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BEGIN:VEVENT
SUMMARY:William Beckner (University of Texas at Austin)
DTSTART;VALUE=DATE-TIME:20200720T130000Z
DTEND;VALUE=DATE-TIME:20200720T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/1
DESCRIPTION:Title: Symmetry in Fourier Analysis – Heisenberg to Stein-We
iss\nby William Beckner (University of Texas at Austin) as part of Geometr
ic and functional inequalities and applications\n\n\nAbstract\nEmbedded sy
mmetry within the Heisenberg group is used to couple geometric insight and
analytic calculation to obtain a new sharp Stein-Weiss inequality with mi
xed homogeneity on the line of duality. SL(2\,R) invariance and Riesz pote
ntials define a natural bridge for encoded information that connects disti
nct geometric structures. Insight for Stein-Weiss integrals is gained from
vortex dynamics\, embedding on hyperbolic space\, and conformal geometry.
The intrinsic character of the Heisenberg group makes it the natural play
ing field on which to explore the laws of symmetry and the interplay betwe
en analysis and geometry on a manifold.\n\nZoom link: https://brown.zoom.u
s/j/91683612862\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Malchiodi (Scuola Normale Superiore)
DTSTART;VALUE=DATE-TIME:20200720T140000Z
DTEND;VALUE=DATE-TIME:20200720T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/2
DESCRIPTION:Title: On the Sobolev quotient in sub-Riemannian geometry\nby
Andrea Malchiodi (Scuola Normale Superiore) as part of Geometric and funct
ional inequalities and applications\n\n\nAbstract\nWe consider three-dimen
sional CR manifolds\, which are modelled on the Heisenberg group.\nWe intr
oduce a natural concept of “mass” and prove its positivity under the c
ondition that\nthe scalar curvature is positive and in relation to their (
holomorphic) embeddability properties.\nWe apply this result to the CR Yam
abe problem\, and we discuss extremality of Sobolev-type\nquotients\, givi
ng some counterexamples for “Rossi spheres”.\nThis is joint work with
J.H.Cheng and P.Yang.\n\nZoom link: https://brown.zoom.us/j/91683612862\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Cabre (ICREA and UPC (Barcelona))
DTSTART;VALUE=DATE-TIME:20200727T130000Z
DTEND;VALUE=DATE-TIME:20200727T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/3
DESCRIPTION:Title: Stable solutions to semilinear elliptic equations are s
mooth up to dimension 9\nby Xavier Cabre (ICREA and UPC (Barcelona)) as pa
rt of Geometric and functional inequalities and applications\n\n\nAbstract
\nThe regularity of stable solutions to semilinear elliptic PDEs has been
studied since the 1970's. In dimensions 10 and higher\, there exist singul
ar stable energy solutions. In this talk I will describe a recent work in
collaboration with Figalli\, Ros-Oton\, and Serra\, where we prove that st
able solutions are smooth up to the optimal dimension 9. This answers to a
n open problem posed by Brezis in the mid-nineties concerning the regulari
ty of extremal solutions to Gelfand-type problems.\n\nZoom link: https://b
rown.zoom.us/j/91683612862\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jerison (MIT)
DTSTART;VALUE=DATE-TIME:20201109T140000Z
DTEND;VALUE=DATE-TIME:20201109T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/4
DESCRIPTION:by David Jerison (MIT) as part of Geometric and functional ine
qualities and applications\n\nInteractive livestream: https://brown.zoom.u
s/j/91683612862\nAbstract: TBA\n
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiming Zhao (MIT)
DTSTART;VALUE=DATE-TIME:20200803T130000Z
DTEND;VALUE=DATE-TIME:20200803T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/5
DESCRIPTION:Title: Reconstruction of convex bodies via Gauss map\nby Yimin
g Zhao (MIT) as part of Geometric and functional inequalities and applicat
ions\n\n\nAbstract\nIn this talk\, we will discuss the Gauss image problem
\, a problem that reconstructs the shape of a convex body using partial da
ta regarding its Gauss map. In the smooth category\, this problem reduces
to a Monge-Ampere type equation on the sphere. But\, we will use a variati
onal argument that works with generic convex bodies. This is joint work wi
th Károly Böröczky\, Erwin Lutwak\, Deane Yang\, and Gaoyong Zhang.\n\n
Zoom link: https://brown.zoom.us/j/91683612862\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20200817T140000Z
DTEND;VALUE=DATE-TIME:20200817T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/6
DESCRIPTION:Title: Rigidity Results for Allen-Cahn Equation\nby Juncheng W
ei (University of British Columbia) as part of Geometric and functional in
equalities and applications\n\nInteractive livestream: https://brown.zoom.
