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BEGIN:VEVENT
SUMMARY:Daniel Luckhardt (Ben-Gurion University)
DTSTART:20200605T150000Z
DTEND:20200605T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/1
DESCRIPTION:Title: A volume comparison theorem for characteristic numbers\nby D
aniel Luckhardt (Ben-Gurion University) as part of mms&convergence\n\n\nAb
stract\nWe show that assuming lower bounds on the Ricci curvature and the\
ninjectivity radius the absolute value of any \ncharacteristic number of a
Riemannian manifold M is bounded \nproportional to the volume\, i.e. bou
nded by Cvol(M) where C \ndepends only on the characteristic number\, \nth
e dimension of M\, and both bounds. The proof relies \non the definition o
f a connection for an harmonic Hölder \nregular metric tensor as they app
ear for instance as \nGromov-Hausdorff limits of Riemannian manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Ketterer (Toronto University)
DTSTART:20200612T150000Z
DTEND:20200612T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/2
DESCRIPTION:Title: Applications of needle decomposition for metric measure spaces\nby Christian Ketterer (Toronto University) as part of mms&convergence\
n\n\nAbstract\nIn this talk I show how one can formulate and prove the\nHe
intze-Karcher inequality in the context of nonsmooth spaces that\nsatisfy
a Ricci curvature bound in the sense of Lott\, Sturm and\nVillani. As a by
-product one obtains a notion of mean curvature for\nthe boundary of Borel
sets in such spaces. My approach is based on the\nneedle decomposition me
thod introduced for this framework by\nCavalletti and Mondino.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Zamora (Penn State University)
DTSTART:20200619T150000Z
DTEND:20200619T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/3
DESCRIPTION:Title: Fundamental Groups and Limits of Almost Homogeneous Spaces\n
by Sergio Zamora (Penn State University) as part of mms&convergence\n\n\nA
bstract\nWe show that for a sequence of proper length spaces $X_n$ with gr
oups $\\Gamma_n$ acting discretely and almost transitively by isometries\,
if they converge to a proper finite dimensional length space $X$\, then $
X$ is a nilpotent Lie group with an invariant sub-Finsler Carnot metric. A
lso\, for large enough $n$\, there are subgroups $\\Lambda_n \\leq \\pi_1(
X_n)$ and surjective morphisms $\\Lambda_n\\to \\pi_1(X)$.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Mondello (Université de Paris Est Créteil)
DTSTART:20200626T150000Z
DTEND:20200626T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/4
DESCRIPTION:Title: Ricci limit spaces : an introduction to the tools of Cheeger-Jia
ng-Naber's work\nby Ilaria Mondello (Université de Paris Est Créteil
) as part of mms&convergence\n\n\nAbstract\nThe goal of this expository ta
lk is to explain parts of the work of J. Cheeger\, W. Jiang and A. Naber:\
nhttps://arxiv.org/abs/1805.07988 For a converging\, non-collapsing sequen
ce of Riemannian manifolds with a uniform Ricci lower bound\, they proved
that singular strata of the limit space are rectifiable. Some of the key t
ools in the proof include quantitative stratification\, which was first in
troduced in previous work of Cheeger-Naber\, and new related volume estima
tes\, together with a precise study of neck regions. After a brief review
of Cheeger-Colding theory\, the talk will focus on explaining the notions
of quantitative stratifications\, neck regions and their role in the proof
.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Allen (University of Hartford)
DTSTART:20200703T150000Z
DTEND:20200703T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/5
DESCRIPTION:Title: Null Distance and Convergence of Warped Product Spacetimes\n
by Brian Allen (University of Hartford) as part of mms&convergence\n\n\nAb
stract\nThe null distance was introduced by Christina Sormani and Carlos V
ega as a way of turning a spacetime into a metric space. This is particula
rly important for geometric stability questions relating to spacetimes suc
h as the stability of the positive mass theorem. In this talk\, we will de
scribe the null distance\, present properties of the metric space structur
e\, and examine the convergence of sequences of warped product spacetimes
equipped with the null distance. This is joint work with Annegret Burtsche
r.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Carron (Université de Nantes)
DTSTART:20200904T150000Z
DTEND:20200904T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/6
DESCRIPTION:Title: Euclidean heat kernel rigidity\nby Gilles Carron (Universit
é de Nantes) as part of mms&convergence\n\n\nAbstract\nThis is joint wor
k with David Tewodrose (Cergy). I will explain that a metric measure space
with Euclidean heat kernel are Euclidean. An almost rigidity result comes
then for free\, and this can be used to give another proof of Colding's
almost rigidity for complete manifold with non negative Ricci curvature an
d almost Euclidean growth.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danka Lučić (University of Jyväskylä)
DTSTART:20200911T150000Z
DTEND:20200911T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/7
