities\, we define a notion of\n$L^p$-parabolicity of Riemannia
n manifolds which extends the usual\nparabolicity\, corresponding to $p=1$
\, to the whole range $1\\leq p\\leq\n\\infty$. $L^p$-parabolicity turns o
ut to be equivalent to the\n$L^q$-Liouville property for positive superhar
monic functions\, where $p$\nand $q$ are H\\"older conjugate exponents\, a
nd\, when $p=2$ it coincides\nwith the biparabolicity as defined by S.Far
aji and A. Grigor'yan. We\nalso provide a new capacitary characterizatio
n of the $L^1$-Liouville\nproperty. Finally we obtain an almost optimal vo
lume growth conditions implying $L^p$-parabolicity for $1< p\\leq2$ as w
ell as a sharp volume condition valid for all $1< p <\\infty$ in the
case of model manifolds.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiumin Du (Northwestern University)
DTSTART:20240909T140000Z
DTEND:20240909T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/141
DESCRIPTION:Title: Weighted refined decoupling and Falconer distance set problem\nby Xiumin Du (Northwestern University) as part of Geometric and functi
onal inequalities and applications\n\n\nAbstract\nIn this talk\, I’ll di
scuss a refinement of Bourgain--Demeter’s decoupling inequality in the w
eighted setting and the case that the directions of wave packets are in a
small neighborhood of a subspace. Such inequalities arise from the study o
f Falconer distance set problem. Combining weighted refined decoupling and
new radial projection estimates by Ren\, we proved the following result:
if a compact set $E\\subset \\mathbb{R}^d$ has Hausdorff dimension larger
than $\\frac{d}{2}+\\frac{1}{4}-\\frac{1}{8d+4}$\, where $d\\geq 4$\, then
there is a point $x\\in E$ such that the pinned distance set $\\Delta_x(E
):=\\{|x-y|:y\\in E\\}$ has positive Lebesgue measure. The result also hol
ds for dimension $d=3$\, but it requires more geometric input. Joint work
with Yumeng Ou\, Kevin Ren\, and Ruixiang Zhang.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ovidiu Savin (Columbia University)
DTSTART:20240923T140000Z
DTEND:20240923T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/142
DESCRIPTION:Title: Non C^1 solutions to the special Lagrangian equation\nby Ov
idiu Savin (Columbia University) as part of Geometric and functional inequ
alities and applications\n\n\nAbstract\nThe special Lagrangian equation (S
LE) was introduced by Harvey and Lawson in the context of calibrated geome
tries. We will talk about the construction of singular viscosity solutions
to SLE that are Lipschitz but not C^1\, and have non-minimal gradient gra
phs. We also discuss certain degenerate Bellman equations that appear in t
he study of this type of singularities. This is a joint work with C. Moone
y.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allan Greenleaf (University of Rochester)
DTSTART:20240916T130000Z
DTEND:20240916T140000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/143
DESCRIPTION:Title: Partition Optimization: Multilinear Estimates from Linear Bound
s\nby Allan Greenleaf (University of Rochester) as part of Geometric a
nd functional inequalities and applications\n\n\nAbstract\nThe boundedness
of a linear operator between two function spaces is equivalent to bounded
ness of\nthe corresponding bilinear form\, and this extends to multilinear
operators and forms. I will discuss how\,\nin some situations\, one can u
se this principle to leverage boundedness of linear operators in more vari
ables \nto obtain nontrivial and useful bounds for multilinear ones. After
discussing a general framework\, we will\nfocus on multilinear Radon tran
sforms\, particularly ones arising in configuration set problems.\nThis is
joint work with Alex Iosevich and Krystal Taylor.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabel Fernandez (University of Seville)
DTSTART:20241014T140000Z
DTEND:20241014T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/144
DESCRIPTION:Title: Free Boundary Minimal and CMC Annuli in the Ball\nby Isabel
Fernandez (University of Seville) as part of Geometric and functional ine
qualities and applications\n\n\nAbstract\nFree boundary minimal/CMC surfac
es in a 3-manifold with boundary appear as critical points for the area fu
nctional for surfaces whose boundary varies freely in the boundary of the
ambient manifold. \n\n\n\nIn this talk we will show the existence of free
boundary minimal annuli immersed in the unit ball of Euclidean 3-space\,
the first such examples other than the critical catenoid. We will also con
struct embedded free boundary CMC annuli and embedded capillary minimal an
nuli in the unit ball that are not rotational. \n\n\n\nIn the minimal case
\, this construction answers in the negative a problem of the theory that
dates back to Nitsche in 1985\, who claimed that such annuli could not exi
st. In the CMC case\, the existence of these embedded annuli is seemingly
unexpected\, and solves a problem by Wente (1995). Joint work with Mira-Ha
uswirth (for the minimal case) and Cerezo-Mira (for the CMC case).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francois Golse (École Polytechnique)
DTSTART:20241007T140000Z
DTEND:20241007T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/145
DESCRIPTION:Title: Quantum Wasserstein and Observability\nby Francois Golse (
École Polytechnique) as part of Geometric and functional inequalities and
applications\n\n\nAbstract\nThis talk discusses the observation problem i
n quantum dynamics (what kind of \npartial information is needed on the so
lution of the quantum Liouville equation in \norder to determine the solut
ion completely?) An observation inequality is obtained\nfor this problem w
hich is based on \n(1) a geometric condition due to Bardos\, Lebeau and Ra
uch\, used in the control\nof solutions to the wave equation\, and\n(2) a
quantum analogue of the optimal transport metric known as the Wasserstein\
,\nor Monge-Kantorovich distance of order 2\, introduced in an earlier col
laboration\nwith T. Paul.\nThe observation inequality so obtained involves
