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BEGIN:VEVENT
SUMMARY:David Bate (Warwick University)
DTSTART;VALUE=DATE-TIME:20210209T133000Z
DTEND;VALUE=DATE-TIME:20210209T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/1
DESCRIPTION:Title: Characterising rectifiable metric spaces using tangent measures\
nby David Bate (Warwick University) as part of Analysis Seminar Trento\n\n
\nAbstract\nA classical result of Marstrand and Mattila states that a set
$S\\subset \\mathbb{R}^m$ (satisfying mild dimension assumptions) is $n$-r
ectifiable if and only if\, for $\\mathcal{H}^n$-a.e. $x\\in S$\, all tang
ent spaces of $\\mathcal{H}^n|_S$ at $x$ are $n$-dimensional subspaces. He
re a "tangent space" is defined using Preiss's tangent measures.\n\nThis t
alk will present a generalisation of this result that replaces the ambient
$\\mathbb{R}^m$ with an arbitrary metric space.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ihsan Topaloglu (Virginia Commonwealth University)
DTSTART;VALUE=DATE-TIME:20210216T133000Z
DTEND;VALUE=DATE-TIME:20210216T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/2
DESCRIPTION:Title: A nonlocal isoperimetric problem with density perimeter\nby Ihsa
n Topaloglu (Virginia Commonwealth University) as part of Analysis Seminar
Trento\n\n\nAbstract\nIn this talk I will present recent results on a var
iant of Gamow's liquid drop model where we consider the mass-constrained m
inimization of an energy functional given as the sum of a density perimete
r term and a nonlocal interaction term of Riesz type. In particular\, I wi
ll show that for a wide class of density functions this energy admits a mi
nimizer for any choice of parameters\, and that for monomial densities the
unique minimizer is given by the ball of fixed volume when the nonlocal e
ffects are sufficiently small. This is a joint work with S. Alama\, L. Bro
nsard\, and A. Zuniga.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Neumayer (Northwestern University)
DTSTART;VALUE=DATE-TIME:20210223T133000Z
DTEND;VALUE=DATE-TIME:20210223T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/3
DESCRIPTION:Title: Quantitative stability for minimizing Yamabe metrics\nby Robin N
eumayer (Northwestern University) as part of Analysis Seminar Trento\n\n\n
Abstract\nThe Yamabe problem asks whether\, given a closed Riemannian mani
fold\, one can find a conformal metric of constant scalar curvature (CSC).
An affirmative answer was given by Schoen in 1984\, following contributio
ns from Yamabe\, Trudinger\, and Aubin\, by establishing the existence of
a function that minimizes the so-called Yamabe energy functional\; the min
imizing function corresponds to the conformal factor of the CSC metric. We
address the quantitative stability of minimizing Yamabe metrics. On any c
losed Riemannian manifold we show—in a quantitative sense—that if a fu
nction nearly minimizes the Yamabe energy\, then the corresponding conform
al metric is close to a CSC metric. Generically\, this closeness is contro
lled quadratically by the Yamabe energy deficit. However\, we construct an
example demonstrating that this quadratic estimate is false in the genera
l. This is joint work with Max Engelstein and Luca Spolaor.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Speight (University of Cincinnati)
DTSTART;VALUE=DATE-TIME:20210302T133000Z
DTEND;VALUE=DATE-TIME:20210302T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/4
DESCRIPTION:Title: Whitney Extension and Lusin Approximation in Carnot Group\nby Ga
reth Speight (University of Cincinnati) as part of Analysis Seminar Trento
\n\n\nAbstract\nThe classical Lusin theorem states that any measurable fun
ction can be approximated by a continuous function except on a set of smal
l measure. Analogous results for higher smoothness give conditions under w
hich a function can be approximated by a C^m function up to a set of small
measure. Proving these results depends on applying a suitable Whitney ext
ension theorem. After recalling the classical results in Euclidean spaces\
, we discuss recent work extending some of these results to Carnot groups.