DESCRIPTION:Title: Techniques for proving infinitesimal Hilbertianity\nby Danka
Lučić (University of Jyväskylä) as part of mms&convergence\n\n\nAbstr
act\nA metric space is said to be "universally infinitesimally Hilbertian"
if\, when endowed with any arbitrary Radon measure\, its associated 2-Sob
olev space is Hilbert. For instance\, all (sub)Riemannian manifolds and CA
T(K) spaces have this property. In this talk\, we will illustrate three di
fferent strategies to prove the universal infinitesimal Hilbertianity of t
he Euclidean space\, which is the base case and where all the known approa
ches work.\nThe motivations come\, among others\, from the study of rectif
iable metric measure spaces\, of metric-valued harmonic maps\, and of vari
ational problems (such as models representing low-dimensional elastic stru
ctures).\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (University of Oxford)
DTSTART:20200925T150000Z
DTEND:20200925T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/9
DESCRIPTION:Title: An optimal transport formulation of the Einstein equations of ge
neral relativity\nby Andrea Mondino (University of Oxford) as part of
mms&convergence\n\n\nAbstract\nIn the seminar I will present a recent work
joint with S. Suhr (Bochum) giving an optimal transport formulation of th
e full Einstein equations of general relativity\, linking the (Ricci) curv
ature of a space-time with the cosmological constant and the energy-moment
um tensor. Such an optimal transport formulation is in terms of convexity/
concavity properties of the Shannon-Bolzmann entropy along curves of proba
bility measures extremizing suitable optimal transport costs. The result\,
together with independent work by McCann on lower bounds for Lorentzian R
icci Curvature\, gives a new connection between general relativity and opt
imal transport\; moreover it gives a mathematical reinforcement of the str
ong link between general relativity and thermodynamics/information theory
that emerged in the physics literature of the last years.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Flavia Santarcangelo (SISSA)
DTSTART:20201002T150000Z
DTEND:20201002T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/10
DESCRIPTION:Title: Independence of synthetic Curvature Dimension conditions on tra
nsport distance exponent\nby Flavia Santarcangelo (SISSA) as part of m
ms&convergence\n\n\nAbstract\nThe celebrated Lott-Sturm-Villani theory of
metric measure spaces furnishes synthetic notions of a Ricci curvature lo
wer bound $K$ joint with an upper bound $N$ on the dimension. \nTheir con
dition\, called the Curvature-Dimension condition and denoted by $\\maths
f{CD}(K\,N)$\, is formulated in terms of a modified displacement convexit
y of an entropy functional along $W_{2}$-Wasserstein geodesics. In a join
t work with A. Akdemir\, F. Cavalletti\, A. Colinet and R. McCann\, we s
how that the choice of the squared-distance function as transport cost doe
s not influence the theory. In particular\, by denoting with $\\mathsf{
CD}_{p}(K\,N)$ the analogous condition but with the cost given by the $p^
{th}$ power of the distance\, we prove that $\\CD_{p}(K\,N)$ are all equi
valent conditions for any $p>1$ --- at least in spaces whose geodesics do
not branch. \nFollowing the strategy introduced in the work by Cavalletti
-Milman\, we also establish the local-to-global property of $\\mathsf{C
D}_{p}(K\,N)$ spaces. \n\nFinally\, we will present a result obtained in
collaboration with F. Cavalletti and N. Gigli that\, combined with the on
e previously described\, allows to conclude that for any $p\\geq1$\, all
the $\\mathsf{CD}_{p}(K\,N)$ conditions\, when expressed in terms of di
splacement convexity\, are equivalent\, provided the space $X$ satisfies t
he appropriate essentially non-branching condition.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Semola (Scuola Normale Superiore)
DTSTART:20201009T150000Z
DTEND:20201009T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/11
DESCRIPTION:Title: Rectifiability of RCD(K\,N) spaces via delta-splitting maps
\nby Daniele Semola (Scuola Normale Superiore) as part of mms&convergence\
n\n\nAbstract\nThe theory of metric measure spaces verifying the Riemannia
n-Curvature-Dimension condition RCD(K\,N) has attracted a lot of interest
in the last years. They can be thought as a non smooth counterpart of the
class of Riemannian manifolds with Ricci curvature bounded from below by K
and dimension bounded from above by N.\n\nIn this talk\, after providing
some background and motivations\, I will describe a simplified approach to
the structure theory of these spaces relying on the so-called delta-split
ting maps. This tool\, developed by Cheeger-Colding in the study of Ricci
limits\, has revealed to be extremely powerful also more recently in the s
tudy of RCD spaces. \n\nThe seminar is based on a joint work with Elia Bru
e' and Enrico Pasqualetto.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Chun Lee (The Chinese University of Hong Kong (CUHK) Mathemati
cs)
DTSTART:20211001T150000Z
DTEND:20211001T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/12
DESCRIPTION:Title: d_p convergence and epsilon-regularity theorems for entropy and