only effective constants\, which\ncan be computed explicitly in terms of
the various data involved.\n\n(Joint work with T. Paul)\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (Institute for the Advanced Study)
DTSTART:20241104T150000Z
DTEND:20241104T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/146
DESCRIPTION:Title: Boundary regularity of minimal surfaces\nby Camillo De Lell
is (Institute for the Advanced Study) as part of Geometric and functional
inequalities and applications\n\n\nAbstract\nThe critical points of the ar
ea functional\, usually called minimal surfaces\, have a long history in m
athematics. Perhaps the most famous examples are the solutions of the so-c
alled Plateau's problem\, i.e. surfaces which minimize the area among the
ones spanning a given contour. It is known since long that area minimizier
s can form singularities and several concepts of generalized solutions\, w
hich serve different purposes\, have been introduced in the literature sin
ce the first decades of the last century. A wide field of study is the reg
ularity of the latter objects. While there is a quite good understanding o
f the size of singularities away from the boundary in very many situations
\, the same cannot be said for the case of boundary singularities\, for wh
ich we have very satisfactory theorems only in relatively few\, albeit imp
ortant\, cases. I will review some results of the last decade which touche
d for the first time a category of problems in the area\, I will then expl
ain a recent joint work with Stefano Nardulli and Simone Steinbr\\"uchel w
hich gives a first positive answer to a question of Allard and White and f
inally\, if time allows\, mention recent further developments in the same
direction by Fleschler and Resende.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xueying Yu (Oregon State University)
DTSTART:20240930T140000Z
DTEND:20240930T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/147
DESCRIPTION:Title: Some unique continuation results for Schrödinger equations
\nby Xueying Yu (Oregon State University) as part of Geometric and functio
nal inequalities and applications\n\n\nAbstract\nThis talk focuses on a fu
ndamental concept in the field of partial differential equations — uniqu
e continuation principles. Such a principle describes the propagation of t
he zeros of solutions to PDEs. Specifically\, it answers the question: wha
t condition is required to guarantee that if a solution to a PDE vanishes
on a certain subset of the spatial domain\, then it must also vanish on a
larger subset of the domain. Motivated by Hardy’s uncertainty principle\
, Escauriaza\, Kenig\, Ponce\, and Vega were able to show in a series of p
apers that if a linear Schrödinger solution decays sufficiently fast at t
wo different times\, the solution must be trivial. In this talk\, we will
discuss unique continuation properties of solutions to higher-order Schrö
dinger equations and variable-coefficient Schrödinger equations\, and ext
end the classical Escauriaza-Kenig-Ponce-Vega type of result to these mode
ls. This is based on joint works with S. Federico-Z. Li\, and Z. Lee.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford University)
DTSTART:20241021T140000Z
DTEND:20241021T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/148
DESCRIPTION:by Eugenia Malinnikova (Stanford University) as part of Geomet
ric and functional inequalities and applications\n\n\nAbstract\nFollowing
the classical work of Donnelly and Fefferman\, we consider eigenfunctions
of the Laplace-Beltrami operators on compact Riemannian manifolds and show
that they behave as polynomials of bounded degree\, governed by the eigen
value. In particular we give a sharp version of the Bernstein inequality a
nd a sharp version of the Remez inequality for the eigenfunctions. We will
describe some applications of these inequalities if times permits.\n\n \n
\nThe talk is based on a joint work with Decio and Nazarov\, and a joint w
ork with Logunov.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng-Chao Han (Rutgers University)
DTSTART:20241111T150000Z
DTEND:20241111T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/149
DESCRIPTION:Title: Asymptotic Behavior and Symmetry of Singular Solutions to Certa
in Geometric PDEs\nby Zheng-Chao Han (Rutgers University) as part of G
eometric and functional inequalities and applications\n\n\nAbstract\nWe wi
ll discuss some results on the asymptotic behavior or symmetry of singular
solutions to \ncertain geometric PDEs. A prototype problem is the singula
r Yamabe problem\, where the solution \nbecomes singular on approach to a
singular set of dimension $k$\, and the central question is whether \nther
e is a universal growth rate of the solution on approach to the singular s
et\; whether\, when the domain of solution is the round sphere with a low
er dimensional sphere removed\, which exhibits a lot of symmetry\, then th
e singular solution also exhibits corresponding symmetry\; and whether\, i
n certain cases\, one can get more precise asymptotic behavior of the sing
ular solution?\n\nI will discuss some results\, joint with Alice Chang a
nd Paul Yang\, on the growth rate and symmetry of complete\, locally confo
rmally flat metrics on canonical domains of the round sphere with constant
Q-curvature\, which in some sense relate to earlier work of Löwner-Nire
nberg\, Schoen\, Delanoè\, and Finn-McOwen. \n\nI will also discuss joint
work with Jingang Xiong (Beijing Normal University) and\nLei Zhang (Unive
rsity of Florida)\, which proves that any positive solution of the Yamabe
equation on an asymptotically flat $n$-dimensional manifold of flatness or
der at least (n-2)/2\nand n no greater than 24 must converge at infinity e
ither to a fundamental solution of the Laplace operator on the Euclidean s
pace or to a radial Fowler solution defined on the entire Euclidean space.
\nThe flatness order (n-2)/2 is the minimal flatness order required to de
fine ADM mass in general relativity\; the dimension 24 is the dividing dim
ension of the validity of compactness of solutions to the Yamabe problem.