Based on joint work with Andrea Pinamonti and Marco Capolli.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Vittone (University of Padova)
DTSTART;VALUE=DATE-TIME:20210309T133000Z
DTEND;VALUE=DATE-TIME:20210309T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/5
DESCRIPTION:Title: Differentiability of intrinsic Lipschitz graphs in Carnot groups
\nby Davide Vittone (University of Padova) as part of Analysis Seminar Tre
nto\n\n\nAbstract\nSubmanifolds with intrinsic Lipschitz regularity in sub
-Riemannian Carnot groups can be introduced using the theory of intrinsic
Lipschitz graphs started by B. Franchi\, R. Serapioni and F. Serra Cassano
almost 15 years ago. One of the main related questions concerns a Rademac
her-type theorem (i.e.\, almost everywhere existence of a tangent plane) f
or such graphs: in this talk I will discuss a recent positive solution to
the problem in Heisenberg groups. The proof uses the language of currents
in Heisenberg groups (in particular\, a version of the celebrated Constanc
y Theorem) and a number of complementary results such as extension and smo
oth approximation theorems for intrinsic Lipschitz graphs. I will also sho
w a recent example (joint with A. Julia and S. Nicolussi Golo) of an intri
nsic Lipschitz graph in a Carnot group that is nowhere intrinsically diffe
rentiable. The talk will be kept at an introductory level.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Young (NYU Courant)
DTSTART;VALUE=DATE-TIME:20210316T150000Z
DTEND;VALUE=DATE-TIME:20210316T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/6
DESCRIPTION:Title: Metric differentiation and embeddings of the Heisenberg group\nb
y Robert Young (NYU Courant) as part of Analysis Seminar Trento\n\n\nAbstr
act\nPansu and Semmes used a version of Rademacher's differentiation theor
em to show that there is no bilipschitz embedding from the Heisenberg grou
ps into Euclidean space. More generally\, the non-commutativity of the Hei
senberg group makes it impossible to embed into any $L_p$ space for $p\\in
(1\,\\infty)$. Recently\, with Assaf Naor\, we proved sharp quantitative
bounds on embeddings of the Heisenberg groups into $L_1$ and constructed
a metric space based on the Heisenberg group which embeds into $L_1$ and $
L_4$ but not in $L_2$\; our construction is based on constructing a surfac
e in $\\mathbb{H}$ which is as bumpy as possible. In this talk\, we will d
escribe what are the best ways to embed the Heisenberg group into Banach s
paces\, why good embeddings of the Heisenberg group must be "bumpy" at man
y scales\, and how to study embeddings into $L_1$ by studying surfaces in
$\\mathbb{H}$.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Malchiodi (SNS Pisa)
DTSTART;VALUE=DATE-TIME:20210323T133000Z
DTEND;VALUE=DATE-TIME:20210323T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/7
DESCRIPTION:Title: Prescribing Morse scalar curvatures in high dimension\nby Andrea
Malchiodi (SNS Pisa) as part of Analysis Seminar Trento\n\n\nAbstract\nWe
consider the classical question of prescribing the scalar curvature of a
manifold via conformal deformations of the metric\, dating back to works b
y Kazdan and Warner. This problem is mainly understood in low dimensions\,
where blow-ups of solutions are proven to be "isolated simple". We find n
atural conditions to guarantee this also in arbitrary dimensions\, when th
e prescribed curvatures are Morse functions. As a consequence\, we improve
some pinching conditions in the literature and derive existence and non-e
xistence results of new type. This is joint work with M. Mayer.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (Oxford University)
DTSTART;VALUE=DATE-TIME:20210330T123000Z
DTEND;VALUE=DATE-TIME:20210330T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/8
DESCRIPTION:Title: Optimal transport and quantitative geometric inequalities\nby An
drea Mondino (Oxford University) as part of Analysis Seminar Trento\n\n\nA
bstract\nThe goal of the talk is to discuss a proof of the Levy-Gromov ine
quality for metric measure spaces (joint with Cavalletti)\, a quantitative
version of the Levy- Gromov isoperimetric inequality (joint with Cavallet
ti and Maggi) as well as other geometric/functional inequalities (joint wi
th Cavalletti and Semola). Given a closed Riemannian manifold with strictl
y positive Ricci tensor\, one estimates the measure of the symmetric diffe
rence of a set with a metric ball with the deficit in the Levy- Gromov ine
quality. The results are obtained via a quantitative analysis based on the
localisation method via L1-optimal transport.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Saracco (SISSA Trieste)
DTSTART;VALUE=DATE-TIME:20210413T123000Z
DTEND;VALUE=DATE-TIME:20210413T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/9
DESCRIPTION:Title: The isoperimetric problem with a double density\nby Giorgio Sara
cco (SISSA Trieste) as part of Analysis Seminar Trento\n\n\nAbstract\nIt i
s well-known that for any given volume\, the sets that enclose said volume
with the least perimeter are balls. What happens when one in place of the
standard Euclidean volume and perimeter considers weighted counterparts?