scalar curvature lower bound\nby Man-Chun Lee (The Chinese University
of Hong Kong (CUHK) Mathematics) as part of mms&convergence\n\n\nAbstract
\nIn this talk\, we consider Riemannian manifolds with almost non-negative
scalar curvature and Perelman entropy. We establish an\nepsilon-regularit
y theorem showing that such a space must be close to Euclidean space in a
suitable sense. We will illustrate examples showing that\nthe result is fa
lse with respect to the Gromov-Hausdorff and Intrinsic Flat distances\, an
d more generally the metric space structure is not\ncontrolled under entro
py and scalar lower bounds. We will introduce the notion of the d_p distan
ce between (in particular) Riemannian manifolds\,\nwhich measures the dist
ance between W^{1\,p} Sobolev spaces\, and it is with respect to this dist
ance that the epsilon regularity theorem holds. This\nis joint work with A
. Naber and R. Neumayer.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qin Deng (Massachusetts Institute of Technology)
DTSTART:20210917T150000Z
DTEND:20210917T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/13
DESCRIPTION:Title: Hölder continuity of tangent cones in RCD(K\,N) spaces and app
lications to non-branching\nby Qin Deng (Massachusetts Institute of Te
chnology) as part of mms&convergence\n\n\nAbstract\nIt is known by a resul
t of Colding-Naber that for any two points in a Ricci limit space\, there
exists a minimizing geodesic where the geometry of small balls centred alo
ng the interior of the geodesic change in at most a Hölder continuous man
ner. This was shown using an extrinsic argument and had several key applic
ations for the structure theory of Ricci limits. In this talk\, I will dis
cuss how to overcome the use of smooth structure in the Colding-Naber argu
ment in order to generalize this result to the setting of metric measure s
paces satisfying the synthetic lower Ricci curvature bound condition RCD(K
\,N). As an application\, I will show that all RCD(K\,N) spaces are non-br
anching\, a result which was previously unknown for Ricci limit spaces.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Farinelli (SISSA)
DTSTART:20211008T150000Z
DTEND:20211008T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/14
DESCRIPTION:Title: The size of the nodal set of Laplace eigenfunctions in singular
spaces via optimal transport\nby Sara Farinelli (SISSA) as part of mm
s&convergence\n\n\nAbstract\nUpper and lower bounds of the Hausdorff measu
re of nodal sets of Laplace eigenfunctions have been largely studied in t
he context of smooth Riemannian manifolds.\nIn the talk we will investigat
e this problem in the setting of singular metric measure spaces satisfying
a synthetic curvature condition. In particular we prove a lower bound for
the measure of the nodal set. We follow an approach introduced by Steiner
berger in the smooth case\, which uses an indeterminacy estimate involving
optimal transport. Further exploring the relation between eigenfunctions
and optimal transport\, we will also present a lower bound for the Wassers
tein distance between the positive part and the negative part of an eigenf
unction\, conjectured by Steinerberger. These are joint works with Fabio C
avalletti and Nicolò De Ponti.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Pasqualetto (Scuola Normale Superiore)
DTSTART:20210924T150000Z
DTEND:20210924T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/15
DESCRIPTION:Title: The role of test plans in metric measure geometry\nby Enric
o Pasqualetto (Scuola Normale Superiore) as part of mms&convergence\n\n\nA
bstract\nA test plan on a metric measure space is a probability measure on
curves having bounded compression and finite kinetic energy\; the former
means that it does not concentrate mass at any time\, the latter that the
metric speed functional satisfies a suitable integral bound with respect t
o the test plan.\nIn the first part of the talk\, I will discuss the promi
nent role that test plans played in the development of Sobolev and BV calc
ulus on metric measure spaces\, as well as their strong connections (on sp
aces with lower Ricci bounds) with Optimal Transport and the theory of Reg
ular Lagrangian Flows.\nIn the second part of the talk\, I will report on
some recent results concerning "master test plans": roughly speaking\, the
se results say that under suitable assumptions on the underlying space\, s
maller classes of test plans are still sufficient to entirely recover the
Sobolev and BV calculus. As a consequence\, I will show that on finite-dim
ensional RCD spaces the reduced boundaries of finite perimeter sets have c
onstant dimension.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Kopfer (IAM Universität Bonn)
DTSTART:20211015T130000Z
DTEND:20211015T140000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/16
DESCRIPTION:Title: Optimal transport and homogenization\nby Eva Kopfer (IAM Un
iversität Bonn) as part of mms&convergence\n\n\nAbstract\nWe consider dis
crete dynamical transport costs on periodic network graphs and compute the
limit cost as the mesh size of the graphs is getting finer and finer. A p
rominent example is given by the\nBenamou-Brenier formulation of the Wasse