us/j/91683612862\n\nAbstract\nI will discuss two recent rigidity results f
or Allen-Cahn: the first is Half Space Theorem which states that if the no
dal set lies above a half space then it must be one-dimensional. The secon
d result is the stability of Cabre-Terra saddle solutions in R^8\, R^{10}
and R^{12}.\n
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fengbo Hang (New York University)
DTSTART;VALUE=DATE-TIME:20200810T140000Z
DTEND;VALUE=DATE-TIME:20200810T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/7
DESCRIPTION:Title: Concentration compactness principle in critical dimensi
ons revisited\nby Fengbo Hang (New York University) as part of Geometric a
nd functional inequalities and applications\n\n\nAbstract\nConcentration c
ompactness principle for functions in $W^{1\,n}_0$ on a\nn-dimensional dom
ain was introduced by Lions in 1985 with the\nMoser-Trudinger inequality i
n mind. We will discuss some further\nrefinements after Cerny-Cianchi-Henc
l's improvement in 2013. These\nrefinements unifiy the approach for n=2 an
d n>2 cases and work for higher\norder or fractional order Sobolev spaces
as well. They are motivated by\nand closely related to the recent derivati
on of Aubin's Moser-Trudinger\ninequality for functions with vanishing hig
her order moments on the\nstandard 2-sphere (one may see\nhttp://math.sjtu
.edu.cn/conference/2020p&g/videos/20200707_FengboHang_M1.html\nfor that pa
rt).\n\nZoom link: https://brown.zoom.us/j/91683612862\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert Frank (CalTech)
DTSTART;VALUE=DATE-TIME:20200824T143000Z
DTEND;VALUE=DATE-TIME:20200824T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/8
DESCRIPTION:by Rupert Frank (CalTech) as part of Geometric and functional
inequalities and applications\n\nInteractive livestream: https://brown.zoo
m.us/j/91683612862\n\nAbstract\nTBA\n\nPlease note the special time of thi
s talk.\n
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pengfei Guan (McGill University)
DTSTART;VALUE=DATE-TIME:20200831T140000Z
DTEND;VALUE=DATE-TIME:20200831T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/9
DESCRIPTION:Title: A mean curvature type flow and isoperimetric problem in
warped product spaces\nby Pengfei Guan (McGill University) as part of Geo
metric and functional inequalities and applications\n\nInteractive livestr
eam: https://brown.zoom.us/j/91683612862\n\nAbstract\nWe will discuss a me
an curvature type flow with the goal to solve isoperimetric problem. The f
low is induced from the variational properties associated to conformal Kil
ling fields. Such flow was first introduced in space forms in a previous j
oint work with Junfang Li\, where we provided a flow approach to the class
ical isoperimetric inequality in space form. Later\, jointly with Junfang
Li and Mu-Tao Wang\, we considered the similar flow in warped product spac
es with general base. Under some natural conditions\, the flow preserves t
he volume of the bounded domain enclosed by a graphical hypersurface\, and
monotonically decreases the hypersurface area. Furthermore\, the regulari
ty and convergence of the flow can be established\, thereby the isoperimet
ric problem in warped product spaces can be solved. The flow serves as an
interesting way to achieve the optimal solution to the isoperimetric probl
em.\n
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Hebey (Université de Cergy-Pontoise)
DTSTART;VALUE=DATE-TIME:20201116T140000Z
DTEND;VALUE=DATE-TIME:20201116T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/10
DESCRIPTION:by Emmanuel Hebey (Université de Cergy-Pontoise) as part of G
eometric and functional inequalities and applications\n\nInteractive lives
tream: https://brown.zoom.us/j/91683612862\n\nAbstract\nTBA\n
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Wang (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20200907T130000Z
DTEND;VALUE=DATE-TIME:20200907T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/11
DESCRIPTION:by Yi Wang (Johns Hopkins University) as part of Geometric and
functional inequalities and applications\n\nInteractive livestream: https
://brown.zoom.us/j/91683612862\nAbstract: TBA\n
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongmeng Xi (NYU)
DTSTART;VALUE=DATE-TIME:20200803T140000Z
DTEND;VALUE=DATE-TIME:20200803T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/12
DESCRIPTION:Title: An isoperimetric type inequality via a modified Steiner
symmetrization scheme\nby Dongmeng Xi (NYU) as part of Geometric and func
tional inequalities and applications\n\n\nAbstract\nWe establish an affine
isoperimetric inequality using a symmetrization scheme that involves a to
tal of 2n elaborately chosen Steiner symmetrizations at a time. The necess
ity of this scheme\, as opposed to the usual Steiner symmetrization\, will
be demonstrated with an example. This is a joint work with Dr. Yiming Zha
o.\n\nZoom link: https://brown.zoom.us/j/91683612862\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phan Thành Nam (LMU Munich)
DTSTART;VALUE=DATE-TIME:20200921T130000Z
DTEND;VALUE=DATE-TIME:20200921T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/13
DESCRIPTION:by Phan Thành Nam (LMU Munich) as part of Geometric and funct
ional inequalities and applications\n\nInteractive livestream: https://bro
wn.zoom.us/j/91683612862\nAbstract: TBA\n
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Minicozzi (MIT)
DTSTART;VALUE=DATE-TIME:20201026T140000Z
DTEND;VALUE=DATE-TIME:20201026T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T034934Z
UID:GeomInequAndPDEs/14
DESCRIPTION:by William Minicozzi (MIT) as part of Geometric and functional
inequalities and applications\n\nInteractive livestream: https://brown.zo
om.us/j/91683612862\nAbstract: TBA\n
URL:https://brown.zoom.us/j/91683612862
END:VEVENT
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