Given densities $f: \\mathbb{R}^N \\to \\mathbb{R}^+$ and $h:\\mathbb{R}^N
\\times \\mathbb{S}^{N-1} \\to \\mathbb{R}^+$ to weigh\, resp.\, the volu
me and the perimeter\, we shall discuss under which hypotheses isoperimetr
ic sets exist for all volumes. Furthermore\, we shall introduce the $\\var
epsilon-\\varepsilon^\\beta$ property\, which readily allows to prove boun
dedness. If time allows\, some regularity results shall be discussed.\n\nB
ased on joint works with A. Pratelli (Università di Pisa)\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Daneri (GSSI L'Aquila)
DTSTART;VALUE=DATE-TIME:20210420T123000Z
DTEND;VALUE=DATE-TIME:20210420T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/10
DESCRIPTION:Title: Symmetry breaking and pattern formation for local/nonlocal interact
ion functionals\nby Sara Daneri (GSSI L'Aquila) as part of Analysis Se
minar Trento\n\n\nAbstract\nIn this talk I will review some recent results
obtained in collaboration with E. Runa and A. Kerschbaum on the one-dimen
sionality of the minimizers\nof a family of continuous local/nonlocal inte
raction functionals in general dimension. Such functionals have a local te
rm\, typically a perimeter term or its Modica-Mortola approximation\, whic
h penalizes interfaces\, and a nonlocal term favouring oscillations which
are high in frequency and in amplitude. The competition between the two te
rms is expected by experiments and simulations to give rise to periodic pa
tterns at equilibrium. Functionals of this type are used to model pattern
formation\, either in material science or in biology. One of the main dif
ficulties in proving the emergence of such regular structures\, together w
ith nonlocality\, is due to the fact that the functionals retain more symm
etries (in this case symmetry with respect to permutation of coordinates)
than the minimizers. We will present new techniques and results showing t
hat for two classes of functionals (used to model generalized anti-ferroma
gnetic systems\, respectively colloidal suspensions)\, both in sharp inte
rface and in diffuse interface models\, minimizers are (in general dimensi
on) one-dimensional and periodic. In the discrete setting such results had
been previously obtained for a smaller set of functionals with a differen
t approach by Giuliani and Seiringer.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Borghini (Milano Bicocca)
DTSTART;VALUE=DATE-TIME:20210427T123000Z
DTEND;VALUE=DATE-TIME:20210427T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/11
DESCRIPTION:Title: Torsion problem for ring-shaped domains\nby Stefano Borghini (M
ilano Bicocca) as part of Analysis Seminar Trento\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Colombo (EPFL Lausanne)
DTSTART;VALUE=DATE-TIME:20210504T123000Z
DTEND;VALUE=DATE-TIME:20210504T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/12
DESCRIPTION:Title: Partial regularity for the supercritical surface quasigeostrophic e
quation\nby Maria Colombo (EPFL Lausanne) as part of Analysis Seminar
Trento\n\n\nAbstract\nThe surface quasigeostrophic equation (SGQ) is a 2d
physical model equation which emerges in meteorology and shares many of th
e essential difficulties of 3d fluid dynamics. In the supercritical regime
for instance\, where dissipation is modelled by a fractional Laplacian of
order less than 1/2\, it is not known whether or not smooth solutions blo
w-up in finite time. \n\nThe goal of the talk is to show that every $L^2$
initial datum admits an a.e. smooth solution of the dissipative surface qu
asigeostrophic equation (SGQ)\; more precisely\, we prove that those solut
ions are smooth outside a compact set (away from t=0) of quantifiable Haus
dorff dimension. We draw analogies between SQG and other PDEs in fluid dyn
amics in several aspects\, including the partial regularity results\, and
underline some extra structure that SQG enjoys. \n\nThis is a joint work w
ith Silja Haffter (EPFL).\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salvatore Stuvard (University of Texas at Austin)
DTSTART;VALUE=DATE-TIME:20210511T123000Z
DTEND;VALUE=DATE-TIME:20210511T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/13
DESCRIPTION:Title: Mean curvature flow with prescribed boundary: a dynamical approach
to Plateau’s problem\nby Salvatore Stuvard (University of Texas at A
ustin) as part of Analysis Seminar Trento\n\n\nAbstract\nThe Brakke flow i
s a measure-theoretic generalization of the mean curvature flow which desc
ribes the evolution by mean curvature of surfaces with singularities. In t
he first part of the talk\, I am going to discuss global existence and lar
ge time asymptotics of solutions to the Brakke flow with fixed boundary wh
en the initial datum is given by any arbitrary rectifiable closed subset o
f a convex domain which disconnects the domain into finitely many "grains"
. Such flow represents the motion of material interfaces constrained at th
e boundary of the domain\, and evolving towards a configuration of mechani
cal equilibrium according to\nthe gradient of their potential energy due t
o surface tension. In the second part\, I will focus on the case when the