rstein distance.\n\nNotice the unusual time.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattia Fogagnolo (Scuola Normale Superiore)
DTSTART:20211022T150000Z
DTEND:20211022T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/17
DESCRIPTION:Title: Minkowski inequalities in manifolds with nonnegative Ricci curv
ature\nby Mattia Fogagnolo (Scuola Normale Superiore) as part of mms&c
onvergence\n\n\nAbstract\nWe provide\, in manifolds with nonnegative Ricci
curvature\, a sharp estimate of the total curvature of a hypersurface in
terms of a power of the perimeter of is minimizing hull.\nIn particular\,
it yields a new sharp Minkowski inequality for outward minimizing sets. Th
e proof relies on full monotonicity formulas along the level sets of p-har
monic functions\nand on the sharp iso-p-capacitary inequality derived from
the recent Brendle's isoperimetric inequality.\nThese results are obtaine
d in a joint work with L. Benatti and L. Mazzieri.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Hallgren (Cornell University)
DTSTART:20211029T150000Z
DTEND:20211029T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/18
DESCRIPTION:Title: Ricci Flow with a Lower Bound on Ricci Curvature\nby Max Ha
llgren (Cornell University) as part of mms&convergence\n\n\nAbstract\nIn t
his talk\, we will investigate the possible singularity behavior of closed
solutions of Ricci flow whose Ricci curvature is uniformly bounded below\
, and whose volume does not go to zero. In four dimensions\, we will see t
hat only orbifold singularities can arise\, and prove integral curvature e
stimates on time slices. We will also see a rough picture of singularity f
ormation in higher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Violo (University of Jyväskylä (JYU))
DTSTART:20211105T160000Z
DTEND:20211105T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/19
DESCRIPTION:Title: Rigidity and almost-rigidity of the Sobolev inequality under lo
wer Ricci curvature bounds\nby Ivan Violo (University of Jyväskylä (
JYU)) as part of mms&convergence\n\n\nAbstract\nIn this seminar we will pr
esent a new rigidity principle related to the value of the optimal consta
nt in the Sobolev inequality\, for n-dimensional Riemannian manifolds with
Ricci curvature bounded below by n-1. The analysis will be carried out in
the more general class of (non-smooth) RCD-spaces\, which will allow us t
o get also an almost-rigidity result.\n\nThe arguments are based on a Euc
lidean Polya-Szego inequality on metric measure spaces and on a version of
Lions' concentration-compactness principle under varying ambient space. T
his is joint work with Francesco Nobili.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Creutz (University of Cologne)
DTSTART:20211203T160000Z
DTEND:20211203T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/20
DESCRIPTION:Title: Area minimizing surfaces for singular boundary values\nby P
aul Creutz (University of Cologne) as part of mms&convergence\n\n\nAbstrac
t\nFix a nonnegative integer g and a finite configuration of \ndisjoint J
ordan curves in Euclidean space. Then\, by a classical result \nof Dougla
s\, there is an area minimizer among all surfaces of genus at \nmost g wh
ich span the given curve configuration. In the talk I will \ndiscuss a ge
neralization of this theorem to singular configurations of \npossibly non
-disjoint or self-intersecting curves. The proof relies on \nan existence
result for minimal surfaces in singular metric spaces and \ndoes not see
m amenable by classical smooth techniques. This is joint \nwork with M. F
itzi.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Bate (University of Warwick)
DTSTART:20211112T160000Z
DTEND:20211112T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/21
DESCRIPTION:Title: Characterising rectifiable metric spaces using tangent spaces\nby David Bate (University of Warwick) as part of mms&convergence\n\n\n
Abstract\nWe characterise rectifiable subsets of a complete metric space $
X$ in terms of local approximation\, with respect to the Gromov--Hausdorff
distance\, by an $n$-dimensional Banach space. In fact\, if $E\\subset X$
with $\\H^n(E)<\\infty$ and has positive lower density almost everywhere\
, we prove that it is sufficient that\, at almost every point and each suf
ficiently small scale\, $E$ is approximated by a bi-Lipschitz image of Euc
lidean space.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathias Braun (IAM Universität Bonn)
DTSTART:20211119T160000Z
DTEND:20211119T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/22
DESCRIPTION:Title: Vector calculus for tamed Dirichlet spaces\nby Mathias Brau
n (IAM Universität Bonn) as part of mms&convergence\n\n\nAbstract\nWe out
line the construction of a first order calculus on a \ntopological Lusin m
easure space $(M\, \\mathfrak{m})$ carrying a \nquasi-regular\, strongly l
ocal Dirichlet form $\\mathcal{E}$ in the language \nof $L^\\infty$-module
s proposed by Gigli. Furthermore\, we show how to develop \na second order
calculus if $(M\,\\mathcal{E}\,\\mathfrak{m})$ is tamed by a \nsigned mea
sure in the extended Kato class in the sense of Erbar\, Rigoni\, \nSturm a
nd Tamanini. These types of Ricci bounds typically arise on spaces \ne.g.