We also prove such alternatives for bounded solutions when n>24.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiangdong Xie (Bowling Green State University)
DTSTART:20241118T150000Z
DTEND:20241118T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/150
DESCRIPTION:Title: Uniform quasiconformal groups of nilpotent Lie groups\nby X
iangdong Xie (Bowling Green State University) as part of Geometric and fun
ctional inequalities and applications\n\n\nAbstract\nA group of quasiconf
ormal maps of a metric space X is called a uniform quasiconformal group if
there is some constant\n K such that each element of the group is K-quas
iconformal.\n Clearly a quasiconformal conjugate of a conformal group is
a uniform quasiconformal group. A natural question is when the converse
holds.\n Tukia's theorem says that if a uniform quasiconformal group of t
he n-sphere (for n at least 2) is big enough\, then the converse holds. W
e present a generalization of Tukia's theorem to uniform quasiconformal gr
oups of two classes of nilpotent Lie groups: Carnot groups and Carnot-by-C
arnot groups. This has consequences for the quasiisometric rigidity of so
lvable Lie groups and finitely generated solvable groups. This talk is ba
sed on joint work with Tullia Dymarz and David Fisher.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raoni Ponciano (Universidade Federal do ABC (UFABC))
DTSTART:20241209T150000Z
DTEND:20241209T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/151
DESCRIPTION:Title: Sharp Sobolev and Adams-Trudinger-Moser embeddings for symmetri
c functions without boundary conditions on hyperbolic spaces\nby Raoni
Ponciano (Universidade Federal do ABC (UFABC)) as part of Geometric and f
unctional inequalities and applications\n\n\nAbstract\nEmbedding theorems
for symmetric functions without any boundary conditions have been studied
on flat Riemannian manifolds\, such as the Euclidean space. However\, thes
e theorems have only been established on hyperbolic spaces for functions w
ith homogeneous Dirichlet conditions. In this presentation\, we focus on s
harp Sobolev and Adams–Trudinger–Moser embeddings for radial functions
in hyperbolic spaces\, considering both bounded and unbounded domains. On
e of the main features of our approach is that we do not assume any bounda
ry conditions for symmetric functions on geodesic balls or the entire hype
rbolic space. Our main results establish weighted Sobolev embedding theore
ms and present Adams-Trudinger-Moser type of embedding theorems. In partic
ular\, a key result is a highly nontrivial comparison between norms of the
higher order covariant derivatives and higher order derivatives of the ra
dial functions. Higher order asymptotic behavior of radial functions on hy
perbolic spaces is established to prove our main theorems. This approach i
ncludes novel radial lemmas and decay properties of higher order radial So
bolev functions defined in hyperbolic space.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford University)
DTSTART:20250127T150000Z
DTEND:20250127T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/152
DESCRIPTION:Title: Inequalities for Laplace eigenfunction.\nby Eugenia Malinni
kova (Stanford University) as part of Geometric and functional inequalitie
s and applications\n\n\nAbstract\nFollowing the classical work of Donnelly
and Fefferman\, we consider eigenfunctions of the Laplace-Beltrami operat
ors on compact Riemannian manifolds and show that they behave as polynomia
ls of bounded degree\, governed by the eigenvalue. In particular we give a
sharp version of the Bernstein inequality and a sharp version of the Reme
z inequality for the eigenfunctions. We will describe some applications of
these inequalities if times permits.\n\n \n\nThe talk is based on a joint
work with Decio and Nazarov\, and a joint work with Logunov.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongjie Dong (Brown University)
DTSTART:20250203T150000Z
DTEND:20250203T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/153
DESCRIPTION:Title: Recent results on Hopf type lemma\nby Hongjie Dong (Brown U
niversity) as part of Geometric and functional inequalities and applicatio
ns\n\n\nAbstract\nThe classical Hopf lemma asserts that if a positive harm
onic function in a sufficiently smooth domain vanishes at a boundary point
\, then its inner normal derivative at that point is strictly positive. Th
is foundational result extends to elliptic equations in non-divergence for
m with measurable coefficients\, provided the domain is $C^{1\,\\alpha}$ o
r $C^{1\,Dini}$.\n\nIn this talk\, I will discuss some recent work on rela
ted work for divergence form equations and double divergence form equation
s (adjoint equations for non-divergence form equations). Some applications
will also be mentioned.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serena Dipierro (The University of Western Australia)
DTSTART:20250217T150000Z
DTEND:20250217T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/154
DESCRIPTION:Title: A strict maximum principle for nonlocal minimal surfaces\nb
y Serena Dipierro (The University of Western Australia) as part of Geometr
ic and functional inequalities and applications\n\n\nAbstract\nSuppose tha
t two nonlocal minimal surfaces are included one into the other and touch
at a point. Then\, they must coincide. But this is perhaps less obvious th
an what it seems at first glance.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Seiringer (Institute of Science and Technology Austria)
DTSTART:20250303T150000Z
DTEND:20250303T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/155
DESCRIPTION:Title: Lieb—Thirring Inequalities: a density-functional point of vie
w\nby Robert Seiringer (Institute of Science and Technology Austria) a
s part of Geometric and functional inequalities and applications\n\n\nAbst
ract\nThe Lieb—Thirring Inequalities give a lower bound on the sum of th
e gradient norms of orthonormal functions in terms of an L^p-norm of the c
orresponding density (the sum of the squares of the functions). They impro
ve upon Sobolev Inequalities by taking into account the orthogonality of t
he functions. They were introduced in 1976 by Lieb and Thirring to give a
proof of the stability of matter in quantum mechanics\, and have since pro
ved very useful in many other applications. We present a new and simple pr
oof of a refined version of the inequalities\, and explain their connectio
n to the local density approximation in density-functional theory. (Joint
work with Jan Philip Solovej)\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kiselev (Duke University)
DTSTART:20250224T150000Z
DTEND:20250224T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/157
DESCRIPTION:Title: Suppression of chemotactic blow up by active scalar\nby Ale
xander Kiselev (Duke University) as part of Geometric and functional inequ
alities and applications\n\n\nAbstract\nThere exist many regularization me
chanisms in nonlinear PDE that help\nmake solutions more regular or preven
t formation\nof singularity: diffusion\, dispersion\, damping. A relativel
y less\nunderstood regularization mechanism is transport.\nThere is eviden
ce that in the fundamental PDE of fluid mechanics such as\nEuler or Navier
-Stokes\, transport can play\na regularizing role. In this talk\, I will d
