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BEGIN:VEVENT
SUMMARY:David Bate (Warwick University)
DTSTART:20210209T133000Z
DTEND:20210209T143000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/1
DESCRIPTION:Title: Characterising rectifiable metric spaces using tangent measur
es\nby David Bate (Warwick University) as part of Analysis Seminar Tre
nto\n\n\nAbstract\nA classical result of Marstrand and Mattila states that
a set $S\\subset \\mathbb{R}^m$ (satisfying mild dimension assumptions) i
s $n$-rectifiable if and only if\, for $\\mathcal{H}^n$-a.e. $x\\in S$\, a
ll tangent spaces of $\\mathcal{H}^n|_S$ at $x$ are $n$-dimensional subspa
ces. Here a "tangent space" is defined using Preiss's tangent measures.\n\
nThis talk will present a generalisation of this result that replaces the
ambient $\\mathbb{R}^m$ with an arbitrary metric space.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ihsan Topaloglu (Virginia Commonwealth University)
DTSTART:20210216T133000Z
DTEND:20210216T143000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/2
DESCRIPTION:Title: A nonlocal isoperimetric problem with density perimeter\n
by Ihsan Topaloglu (Virginia Commonwealth University) as part of Analysis
Seminar Trento\n\n\nAbstract\nIn this talk I will present recent results o
n a variant of Gamow's liquid drop model where we consider the mass-constr
ained minimization of an energy functional given as the sum of a density p
erimeter term and a nonlocal interaction term of Riesz type. In particular
\, I will show that for a wide class of density functions this energy admi
ts a minimizer for any choice of parameters\, and that for monomial densit
ies the unique minimizer is given by the ball of fixed volume when the non
local effects are sufficiently small. This is a joint work with S. Alama\,
L. Bronsard\, and A. Zuniga.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Neumayer (Northwestern University)
DTSTART:20210223T133000Z
DTEND:20210223T143000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/3
DESCRIPTION:Title: Quantitative stability for minimizing Yamabe metrics\nby
Robin Neumayer (Northwestern University) as part of Analysis Seminar Trent
o\n\n\nAbstract\nThe Yamabe problem asks whether\, given a closed Riemanni
an manifold\, one can find a conformal metric of constant scalar curvature
(CSC). An affirmative answer was given by Schoen in 1984\, following cont
ributions from Yamabe\, Trudinger\, and Aubin\, by establishing the existe
nce of a function that minimizes the so-called Yamabe energy functional\;
the minimizing function corresponds to the conformal factor of the CSC met
ric. We address the quantitative stability of minimizing Yamabe metrics. O
n any closed Riemannian manifold we show—in a quantitative sense—that
if a function nearly minimizes the Yamabe energy\, then the corresponding
conformal metric is close to a CSC metric. Generically\, this closeness is
controlled quadratically by the Yamabe energy deficit. However\, we const
ruct an example demonstrating that this quadratic estimate is false in the
general. This is joint work with Max Engelstein and Luca Spolaor.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Speight (University of Cincinnati)
DTSTART:20210302T133000Z
DTEND:20210302T143000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/4
DESCRIPTION:Title: Whitney Extension and Lusin Approximation in Carnot Group
\nby Gareth Speight (University of Cincinnati) as part of Analysis Seminar
Trento\n\n\nAbstract\nThe classical Lusin theorem states that any measura
ble function can be approximated by a continuous function except on a set
of small measure. Analogous results for higher smoothness give conditions
under which a function can be approximated by a C^m function up to a set o
f small measure. Proving these results depends on applying a suitable Whit
ney extension 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://stable.researchseminars.org/talk/AnalysisUnitn/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Vittone (University of Padova)
DTSTART:20210309T133000Z
DTEND:20210309T143000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/5
DESCRIPTION:Title: Differentiability of intrinsic Lipschitz graphs in Carnot gro
ups\nby Davide Vittone (University of Padova) as part of Analysis Semi
nar Trento\n\n\nAbstract\nSubmanifolds with intrinsic Lipschitz regularity
in sub-Riemannian Carnot groups can be introduced using the theory of int
rinsic Lipschitz graphs started by B. Franchi\, R. Serapioni and F. Serra