with singularities of unbounded curvature or with nonconvex boundary. \nTh
is procedure allows us to define e.g. Hessians\, covariant and exterior \n
derivatives\, Ricci curvature\, and second fundamental form.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jikang Wang (Rutgers University)
DTSTART:20211126T160000Z
DTEND:20211126T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/23
DESCRIPTION:Title: Ricci limit spaces are semi-locally simply connected\nby Ji
kang Wang (Rutgers University) as part of mms&convergence\n\n\nAbstract\nI
n this talk\, we will discuss local topology of a Ricci limit space $(X\,p
)$\, which is the pointed Gromov-Hausdorff limit of a sequence of complete
$n$-manifolds with a uniform Ricci curvature lower bound. I will show tha
t $(X\,p)$ is semi-locally simply connected\, that is\, for any point $x \
\in X$\, we can find a small ball $B_r(x)$ such that any loop in $B_r(x)$
is contractible in $X$. We will also discuss a slice theorem for pseudo-gr
oup actions on the Ricci limit space and how to use this slice theorem to
construct a homotopy map on the limit space. Partial material of this talk
is joint work with Jiayin Pan.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guofang Wei (UC Santa Barbara)
DTSTART:20211210T160000Z
DTEND:20211210T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/24
DESCRIPTION:Title: Examples of Ricci limit spaces with non-integer Hausdorff dimen
sion\nby Guofang Wei (UC Santa Barbara) as part of mms&convergence\n\n
\nAbstract\nWe give the first examples of collapsing Ricci limit spaces on
which the Hausdorff dimension of the singular set exceeds that of the reg
ular set\; moreover\, the Hausdorff dimension of these spaces can be non-i
ntegers. This answers a question of Cheeger-Colding about collapsing Ricci
limit spaces. This is a joint work with Jiayin Pan.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Oronzio (Università degli studi di Napoli Federico II)
DTSTART:20220204T160000Z
DTEND:20220204T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/25
DESCRIPTION:Title: A Green’s function proof of the positive mass theorem\nby
Francesca Oronzio (Università degli studi di Napoli Federico II) as part
of mms&convergence\n\n\nAbstract\nIn this talk\, we describe a new monoto
nicity formula holding along the level sets of the Green’s function of a
complete one–ended asymptotically flat manifold of dimension 3 with non
negative scalar curvature. Using such formula\, we obtain a simple proof o
f the celebrated positive mass theorem. The results discussed are obtained
in collaboration with Virginia Agostiniani and Lorenzo Mazzieri.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Stern (University of Chicago)
DTSTART:20220211T160000Z
DTEND:20220211T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/26
DESCRIPTION:Title: Level set methods for scalar curvature and applications to ADM
mass\nby Daniel Stern (University of Chicago) as part of mms&convergen
ce\n\n\nAbstract\nIn the last few years\, it has been observed that severa
l classic results (and a few new ones) concerning the geometry of three-ma
nifolds with scalar curvature bounds--and\, relatedly\, initial data sets
in GR--can be recovered by examining the relation between scalar curvature
and the topology of level sets of solutions to certain elliptic equations
\, such as harmonic functions. In this talk\, I'll survey some of these de
velopments and discuss some related open questions.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elefterios Soultanis (Radboud University)
DTSTART:20220218T160000Z
DTEND:20220218T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/27
DESCRIPTION:Title: Homotopic Plateau-Douglas problem\nby Elefterios Soultanis
(Radboud University) as part of mms&convergence\n\n\nAbstract\nThe Plateau
-Douglas problem generalizes Plateau’s famous problem and asks to find a
n area minimizing (weakly conformal) map spanning k given curves (inside a
given ambient space) from a surface with k boundary components and given
genus. In this talk I will describe the homotopic variant of this problem\
, where the area minimizer is subject to further topological restrictions.