iscuss another instance where\nthis phenomenon appears: the Patlak-Keler-S
egel\nequation of chemotaxis. Chemotactic blow up in the context of the\nP
atlak-Keller-Segel equation is an extensively studied phenomenon.\nIn rece
nt years\, it has been shown that the presence of a given fluid\nadvection
can arrest singularity\nformation given that the fluid flow possesses mix
ing or diffusion\nenhancing properties and its amplitude is sufficiently s
trong.\nThis talk will focus on the case when the fluid advection is activ
e: the\nPatlak-Keller-Segel equation coupled with fluid that obeys\nDarcy'
s law for incompressible porous media flow via gravity.\nSurprisingly\, in
this context\, in contrast with the passive advection\,\nactive fluid is
capable of suppressing chemotactic blow up at arbitrary\nsmall coupling st
rength: namely\, the system\nalways has globally regular solutions. The ta
lk is based on work joint\nwith Zhongtian Hu and Yao Yao.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giampiero Palatucci (Universita de Parma)
DTSTART:20250310T140000Z
DTEND:20250310T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/158
DESCRIPTION:Title: The De Giorgi-Nash-Moser theory for kinetic equations with nonl
ocal diffusions\nby Giampiero Palatucci (Universita de Parma) as part
of Geometric and functional inequalities and applications\n\n\nAbstract\nI
will present some recent results in the spirit of the De Giorgi-Nash-Mose
r theory for a wide class of kinetic integral equations\, where the diffus
ion term in velocity is an integro-differential operator having nonnegativ
e kernel of fractional order with merely measurable coefficients. I will m
ainly focus on boundedness estimates and Harnack inequalities. The talk is
based on a series of papers by Anceschi\, Kassmann\, Piccinini\, Weidner
and myself.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Marcos do Ó (Universidade Federal da Paraíba)
DTSTART:20250331T140000Z
DTEND:20250331T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/159
DESCRIPTION:Title: Weighted Hardy-Sobolev type inequalities with remainder\nby
João Marcos do Ó (Universidade Federal da Paraíba) as part of Geometri
c and functional inequalities and applications\n\n\nAbstract\nThis talk fo
cuses on indefinite quasilinear elliptic problems involving weighted terms
on unbounded domains\, potentially with unbounded boundaries. We will exp
lore existence results using variational methods applied to weighted funct
ion spaces and present several Liouville-type results for this class of pr
oblems.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Holmes Fay (University of Wyoming)
DTSTART:20250407T140000Z
DTEND:20250407T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/160
DESCRIPTION:Title: Weak-type inequalities for sparse operators via Bellman functio
ns\nby Irina Holmes Fay (University of Wyoming) as part of Geometric a
nd functional inequalities and applications\n\n\nAbstract\nI’ll discuss
recent joint work with Guillermo Rey and Kristina Skreb\, where we find th
e exact Bellman function governing a certain weak-type inequality for spar
se operators. We work in the dyadic setting\, where sparse operators have
become a standard tool in the last few years - largely due to the sharp re
sults one obtains from strong-type bounds. Several open problems involve w
eak-type bounds\, which are much more difficult to sharpen. We explore thi
s aspect through the Bellman function method.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Ionescu (Princeton University)
DTSTART:20250421T140000Z
DTEND:20250421T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/161
DESCRIPTION:Title: On the wave turbulence theory of 2D gravity waves\nby Alexa
nder Ionescu (Princeton University) as part of Geometric and functional in
equalities and applications\n\n\nAbstract\nOur goal in joint work with Yu
Deng and Fabio Pusateri is to initiate \nthe rigorous investigation of wav
e turbulence for water wave models. \nThis problem has received intense at
tention in recent years in the \ncontext of semilinear models\, such as se
milinear Schrodinger equations \nor multi-dimensional KdV-type equations.
However\, our situation is \ndifferent since water wave systems are quasil
inear and the solutions \ncannot be constructed by iteration of the Duhame
l formula due to \nunavoidable derivative loss.\n\nOur strategy consists o
f two main steps: (1) a deterministic energy \ninequality that provides co
ntrol of (possibly large) Sobolev norms of \nsolutions for long times\, un
der the condition that a certain \n$L^\\infty$-type norm is small\, and (2
) a propagation of randomness \nargument to prove a probabilistic regulari
ty result for long times\, in \na suitable scaling regime.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huai-Dong Cao (Lehigh University)
DTSTART:20250505T140000Z
DTEND:20250505T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/162
DESCRIPTION:Title: Linear stability and first eigenvalue estimates\nby Huai-Do
ng Cao (Lehigh University) as part of Geometric and functional inequalitie
s and applications\n\n\nAbstract\nIn this talk\, we will discuss estimates
of the first eigenvalue of the Laplace operator/Lichnerowicz Laplacian \n
and linear stability of positive Einstein manifolds\, or compact shrinking
Ricci solitons\, with respect to Perelman's $\\nu$-entropy.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Nardulli (Universidade Federal do ABC)
DTSTART:20250414T140000Z
DTEND:20250414T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/163
DESCRIPTION:Title: Interior regularity of area minimizing currents within a $C^{2\
,\\alpha}$-submanifold\nby Stefano Nardulli (Universidade Federal do A
BC) as part of Geometric and functional inequalities and applications\n\n\
nAbstract\nGiven an area-minimizing integral m-current in Σ\, we prove th
at the Hausdorff dimension\nof the interior singular set of T cannot excee
d m−2\, provided that Σ is an embedded (m+n)-submanifold of Rm+n of cla
ss C2\,α\, where α > 0. This result establishes the complete\ncounterpar
t\, in the arbitrary codimension setting\, of the interior regularity theo
ry for area-\nminimizing integral hypercurrents within a Riemannian manifo
ld of class C2\,α.\n\nThis is a joint work with Reinaldo Resende.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcello Lucia (College of Staten Island-CUNY)
DTSTART:20250428T140000Z
DTEND:20250428T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/164
DESCRIPTION:Title: A mountain pass Theorem with a lack of compactness\nby Marc
ello Lucia (College of Staten Island-CUNY) as part of Geometric and functi
onal inequalities and applications\n\n\nAbstract\nIn a very interesting pa
per by Gonçalves-Uhlenbeck\, the authors found that the moduli space of m
inimal immersions of a given closed surface in hyperbolic 3-manifolds is g
iven by the critical points of an energy functional. However\, this one ma
y fail to satisfy the standard compactness conditions\, which does not all
ow to apply immediately the classical variational theory to discuss existe
nce/uniqueness of critical points. \n\nIn this talk I will discuss this cl
ass of functionals in a more abstract framework\, stress what are the diff
iculties that need to be overcome\, and derive as a corollary existence an
d uniqueness of a critical point for the Gonçalves-Uhlenbeck\nfunctional.