Cassano almost 15 years ago. One of the main related questions concerns a
Rademacher-type theorem (i.e.\, almost everywhere existence of a tangent p
lane) for such graphs: in this talk I will discuss a recent positive solut
ion to the problem in Heisenberg groups. The proof uses the language of cu
rrents in Heisenberg groups (in particular\, a version of the celebrated C
onstancy Theorem) and a number of complementary results such as extension
and smooth approximation theorems for intrinsic Lipschitz graphs. I will a
lso show a recent example (joint with A. Julia and S. Nicolussi Golo) of a
n intrinsic Lipschitz graph in a Carnot group that is nowhere intrinsicall
y differentiable. The talk will be kept at an introductory level.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Young (NYU Courant)
DTSTART:20210316T150000Z
DTEND:20210316T160000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/6
DESCRIPTION:Title: Metric differentiation and embeddings of the Heisenberg group
\nby Robert Young (NYU Courant) as part of Analysis Seminar Trento\n\n
\nAbstract\nPansu and Semmes used a version of Rademacher's differentiatio
n theorem to show that there is no bilipschitz embedding from the Heisenbe
rg groups into Euclidean space. More generally\, the non-commutativity of
the Heisenberg group makes it impossible to embed into any $L_p$ space for
$p\\in (1\,\\infty)$. Recently\, with Assaf Naor\, we proved sharp quant
itative bounds on embeddings of the Heisenberg groups into $L_1$ and const
ructed 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
surface in $\\mathbb{H}$ which is as bumpy as possible. In this talk\, we
will describe what are the best ways to embed the Heisenberg group into B
anach spaces\, why good embeddings of the Heisenberg group must be "bumpy"
at many scales\, and how to study embeddings into $L_1$ by studying surfa
ces in $\\mathbb{H}$.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Malchiodi (SNS Pisa)
DTSTART:20210323T133000Z
DTEND:20210323T143000Z
DTSTAMP:20260404T110654Z
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\nAbstr
act\nWe consider the classical question of prescribing the scalar curvatur
e of a manifold via conformal deformations of the metric\, dating back to
works by Kazdan and Warner. This problem is mainly understood in low dimen
sions\, where blow-ups of solutions are proven to be "isolated simple". We
find natural conditions to guarantee this also in arbitrary dimensions\,
when the prescribed curvatures are Morse functions. As a consequence\, we
improve some pinching conditions in the literature and derive existence an
d non-existence results of new type. This is joint work with M. Mayer.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (Oxford University)
DTSTART:20210330T123000Z
DTEND:20210330T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/8
DESCRIPTION:Title: Optimal transport and quantitative geometric inequalities
\nby Andrea Mondino (Oxford University) as part of Analysis Seminar Trento
\n\n\nAbstract\nThe goal of the talk is to discuss a proof of the Levy-Gro
mov inequality for metric measure spaces (joint with Cavalletti)\, a quant
itative version of the Levy- Gromov isoperimetric inequality (joint with C
avalletti and Maggi) as well as other geometric/functional inequalities (j
oint with Cavalletti and Semola). Given a closed Riemannian manifold with
strictly positive Ricci tensor\, one estimates the measure of the symmetri
c difference of a set with a metric ball with the deficit in the Levy- Gro
mov inequality. The results are obtained via a quantitative analysis based
on the localisation method via L1-optimal transport.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Saracco (SISSA Trieste)
DTSTART:20210413T123000Z
DTEND:20210413T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/9
DESCRIPTION:Title: The isoperimetric problem with a double density\nby Giorg
io Saracco (SISSA Trieste) as part of Analysis Seminar Trento\n\n\nAbstrac
t\nIt is 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 counter
parts? Given densities $f: \\mathbb{R}^N \\to \\mathbb{R}^+$ and $h:\\math
bb{R}^N \\times \\mathbb{S}^{N-1} \\to \\mathbb{R}^+$ to weigh\, resp.\, t
he volume and the perimeter\, we shall discuss under which hypotheses isop
erimetric sets exist for all volumes. Furthermore\, we shall introduce the
$\\varepsilon-\\varepsilon^\\beta$ property\, which readily allows to pro
ve boundedness. If time allows\, some regularity results shall be discusse