I will describe the relevant topological data\, namely 1-homotopy classes
\, and discuss the minimization problem in a metric space setting where no
smooth structure is available.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demetre Kazaras (Duke University)
DTSTART:20220311T160000Z
DTEND:20220311T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/28
DESCRIPTION:Title: How does total mass affect spatial geometry?\nby Demetre Ka
zaras (Duke University) as part of mms&convergence\n\n\nAbstract\nIn mathe
matical general relativity\, the ADM mass of an isolated gravitational sys
tem is a geometric invariant measuring the total mass due to matter and ot
her fields present in spacetime. The celebrated Positive Mass Theorem (of
Schoen-Yau and Witten) states that this invariant is non-negative and vani
shes only for flat spacetime.\n\nIn recent work\, we showed how to compute
ADM mass in 3 spatial dimensions by studying harmonic functions. I will e
xplain this\, then use the resulting formula to consider the following que
stion: How flat is an "asymptotically flat" space with very little total m
ass? The existence of wormholes and gravity wells make this question subtl
e. We make progress on this problem on the case when the Ricci curvature h
as a uniform lower bound and partially confirm conjectures made by Huisken
-Ilmanen and Lee-Sormani.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvester Eriksson-Bique (University of Oulu)
DTSTART:20220325T160000Z
DTEND:20220325T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/29
DESCRIPTION:Title: A Differential for Sobolev Functions\nby Sylvester Eriksson
-Bique (University of Oulu) as part of mms&convergence\n\n\nAbstract\nChee
ger showed that a differential calculus was possible in metric measure spa
ces\, which support a Poincare inequality and which are measure doubling.
His differential arose as a derivative of a Lipschitz function with respec
t to a chart -- a pointwise notion. Gigli showed that such a calculus is p
ossible in any metric measure space\, but his differential was essentially
a field\, and arose through a completion process. With Elefterios Soultan
is we worked in between these two regimes\, and constructed a Sobolev diff
erential\, which is pointwise meaningful\, but which is defined in all met
ric measure spaces with finite Hausdorff dimension. It is isomorphic to ei
ther of the previous differentials\, when all are defined. In this talk\,
I will present this differential and its interpretation\, as well as how i
t may simplify some intuition and calculations. I will also briefly discus
s some applications\, such as the p=1 case\, where our construction gives
the first definition of a differential for W^1\,1 functions.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paula Burkhardt-Guim (NYU)
DTSTART:20220401T150000Z
DTEND:20220401T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/30
DESCRIPTION:Title: Lower scalar curvature bounds for C^0 metrics: a Ricci flow app
roach\nby Paula Burkhardt-Guim (NYU) as part of mms&convergence\n\n\nA
bstract\nWe describe some recent work that has been done to generalize the
notion of lower scalar curvature bounds to $C^0$ metrics\, including a lo
calized Ricci flow approach. In particular\, we show the following: that t
here is a Ricci flow definition which is stable under greater-than-second-
order perturbation of the metric\, that there exists a reasonable notion o
f a Ricci flow starting from $C^0$ initial data which is smooth for positi
ve times\, and that the weak lower scalar curvature bounds are preserved u
nder evolution by the Ricci flow from $C^0$ initial data.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vitali Kapovitch (University of Toronto)
DTSTART:20220422T150000Z
DTEND:20220422T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/31
DESCRIPTION:Title: Mixed curvature almost flat manifolds\nby Vitali Kapovitch
(University of Toronto) as part of mms&convergence\n\n\nAbstract\nA celebr
ated theorem of Gromov says that given $n>1$ there is an $\\epsilon(n)>0$
such that if a closed Riemannian manifold $M^n$ satisfies $-\\epsilon < se
c_M < \\epsilon\, diam(M) < 1$ then $M$ is diffeomorphic to an infranilman
ifold. I will show that the lower sectional curvature bound in Gromov’s
theorem can be weakened to the lower Bakry-Emery Ricci curvature bound. I
will also discuss the relation of this result to the study of manifolds wi
th Ricci curvature bounded below.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elia Bruè (Institute for Advanced Study\, Princeton)
DTSTART:20220128T160000Z
DTEND:20220128T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/32
DESCRIPTION:Title: Isoperimetric sets in manifolds with nonnegative Ricci curvatur
e and Euclidean volume growth\nby Elia Bruè (Institute for Advanced S
tudy\, Princeton) as part of mms&convergence\n\n\nAbstract\nI will present
a new existence result for isoperimetric sets of large volume on manifold
s with nonnegative Ricci curvature and Euclidean volume growth\, under an
additional assumption on the structure of tangent cones at infinity.\nAft
er a brief discussion on the sharpness of the additional assumption\, I wi
ll show that it is always verified on manifolds with nonnegative sectional
curvature. I will finally present the main ingredients of proof emphasizi
ng the key role of nonsmooth techniques tailored for the study of RCD spa
ces\, a class of metric measure structures satisfying a synthetic notion o
f Ricci curvature bounded below.\n\nThis is based on a joint work with G.