\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Van Hoang Nguyen (FPT University)
DTSTART:20250512T140000Z
DTEND:20250512T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/166
DESCRIPTION:Title: The stability estimate for sharp Caffarelli-Kohn-Nirenberg ineq
uality for curl-free vector fields.\nby Van Hoang Nguyen (FPT Universi
ty) as part of Geometric and functional inequalities and applications\n\n\
nAbstract\nIn this talk\, we present a stablity version of the sharp Caffa
relli-Kohn-Nirenberg inequality for curl-free vector fields recently estab
lished by Cazacu\, Flynn and Lam. We show that the discrepancy of both sid
es of the inequality control the weighted $L_2$-norm from the curl-free ve
ctor filed to the set of extremizers. Our approach is based on the spheric
al decomposition and the sharp one dimensional inequalities. We also show
that this approach yields the sharp Caffarelli-Kohn-Nirenberg inequality f
or second order derivatives and its stablity version. (The talk is based o
n joint work with Duong Anh Tuan)\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunther Uhlmann (University of Washington)
DTSTART:20250908T140000Z
DTEND:20250908T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/168
DESCRIPTION:Title: The fractional Anisotropic Calderon Problem\nby Gunther Uhl
mann (University of Washington) as part of Geometric and functional inequa
lities and applications\n\n\nAbstract\nWe discuss some recent progress on
the anisotropic Calderón problem for the fractional Laplacian.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (CIMS-New York University)
DTSTART:20250929T140000Z
DTEND:20250929T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/169
DESCRIPTION:Title: Furstenberg sets estimate in the plane\nby Hong Wang (CIMS-
New York University) as part of Geometric and functional inequalities and
applications\n\n\nAbstract\nA $(s\,t)$-Furstenberg set is a set $E$ in the
plane with the following property: there exists a $t$-dim family of lines
such that each line intersects $E$ in a $\\geq s$--dimensional set. An un
published conjecture of Furstenberg states that any $(s\,1)$-Furstenberg s
et has dimension at least $(3s+1)/2$. The Furstenberg set problem can be
viewed as a natural generalization of Davies's result that a Kakeya set in
the plane (a set that contains a line segment in any direction) has dimen
sion 2.\n\nWe will survey a sequence of results by Orponen\, Shmerkin\, a
nd a joint work with Ren that lead to the solution of the Furstenberg set
conjecture in the plane: any $(s\,t)$-Furstenberg set has Hausdorff dimens
ion at least $\\min \\{s+t\, (3s+t)/2\, s+1\\}$.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State U.)
DTSTART:20250922T140000Z
DTEND:20250922T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/170
DESCRIPTION:Title: On the Euler equations with in-flow and out-flow boundary condi
tions\nby Anna Mazzucato (Penn State U.) as part of Geometric and func
tional inequalities and applications\n\n\nAbstract\nI will discuss recent
results concerning the well-posedness and regularity for the incompressibl
e Euler equations when in-flow and out-flow boundary conditions are impo
sed on parts of the boundary\, motivated by applications to boundary layer
s. This is joint work with Gung-Min Gie (U. Louisville\, USA) and James Ke
lliher (UC Riverside\, USA). I will also discuss energy dissipation and en
strophy production in the zero-viscosity limit at outflow\, joint work w
ith (Jincheng Yang\, U Chicago and IAS)\, Vincent Martinez (CUNY\, Hunter
College)\, and Alexis Vasseur (UT Austin).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruoyu Wang (Yale University)
DTSTART:20250519T140000Z
DTEND:20250519T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/171
DESCRIPTION:Title: Carleman inequalities for fractional Laplacians\nby Ruoyu W
ang (Yale University) as part of Geometric and functional inequalities and
applications\n\n\nAbstract\nInside any fixed open subset of compact manif
olds\, Laplace eigenfunctions cannot decay faster than exponentially (in e
igenvalue): this is called a Carleman inequality. We discuss a new Carlema
n inequality for fractional Laplacian quasimodes\, and a few related resul
ts\, with their application in obtaining new decay estimates for linearise
d gravity and capillary water waves.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20251006T130000Z
DTEND:20251006T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/172
DESCRIPTION:by No Talk as part of Geometric and functional inequalities an
d applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wang (IHES)
DTSTART:20251020T140000Z
DTEND:20251020T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/174
DESCRIPTION:Title: Geometry of Riemann surfaces through the lens of probability\nby Yilin Wang (IHES) as part of Geometric and functional inequalities a
nd applications\n\n\nAbstract\nThe goal of this talk is to showcase how we
can use stochastic processes to study the geometry of surfaces. After rec
alling basic facts about surfaces with constant curvature\, their length s
pectrum\, and Brownian motion on them\, we use the Brownian loop measure t
o express the lengths of closed geodesics on a hyperbolic surface and zeta
-regularized determinant of the Laplace-Beltrami operator. This gives a to
ol to study the length spectra of a hyperbolic surface and we obtain a new
identity between the length spectrum of a compact surface and that of the
same surface with an arbitrary number of additional cusps. This is mainly
based on a recent joint work with Yuhao Xue (IHES).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vlassis Mastrantonis (University of Maryland)
DTSTART:20250526T140000Z
DTEND:20250526T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/175
DESCRIPTION:Title: $L^p$-smoothing in the study of Mahler volumes\, Bergman kernel
s\, and the isotropic constant\nby Vlassis Mastrantonis (University of
Maryland) as part of Geometric and functional inequalities and applicatio
ns\n\n\nAbstract\nWe discuss three problems: Mahler’s conjectures\, Bour
gain’s slicing problem\, and Blocki’s conjecture on the sharp lower bo
und of Bergman kernels of tube domains. Starting from Nazarov’s bound on
the Mahler volume\, and our subsequent extension to the non-symmetric cas
e\, we show how Mahler’s and Blocki’s conjectures are two faces of the
same coin. By introducing an L^p smoothing of the support function\, we d
efine the L^p-polar body\, and interpret the Bergman kernels of tube domai
ns as the L^1-Mahler volume. The classical Mahler volume corresponds to th
e L^infty-case. This perspective allows us to use well-established methods
to obtain sharp lower bounds for the Bergman kernels of tube domains in d
imension two\, verifying Błocki’s conjecture in that dimension\, as wel
l as an upper bound in all dimensions. Time permitting\, we discuss functi