initial datum is already in equilibrium (a generalized minimal surface): I
will prove that\, in presence of certain singularity types in the initial
datum\, there always exists a non-constant solution to the Brakke flow. T
his suggests that the class of dynamically stable minimal surfaces\, that
is minimal surfaces which do not move by Brakke flow\, may be worthy of fu
rther study within the investigation on the regularity properties of minim
al surfaces. Based on joint works with Yoshihiro Tonegawa (Tokyo Institute
of Technology).\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Bonicatto (Warwick University)
DTSTART;VALUE=DATE-TIME:20210518T123000Z
DTEND;VALUE=DATE-TIME:20210518T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/14
DESCRIPTION:Title: Decomposition of integral metric currents\nby Paolo Bonicatto (
Warwick University) as part of Analysis Seminar Trento\n\n\nAbstract\nCurr
ents are nowadays a widely used tool in geometric measure theory and calcu
lus of variations\, as they allow to give a weak formulation of a variety
of geometric problems. The theory of normal and integral currents (initiat
ed mostly by Federer and Fleming in the '60s) was developed in the context
of Euclidean spaces. In 2000\, Ambrosio and Kirchheim introduced metric c
urrents\, defined on complete metric spaces. The talk will be devoted to i
ntegral metric currents: we show that integral currents can be decomposed
as a sum of indecomposable components and\, in the special case of one-dim
ensional integral currents\, we also characterise the indecomposable ones
as those associated with injective Lipschitz curves or injective Lipschitz
loops. This generalises to the metric setting a previous result by Federe
r. Joint work with Giacomo Del Nin (Warwick) and Enrico Pasqualetto (Scuol
a Normale Superiore).\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Xia (Xiamen University)
DTSTART;VALUE=DATE-TIME:20210525T123000Z
DTEND;VALUE=DATE-TIME:20210525T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/15
DESCRIPTION:Title: Anisotropic Minkowski inequality for non-convex domains\nby Cha
o Xia (Xiamen University) as part of Analysis Seminar Trento\n\n\nAbstract
\nIn this talk\, we discuss the anisotropic Minkowski inequality\, which i
s an isoperimetric type inequality between anisotropic mean curvature inte
gral and anisotropic area\, for star-shaped F-mean convex domains or outwa
rd F-minimizing domains. Our method is based on the inverse anisotropic me
an curvature flow and the anisotropic capacity\, respectively. Part of the
work is joint with Dr. Jiabin Yin.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Semola (Oxford University)
DTSTART;VALUE=DATE-TIME:20210601T123000Z
DTEND;VALUE=DATE-TIME:20210601T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/16
DESCRIPTION:Title: Boundary regularity and stability under lower Ricci curvature bound
s\nby Daniele Semola (Oxford University) as part of Analysis Seminar T
rento\n\n\nAbstract\nThe theory of non smooth spaces with lower Ricci Curv
ature bounds has undergone huge developments in the last thirty years. On
the one hand the impetus came from Gromov’s precompactness theorem and f
rom the Cheeger-Colding theory of Ricci limit spaces. On the other hand
“synthetic” theories of lower Ricci bounds have been developed\, based
on semigroup tools (the Bakry-Émery theory) and on Optimal Transport (th
e Lott-Sturm-Villani theory). The Cheeger-Colding theory did not consider
manifolds with boundary\, while in the synthetic framework even understand
ing what is a good definition of boundary is a challenge. The aim of this
talk is to present some recent results obtained in collaboration with E. B
ruè (IAS\, Princeton) and A. Naber (Northwestern University) about regula
rity and stability for boundaries of spaces with lower Ricci Curvature bou
nds.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Violo (SISSA Trieste)
DTSTART;VALUE=DATE-TIME:20210608T123000Z
DTEND;VALUE=DATE-TIME:20210608T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T165859Z
UID:AnalysisUnitn/17
DESCRIPTION:Title: Monotonicity formula for harmonic functions in RCD(0\,N) spaces
\nby Ivan Violo (SISSA Trieste) as part of Analysis Seminar Trento\n\n\nAb
stract\nA classical result on Riemannian manifolds satisfying a lower boun
d on the Ricci curvature is the monotonicity of the Bishop-Gromov volume r
atio. Colding and Minicozzi ('12-'14) realized that for non-negative Ricci
curvature there exist\nanalogous monotone quantities involving the Green
function. Recently this has been generalized by Agostiniani\, Fogagnolo an
d Mazzieri ('18) from the Green function to the case of an electrostatic p
otential and has proven\nto be fruitful in proving geometric inequalities.
We will see that the same monotonicity formulas can be proven also in the
setting of synthetic lower Ricci curvature bounds. This allows to prove s
ome almost-rigidity results which are new also in the\nsmooth case. This i
s a joint work with professor Nicola Gigli.\n
LOCATION:https://researchseminars.org/talk/AnalysisUnitn/17/
END:VEVENT
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