Antonelli\, M. Fogagnolo and M. Pozzetta.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazuhiro Kuwae (Fukuoka University)
DTSTART:20220225T130000Z
DTEND:20220225T140000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/33
DESCRIPTION:Title: Lower weighted Ricci curvature bounds for non-symmetric Laplaci
an\nby Kazuhiro Kuwae (Fukuoka University) as part of mms&convergence\
n\n\nAbstract\nThis is a survey talk on the Laplacian comparison theorem f
or weighted Laplacian \nand its related geometry based on the following pa
pers: \n\nLaplacian comparison theorem on Riemannian manifolds with modifi
ed $m$-Bakry–Émery Ricci lower bounds for $m\\leq1$ (joint with T. Shuk
uri)\, Tohoku Math. J. 74 (2022)\, no.1\, 1--25. \n\nRigidity phenomena o
n lower N-weighted Ricci curvature bounds with \n$\\varepsilon$-range for
nonsymmetric Laplacian (joint with Y. Sakurai)\, Illinois J. Math. 65 (202
1)\, no. 4\, 847 - 868.\n\nPlease notice the unusual time\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Gigli (SISSA)
DTSTART:20220304T160000Z
DTEND:20220304T170000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/34
DESCRIPTION:Title: Lipschitz continuity of harmonic maps from RCD to CAT(0) spaces
\nby Nicola Gigli (SISSA) as part of mms&convergence\n\n\nAbstract\nIn
`classical’ geometric analysis a celebrated result by Eells-Sampson gra
nts Lipschitz continuity of harmonic maps from manifolds with Ricci curvat
ure bounded from below to simply connected manifolds with non-negative sec
tional curvature. All these concepts\, namely lower Ricci bounds\, upper s
ectional bounds and harmonicity\, make sense in the setting of metric-meas
ure geometry and is therefore natural to ask whether a regularity result l
ike the one of Eells-Sampson hold in this more general setting.\nIn this t
alk I will survey a series of recent papers that ultimately answer affirma
tively to this question.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tapio Rajala (University of Jyväskylä)
DTSTART:20220408T150000Z
DTEND:20220408T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/35
DESCRIPTION:Title: BV- and W^{1\,1}-extensions\nby Tapio Rajala (University of
Jyväskylä) as part of mms&convergence\n\n\nAbstract\nI will discuss the
difference between BV- and W^{1\,1}-extension domains. Emphasis will be o
n planar domains\, but we will also have a look at which tools work on gen
eral metric measure spaces.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shouhei Honda (Tohoku University)
DTSTART:20220318T130000Z
DTEND:20220318T140000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/36
DESCRIPTION:Title: Topological stability theorem from nonsmooth to smooth spaces w
ith Ricci curvature bounded below\nby Shouhei Honda (Tohoku University
) as part of mms&convergence\n\n\nAbstract\nIn this talk\, inspired by a r
ecent work of Bing Wang and\nXinrui Zhao\, we prove that for a fixed $n$-d
imensional closed\nRiemannian manifold $(M^n\, g)$\, if an $\\mathrm{RCD}(
K\, n)$ space $(X\,\nd\, m)$ is Gromov-Hausdorff close to $M^n$\, then the
re exists a\nhomeomorphism $F$ from $X$ to $M^n$ such that $F$ is Lipschit
z\ncontinuous and $F^{-1}$ is Hölder continuous\, where the Lipschitz\nco
nstant of $F$\, the Hölder exponent and the Hölder constant of\n$F^{-1}$
can be chosen arbitrary close to $1$. Moreover if $X$ is\nsmooth\, then s
uch a map $F$ can be chosen as a diffeomorphism. This is\na joint work wit
h Yuanlin Peng (Tohoku University).\n\nPlease notice the unusual time.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Ozuch (MIT)
DTSTART:20220429T150000Z
DTEND:20220429T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/37
DESCRIPTION:Title: Noncollapsed degeneration and desingularization of Einstein 4-m
anifolds\nby Tristan Ozuch (MIT) as part of mms&convergence\n\n\nAbstr
act\nWe study the moduli space of unit-volume Einstein 4-manifolds near it