d.\n\nBased on joint works with A. Pratelli (Università di Pisa)\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Daneri (GSSI L'Aquila)
DTSTART:20210420T123000Z
DTEND:20210420T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/10
DESCRIPTION:Title: Symmetry breaking and pattern formation for local/nonlocal i
nteraction functionals\nby Sara Daneri (GSSI L'Aquila) as part of Anal
ysis Seminar Trento\n\n\nAbstract\nIn this talk I will review some recent
results obtained in collaboration with E. Runa and A. Kerschbaum on the on
e-dimensionality of the minimizers\nof a family of continuous local/nonloc
al interaction functionals in general dimension. Such functionals have a l
ocal term\, typically a perimeter term or its Modica-Mortola approximation
\, which penalizes interfaces\, and a nonlocal term favouring oscillations
which are high in frequency and in amplitude. The competition between the
two terms is expected by experiments and simulations to give rise to peri
odic patterns at equilibrium. Functionals of this type are used to model
pattern formation\, either in material science or in biology. One of the m
ain difficulties in proving the emergence of such regular structures\, tog
ether with nonlocality\, is due to the fact that the functionals retain mo
re symmetries (in this case symmetry with respect to permutation of coord
inates) than the minimizers. We will present new techniques and results sh
owing that for two classes of functionals (used to model generalized anti-
ferromagnetic systems\, respectively colloidal suspensions)\, both in sha
rp interface and in diffuse interface models\, minimizers are (in general
dimension) one-dimensional and periodic. In the discrete setting such resu
lts had been previously obtained for a smaller set of functionals with a d
ifferent approach by Giuliani and Seiringer.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Borghini (Milano Bicocca)
DTSTART:20210427T123000Z
DTEND:20210427T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/11
DESCRIPTION:Title: Torsion problem for ring-shaped domains\nby Stefano Borg
hini (Milano Bicocca) as part of Analysis Seminar Trento\n\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Colombo (EPFL Lausanne)
DTSTART:20210504T123000Z
DTEND:20210504T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/12
DESCRIPTION:Title: Partial regularity for the supercritical surface quasigeostr
ophic equation\nby Maria Colombo (EPFL Lausanne) as part of Analysis S
eminar Trento\n\n\nAbstract\nThe surface quasigeostrophic equation (SGQ) i
s a 2d physical model equation which emerges in meteorology and shares man
y of the essential difficulties of 3d fluid dynamics. In the supercritical
regime for instance\, where dissipation is modelled by a fractional Lapla
cian of order less than 1/2\, it is not known whether or not smooth soluti
ons blow-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 sur
face quasigeostrophic equation (SGQ)\; more precisely\, we prove that thos
e solutions are smooth outside a compact set (away from t=0) of quantifiab
le Hausdorff dimension. We draw analogies between SQG and other PDEs in fl
uid dynamics in several aspects\, including the partial regularity results
\, and underline some extra structure that SQG enjoys. \n\nThis is a joint
work with Silja Haffter (EPFL).\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salvatore Stuvard (University of Texas at Austin)
DTSTART:20210511T123000Z
DTEND:20210511T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/13
DESCRIPTION:Title: Mean curvature flow with prescribed boundary: a dynamical ap
proach to Plateau’s problem\nby Salvatore Stuvard (University of Tex
as at Austin) as part of Analysis Seminar Trento\n\n\nAbstract\nThe Brakke
flow is a measure-theoretic generalization of the mean curvature flow whi
ch describes the evolution by mean curvature of surfaces with singularitie
s. In the first part of the talk\, I am going to discuss global existence
and large time asymptotics of solutions to the Brakke flow with fixed boun
dary when the initial datum is given by any arbitrary rectifiable closed s
ubset of a convex domain which disconnects the domain into finitely many "
grains". Such flow represents the motion of material interfaces constraine
d at the boundary of the domain\, and evolving towards a configuration of
mechanical equilibrium according to\nthe gradient of their potential energ
y due to surface tension. In the second part\, I will focus on the case wh
en the initial datum is already in equilibrium (a generalized minimal surf