onal extensions and a functional L^p Santaló inequality\, following the a
pproach of Nakamura—Tsuji via the Fokker—Planck heat flow. We also exp
lore applications of L^p-polarity to Bourgain’s slicing problem\, leadin
g to an “easy” bound on the isotropic constant through complex geometr
ic methods involving Ricci curvature and Bergman Kahler metrics.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guido De Philippis (CIMS-New York University)
DTSTART:20251027T140000Z
DTEND:20251027T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/176
DESCRIPTION:Title: Min-max construction of anisotropic minimal hypersurfaces\n
by Guido De Philippis (CIMS-New York University) as part of Geometric and
functional inequalities and applications\n\n\nAbstract\nWe use the min-max
construction to find closed hypersurfaces which are stationary with resp
ect to anisotropic elliptic integrands in any closed n-dimensional man
ifold. These surfaces are regular outside a closed set of zero n-3 dimen
sion. The critical step is to obtain a uniform upper bound for density rat
ios in the anisotropic min-max construction. This confirms a conjecture po
sed by Allard. The talk is based on a joint work with A. De Rosa and Y. Li
.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20251013T130000Z
DTEND:20251013T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/177
DESCRIPTION:by No Talk as part of Geometric and functional inequalities an
d applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Brendle (Columbia University)
DTSTART:20251117T150000Z
DTEND:20251117T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/178
DESCRIPTION:Title: Systolic inequalities and the Horowitz-Myers conjecture\nby
Simon Brendle (Columbia University) as part of Geometric and functional i
nequalities and applications\n\n\nAbstract\nLet $n$ be an integer with $3
\\leq n \\leq 7$\, and let $g$ be a Riemannian metric on $B^2 \\times T^{n
-2}$ with scalar curvature at least $-n(n-1)$. We establish an inequality
relating the systole of the boundary to the infimum of the mean curvature
on the boundary. As a consequence\, we obtain a new positive energy theore
m where equality holds for the Horowitz-Myers metrics. This is joint work
with Pei-Ken Hung.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasa Sesum (Rutgers University)
DTSTART:20251201T150000Z
DTEND:20251201T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/179
DESCRIPTION:Title: Instability of peanut solution\nby Natasa Sesum (Rutgers Un
iversity) as part of Geometric and functional inequalities and application
s\n\n\nAbstract\nPeanut solutions are examples of degenerate neckpinches i
n both\, the Ricci flow and the mean curvature flow. We show that in every
neighborhood of peanut solution there is an initial data developing a sph
erical singularity\, and at the same time there is an initial data develo
ping a nondegenerate neckpinch singularity. This shows the peanut type sol
ution is highly unstable. This is a joint work with Angenent and Daskalopo
ulos.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Fusco (Università degli Studi di Napoli Federico II)
DTSTART:20251110T150000Z
DTEND:20251110T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/182
DESCRIPTION:Title: The isoperimetric inequality for the capillary energy outside c
onvex sets\nby Nicola Fusco (Università degli Studi di Napoli Federic
o II) as part of Geometric and functional inequalities and applications\n\
n\nAbstract\nI will present an isoperimetric problem for capillary surface
s with a general contact angle $ \\theta \\in (0\, \\pi) $\, lying outsid
e a convex set. We will see that the capillary energy of any set $E$ conta
ined in the complement of a convex set $C$ is strictly larger than that o
f a spherical cap with the same volume and the same contact angle sitting
on a flat support\, unless $E$ is a spherical cap lying on a facet of $C$
. This result extends to the case of general contact angles a well-known
relative isoperimetric inequality\, corresponding to the case $ \\theta =
\\pi/2$\, proved in 2007 by Choe-Ghomi-Ritoré. \nJoint paper with Vesa Ju
lin\, Massimiliano Morini and Aldo Pratelli.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eudes Barboza (Universidade Federal Rural do Pernambuco)
DTSTART:20250721T140000Z
DTEND:20250721T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/183
DESCRIPTION:Title: Existence results for some elliptic problems in $\\mathbb{R}^N$
including variable exponents above the critical growth\nby Eudes Barb
oza (Universidade Federal Rural do Pernambuco) as part of Geometric and fu
nctional inequalities and applications\n\n\nAbstract\nIn this talk\, we e
stablish existence results for the following class of equations involving
variable exponents\n$$\n-\\Delta u +u=|u(x)|^{p(|x|)-1}u(x)+ \\lambda|u(x)
|^{q(|x|)-1}u(x)\, \\quad x\\in\\mathbb{R}^{N}\,\n$$\nwhere $\\lambda\\geq
0$\, $N\\geq 3$ and $p\,q:[0\,+\\infty)\\rightarrow(1\,+\\infty)$ are radi
al continuous functions which satisfy suitable conditions. For this purpos
e\, it is sufficient to consider either subcriticality or criticality with
in a small region near the origin. Surprisingly\, outside this region\, th
e nonlinearity may oscillate between subcritical\, critical\, and supercri
tical growth in the Sobolev sense. Our approach enables the use of the var
iational methods to tackle problems with variable exponents in $\\mathbb
{R}^N$ without imposing restrictions outside of a neighborhood of zero.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Clemente (Federal Rural University of Pernambuco)
DTSTART:20250728T140000Z
DTEND:20250728T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/184
DESCRIPTION:Title: $p$-Harmonic Functions in the Upper Half-space\nby Rodrigo
Clemente (Federal Rural University of Pernambuco) as part of Geometric and
functional inequalities and applications\n\n\nAbstract\nIn this talk\, we
will discuss the existence\, nonexistence\, and qualitative properties of
$p$-harmonic functions in the upper half-space that satisfy nonlinear bou
ndary conditions\, for $1<\;p<\;N$. We will also present a symmetry re
sult for positive solutions\, obtained through the method of moving planes
.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Colding (MIT)
DTSTART:20251208T150000Z
DTEND:20251208T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/185
DESCRIPTION:Title: Deficit function and log Sobolev inequality\nby Tobias Cold
ing (MIT) as part of Geometric and functional inequalities and application
s\n\n\nAbstract\nThere is a long history of parabolic monotonicity formula
s that developed independently from several different fields and a much mo
re recent elliptic theory. The elliptic theory can be localized and there
are additional monotone quantities. There is also a surprising link: Takin
g a high-dimensional limit of the right elliptic monotonicity can give a p