s finite-distance boundary\, that is\, the noncollapsed singularity format
ion. We prove that any smooth Einstein 4-manifold close to a singular one
in a mere Gromov-Hausdorff (GH) sense is the result of a gluing-perturbati
on procedure that we develop and which handles the presence of multiple tr
ees of singularities at arbitrary scales.\n\nIn particular\, this lets us
show that spherical and hyperbolic orbifolds (which are Einstein in a synt
hetic sense) cannot be GH-approximated by smooth Einstein metrics.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiayin Pan (Fields Institute)
DTSTART:20220506T150000Z
DTEND:20220506T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/38
DESCRIPTION:Title: Nonnegative Ricci curvature\, metric cones\, and virtual abeli
anness\nby Jiayin Pan (Fields Institute) as part of mms&convergence\n\
n\nAbstract\nLet M be an open n-manifold with nonnegative Ricci curvature.
\nWe prove that if its escape rate is not 1/2 and its Riemannian universa
l \ncover is conic at infinity\, that is\, every asymptotic cone (Y\,y) of
the \nuniversal cover is a metric cone with vertex y\, then \\pi_1(M) con
tains \nan abelian subgroup of finite index. If in addition the universal
cover \nhas Euclidean volume growth of constant at least L\, we can furthe
r bound \nthe index by a constant C(n\,L).\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Tamanini (Bocconi University)
DTSTART:20220520T150000Z
DTEND:20220520T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/39
DESCRIPTION:Title: From viscosity solutions of Hamilton-Jacobi equation to large d
eviations in RCD spaces\nby Luca Tamanini (Bocconi University) as part
of mms&convergence\n\n\nAbstract\nThe heat kernel plays a crucial role in
geometric and stochastic analysis and understanding its behaviour is ther
efore of particular importance in applications and estimates. In this resp
ect\, a Large Deviation Principle (LDP) provides an accurate quantitative
description.\n\nAfter a brief introduction about background and motivation
s\, the talk will be essentially divided into two parts. \nIn the former w
e will discuss and prove in the full generality of $RCD(K\,\\infty)$ space
s the convergence of solutions to HJB equations towards viscosity solution
s of HJ equations. The proof relies on uniform gradient and Laplacian esti
mates for solutions to HJB equation.\nIn the second part\, leveraging on t
he estimates obtained before\, we will study the small-time Large Deviatio
n Principle for both the heat kernel and the Brownian motion under an addi
tional properness assumption. The relationship between LDP\, viscosity sol
utions and $\\Gamma$-convergence of the relative entropy will be at the ve
ry heart of the proof.\n\n(based on a joint work with N. Gigli and D. Trev
isan)\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Tewodrose (Université de Nantes)
DTSTART:20220527T150000Z
DTEND:20220527T160000Z
DTSTAMP:20260404T110824Z
UID:mmsANDconv/40
DESCRIPTION:Title: Kato limit spaces\nby David Tewodrose (Université de Nante
s) as part of mms&convergence\n\n\nAbstract\nIn this talk\, I will present
a couple of joint works with \nGilles Carron (Nantes Université) and Ila
ria Mondello (Université \nParis Est Créteil) where we study geometric a
nd analytic properties of \nKato limit spaces\, which are measured Gromov-
Hausdorff limits of closed \nRiemannian manifolds with negative part of th
e greatest pointwise lower \nbound of the Ricci curvature in a uniform Kat
o class. This assumption \nallows for the Ricci curvature to degenerate to
- infinity\, but in a way \nthat is controlled by the heat kernel. I will
present our main results\, \nincluding volume continuity\, stratification
of the singular set\, \nrectifiability and Hölder regularity of the regu
lar set.\n
LOCATION:https://stable.researchseminars.org/talk/mmsANDconv/40/
END:VEVENT
END:VCALENDAR