ace): 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. This suggests that the class of dynamically stable minimal surfaces\
, that is minimal surfaces which do not move by Brakke flow\, may be worth
y of further study within the investigation on the regularity properties o
f minimal surfaces. Based on joint works with Yoshihiro Tonegawa (Tokyo In
stitute of Technology).\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Bonicatto (Warwick University)
DTSTART:20210518T123000Z
DTEND:20210518T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/14
DESCRIPTION:Title: Decomposition of integral metric currents\nby Paolo Boni
catto (Warwick University) as part of Analysis Seminar Trento\n\n\nAbstrac
t\nCurrents are nowadays a widely used tool in geometric measure theory an
d calculus of variations\, as they allow to give a weak formulation of a v
ariety of geometric problems. The theory of normal and integral currents (
initiated mostly by Federer and Fleming in the '60s) was developed in the
context of Euclidean spaces. In 2000\, Ambrosio and Kirchheim introduced m
etric currents\, defined on complete metric spaces. The talk will be devot
ed to integral metric currents: we show that integral currents can be deco
mposed as a sum of indecomposable components and\, in the special case of
one-dimensional integral currents\, we also characterise the indecomposabl
e ones as those associated with injective Lipschitz curves or injective Li
pschitz loops. This generalises to the metric setting a previous result by
Federer. Joint work with Giacomo Del Nin (Warwick) and Enrico Pasqualetto
(Scuola Normale Superiore).\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Xia (Xiamen University)
DTSTART:20210525T123000Z
DTEND:20210525T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/15
DESCRIPTION:Title: Anisotropic Minkowski inequality for non-convex domains\
nby Chao Xia (Xiamen University) as part of Analysis Seminar Trento\n\n\nA
bstract\nIn this talk\, we discuss the anisotropic Minkowski inequality\,
which is an isoperimetric type inequality between anisotropic mean curvatu
re integral and anisotropic area\, for star-shaped F-mean convex domains o
r outward F-minimizing domains. Our method is based on the inverse anisotr
opic mean curvature flow and the anisotropic capacity\, respectively. Part
of the work is joint with Dr. Jiabin Yin.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Semola (Oxford University)
DTSTART:20210601T123000Z
DTEND:20210601T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/16
DESCRIPTION:Title: Boundary regularity and stability under lower Ricci curvatur
e bounds\nby Daniele Semola (Oxford University) as part of Analysis Se
minar Trento\n\n\nAbstract\nThe theory of non smooth spaces with lower Ric
ci Curvature bounds has undergone huge developments in the last thirty yea
rs. On the one hand the impetus came from Gromov’s precompactness theore
m and from 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 Transpor
t (the Lott-Sturm-Villani theory). The Cheeger-Colding theory did not cons
ider manifolds with boundary\, while in the synthetic framework even under
standing 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. Bruè (IAS\, Princeton) and A. Naber (Northwestern University) about r
egularity and stability for boundaries of spaces with lower Ricci Curvatur
e bounds.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Violo (SISSA Trieste)
DTSTART:20210608T123000Z
DTEND:20210608T133000Z
DTSTAMP:20260404T110654Z
UID:AnalysisUnitn/17
DESCRIPTION:Title: Monotonicity formula for harmonic functions in RCD(0\,N) spa
ces\nby Ivan Violo (SISSA Trieste) as part of Analysis Seminar Trento\
n\n\nAbstract\nA classical result on Riemannian manifolds satisfying a low
er bound on the Ricci curvature is the monotonicity of the Bishop-Gromov v
olume ratio. Colding and Minicozzi ('12-'14) realized that for non-negativ
e Ricci curvature there exist\nanalogous monotone quantities involving the
Green function. Recently this has been generalized by Agostiniani\, Fogag
nolo and Mazzieri ('18) from the Green function to the case of an electros
tatic potential and has proven\nto be fruitful in proving geometric inequa
lities. 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 some almost-rigidity results which are new also in the\nsmooth case.
This is a joint work with professor Nicola Gigli.\n
LOCATION:https://stable.researchseminars.org/talk/AnalysisUnitn/17/
END:VEVENT
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