arabolic one as a limit. Poincare was the first to observe such a connecti
on. We introduce two deficit functions\, one elliptic and one parabolic\,
then show that the parabolic deficit is pointwise the limit of the ellipti
c and\, that the elliptic satisfies an equation that converges to the equa
tion for the parabolic. These pointwise quantities and their equations rec
over the monotonicities and leads to an elliptic proof of the log Sobolev
inequality as well as new concentration of measure phenomena. The talk is
based on joint work with Bill Minicozzi.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Piccione (University of São Paulo)
DTSTART:20260420T140000Z
DTEND:20260420T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/186
DESCRIPTION:by Paolo Piccione (University of São Paulo) as part of Geomet
ric and functional inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Detang Zhou (Universidade Federal Fluminense)
DTSTART:20260119T150000Z
DTEND:20260119T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/187
DESCRIPTION:Title: Eigenvalue estimate on self shrinkers\nby Detang Zhou (Univ
ersidade Federal Fluminense) as part of Geometric and functional inequalit
ies and applications\n\n\nAbstract\nIn this talk\, I will discuss the drif
ted Laplacian $\\Delta_f$ on a hypersurface $M$ in a Ricci shrinker $(\\ov
erline{M}\,g\,f)$. We proved that the spectrum of $\\Delta_f$ is discrete
for immersed hypersurfaces with bounded weighted mean curvature in a Ricc
i shrinker. I will also discuss a lower bound for the first nonzero eigenv
alue of $\\Delta_f$ when the hypersurface is an embedded $f$-minimal one
. This estimate contains the case of compact minimal hypersurfaces in a p
ositive Einstein manifold\, in particular Choi and Wang's estimate for min
imal hypersurfaces. The estimate also recovers the ones of Ding-Xin and Br
endle-Tsiamis on self-shrinkers.This is a joint work with Franciele Conrad
o.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fausto Ferrari (Università di Bologna)
DTSTART:20260126T150000Z
DTEND:20260126T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/188
DESCRIPTION:Title: Recent regularity results in free boundary problems\nby Fau
sto Ferrari (Università di Bologna) as part of Geometric and functional i
nequalities and applications\n\n\nAbstract\nWe deal with regularity result
s about one and two-phase free boundary problems. In particular\, we discu
ss the regularity of the free boundary in the viscosity setting. Moreover\
, we introduce some recent results obtained in collaboration with Claudia
Lederman IMAS - CONICET and Departamento de Matematica\, Facultad de Cie
ncias Exactas y Naturales\,Universidad de Buenos Aires\, Argentina\, about
flat free boundaries of viscosity solutions of two-phase problems gov
erned by the p(x)-Laplace operator. This research is part of a long standi
ng project\, where many people gave scientific contributions\, and started
with the pioneering papers of Luis Caffarelli.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Muratori (Politecnico di Milano)
DTSTART:20260202T150000Z
DTEND:20260202T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/189
DESCRIPTION:Title: A characterization of stochastic incompleteness via nonlinear d
iffusion\nby Matteo Muratori (Politecnico di Milano) as part of Geomet
ric and functional inequalities and applications\n\n\nAbstract\nA Riemanni
an manifold M is stochastically incomplete if the trajectories of the Brow
nian motion acting on it can diverge\, in finite time\, with non-zero prob
ability. Since the heat kernel of M is precisely the transition probabilit
y density of the Brownian motion\, this is equivalent to the fact that the
heat semigroup loses mass. By exploiting the linearity of the heat equati
on\, it is not difficult to see that such a property is also equivalent to
the existence of multiple bounded solutions of parabolic Cauchy problems
as well as to the existence of non-trivial bounded solutions of the ellipt
ic resolvent equation.\n\nThe main subject of this seminar is the extensio
n of this kind of characterizations to certain non-linear PDEs of diffusiv
e type. Specifically\, I will describe some recent equivalence results bet
ween stochastic incompleteness and non-uniqueness properties of a general
class of nonlinear diffusion equations\, known as filtration equations\, a
nd related semilinear elliptic equations\, obtained in collaboration with
G. Grillo\, K. Ishige\, and F. Punzo.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Trombetti (Università degli Studi di Napoli "Federico II
")
DTSTART:20260223T150000Z
DTEND:20260223T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/190
DESCRIPTION:Title: On a Class of Free Boundary Problems Related to Thermal Insulat
ion\nby Cristina Trombetti (Università degli Studi di Napoli "Federic
o II") as part of Geometric and functional inequalities and applications\n
\n\nAbstract\nFree boundary problems in partial differential equations (PD
Es) constitute a class of mathematical models in which both the solution a
nd the domain where it is defined are unknown and must be determined simul
taneously. Such problems naturally arise in a wide range of physical and e
ngineering applications\, including fluid dynamics\, solid mechanics\, and
heat conduction.\n\nIn this talk\, we focus on a class of free boundary p
roblems related to thermal insulation. In these models\, the free boundary
may represent either an interface whose location is not known a priori or
the optimal configuration of an insulating material. The aim is to charac
terize the resulting free boundaries and to analyze how their geometry inf
luences heat loss and energy efficiency.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Monticelli (Politecnico di Milano)
DTSTART:20260309T140000Z
DTEND:20260309T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/191
DESCRIPTION:Title: Rigidity and classification results for critical elliptic equat
ions\nby Dario Monticelli (Politecnico di Milano) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nIn this talk
I will present some recent classification and rigidity results for positiv
e solutions to some classical nonlinear elliptic equations with critical g
rowth\, both in the Euclidean and in the Riemannian setting. If time permi
ts I will also briefly discuss extensions to degenerate/singular problems
and to the subriemannian setting\, where similar rigidity and classificati
on results occur. The results are joint works with G. Catino (Politecnico
di Milano)\, Y.Y. Li (Rutgers University)\, A. Roncoroni (Politecnico di M
ilano) and X. Wang (Michigan State University).\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aldo Pratelli (University of Pisa)
DTSTART:20260302T150000Z
DTEND:20260302T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/192
DESCRIPTION:Title: Small minimal clusters in manifolds\nby Aldo Pratelli (Univ
ersity of Pisa) as part of Geometric and functional inequalities and appli
cations\n\n\nAbstract\nIn this talk\, we will consider the isoperimetric p
roblem for $m$-clusters in a compact manifold. Since minimal clusters in $
\\mathbb{R}^N$ are known to be connected\, and a Riemannian manifold local
ly looks like $\\mathbb{R}^N$\, one might easily guess that minimal cluste
rs with sufficiently small total volume should be connected. This is well-
known for the case of sets (so\, with $m=1$)\, and we will present a recen
t proof of this fact for the general case. The situation becomes largely d
ifferent if one\, instead\, considers Finsler manifolds: in this case we c
an prove that small minimal clusters can have up to m connected components
\, and an explicit example shows that they do not have to be connected. We
will conclude by considering the intermediate case of the "fixed-norm" ma
nifolds\, and by addressing the optimality issue for the possible number o
f connected components. Most the results are contained in different joint
papers with D. Carazzato\, L. Felicetti\, S. Nardulli\, R. Ponciano.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Olsen (University of St. Andrews)
DTSTART:20260209T150000Z
DTEND:20260209T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/193
DESCRIPTION:Title: The Baire Hierarchy\, multifractal decomposition sets and $\\Pi
^0_{\\gamma}$-completeness\nby Lars Olsen (University of St. Andrews)
as part of Geometric and functional inequalities and applications\n\n\nAbs
tract\nThis talk will discuss the position of the so-called ``multifractal
decomposition sets'' in the Baire Hierarchy. In particular\, we will prov
e that ``multifractal decomposition sets'' are the building blocks from wh
ich all other $\\Pi^0_{\\gamma}$-sets can be constructed\; more precisely\
, ``multifractal decomposition sets'' are $\\Pi^0_{\\gamma}$-complete. As
an application we find the position of the classical Eggleston-Besicovitch
set in the Baire Hierarchy.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Case (Penn State University)
DTSTART:20260323T140000Z
DTEND:20260323T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/194
DESCRIPTION:Title: The sharp $L^2$-Michael-Simon-Sobolev inequality via conformal
geometry\nby Jeffrey Case (Penn State University) as part of Geometric
and functional inequalities and applications\n\n\nAbstract\nWe use method
s from conformal geometry to show that the best constant in the $L^2$-Mich
ael-Simon-Sobolev inequality for an $n$-dimensional minimal submanifold of
Euclidean $(m+n)$-space is equal to the sharp constant in the usual $L^2$
-Sobolev inequality on $\\mathbb{R}^n$ as computed by Aubin and Talenti. T
his removes the codimension restriction $m \\leq 2$ from a result of Brend
le. This is joint work with Dawit Mengesha.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisabeth Werner (Case Western Reserve University)
DTSTART:20260216T150000Z
DTEND:20260216T160000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/195
DESCRIPTION:Title: The $L_p$-Floating Area\, Entropy\, and Isoperimetric Inequalit
ies on the Sphere\nby Elisabeth Werner (Case Western Reserve Universit
y) as part of Geometric and functional inequalities and applications\n\n\n
Abstract\nThe floating area was previously investigated as a natural exten
sion of classical affine surface area to non-Euclidean convex bodies in sp
aces of constant positive curvature. We introduce the family of $L_p$-floa
ting areas for spherical convex bodies\, as an analog to $L_p$-affine sur
face area measures \nfrom Euclidean geometry. We investigate a duality for
mula\, monotonicity and isoperimetric inequalities for this new family of
curvature measures on spherical convex bodies.\n \n\nIf time permits\,
we introduce a new entropy functional for spherical convex bodies using th
e $L_p$-floating area\, and a dual isoperimetric inequality is established
.\n \n\nBased on joint works with Florian Besau.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Sormani (CUNY-Lehman College)
DTSTART:20260330T140000Z
DTEND:20260330T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/196
DESCRIPTION:Title: Geometric Stability of the Schoen-Yau Zero Mass Theorem: A Surv
ey\nby Christina Sormani (CUNY-Lehman College) as part of Geometric an
d functional inequalities and applications\n\n\nAbstract\nIn 1979\, Schoen
and Yau proved their 3D Positive Mass Theorem which is a comparison theor
em and a rigidity theorem. The comparison theorem compares Euclidean spa
ce with a three dimensional asymptotically flat Riemannian manifold\, M\,
with nonnegative scalar curvature and concludes that the ADM mass of M is
greater than or equal to the ADM mass of Euclidean Space (which is zero).
Their zero mass rigidity theorem states that if such a manifold\, M\,
has zero ADM mass then it is isometric to Euclidean space. Here we re
view results and open questions on the geometric stability or almost rigid
ity of their zero mass rigidity theorem: if such a manifold\, M\, has al
most zero mass\, how close is the geometry of M to that of Euclidean space
? We will review examples of sequences of such manifolds with mass appro
aching zero whose geometry is quite far from that of Euclidean space and r
eview theorems proving that (under additional hypotheses) regions in these
manifolds may have geometries that converge to regions in Euclidean space
. Although there has been much progress\, it is still an open question
(even in dimension three): exactly which geometric notion of convergence a
nd closeness works best to capture the geometric stability of this famous
rigidity theorem.\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Sinestrari (Università di Roma "Tor Vergata")
DTSTART:20260413T140000Z
DTEND:20260413T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/197
DESCRIPTION:by Carlo Sinestrari (Università di Roma "Tor Vergata") as par
t of Geometric and functional inequalities and applications\n\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Milman (Israel Institute of Technology)
DTSTART:20260511T140000Z
DTEND:20260511T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/198
DESCRIPTION:by Emanuel Milman (Israel Institute of Technology) as part of
Geometric and functional inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (UC Berkely)
DTSTART:20260406T140000Z
DTEND:20260406T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/199
DESCRIPTION:by Ruixiang Zhang (UC Berkely) as part of Geometric and functi
onal inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gigliola Staffilani (MIT)
DTSTART:20260427T140000Z
DTEND:20260427T150000Z
DTSTAMP:20260314T084004Z
UID:GeomInequAndPDEs/200
DESCRIPTION:by Gigliola Staffilani (MIT) as part of Geometric and function
al inequalities and applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeomInequAndPDEs/200/
END:VEVENT
END:VCALENDAR