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BEGIN:VEVENT
SUMMARY:Daniel Luckhardt (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20200605T150000Z
DTEND;VALUE=DATE-TIME:20200605T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/1
DESCRIPTION:Title: A volume comparison theorem for characteristic numbers\nby Daniel L
uckhardt (Ben-Gurion University) as part of mms&convergence\n\n\nAbstract\
nWe show that assuming lower bounds on the Ricci curvature and the\ninject
ivity radius the absolute value of any \ncharacteristic number of a Rieman
nian manifold M is bounded \nproportional to the volume\, i.e. bounded by
Cvol(M) where C \ndepends only on the characteristic number\, \nthe dimen
sion of M\, and both bounds. The proof relies \non the definition of a con
nection for an harmonic Hölder \nregular metric tensor as they appear for
instance as \nGromov-Hausdorff limits of Riemannian manifolds.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Ketterer (Toronto University)
DTSTART;VALUE=DATE-TIME:20200612T150000Z
DTEND;VALUE=DATE-TIME:20200612T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
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\nAb
stract\nIn this talk I show how one can formulate and prove the\nHeintze-K
archer inequality in the context of nonsmooth spaces that\nsatisfy a Ricci
curvature bound in the sense of Lott\, Sturm and\nVillani. As a by-produc
t one obtains a notion of mean curvature for\nthe boundary of Borel sets i
n such spaces. My approach is based on the\nneedle decomposition method in
troduced for this framework by\nCavalletti and Mondino.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Zamora (Penn State University)
DTSTART;VALUE=DATE-TIME:20200619T150000Z
DTEND;VALUE=DATE-TIME:20200619T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/3
DESCRIPTION:Title: Fundamental Groups and Limits of Almost Homogeneous Spaces\nby Serg
io Zamora (Penn State University) as part of mms&convergence\n\n\nAbstract
\nWe show that for a sequence of proper length spaces $X_n$ with groups $\
\Gamma_n$ acting discretely and almost transitively by isometries\, if the
y converge to a proper finite dimensional length space $X$\, then $X$ is a
nilpotent Lie group with an invariant sub-Finsler Carnot metric. Also\, f
or large enough $n$\, there are subgroups $\\Lambda_n \\leq \\pi_1(X_n)$ a
nd surjective morphisms $\\Lambda_n\\to \\pi_1(X)$.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Mondello (Université de Paris Est Créteil)
DTSTART;VALUE=DATE-TIME:20200626T150000Z
DTEND;VALUE=DATE-TIME:20200626T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/4
DESCRIPTION:Title: Ricci limit spaces : an introduction to the tools of Cheeger-Jiang-Nabe
r's work\nby Ilaria Mondello (Université de Paris Est Créteil) as pa
rt of mms&convergence\n\n\nAbstract\nThe goal of this expository talk is t
o explain parts of the work of J. Cheeger\, W. Jiang and A. Naber:\nhttps:
//arxiv.org/abs/1805.07988 For a converging\, non-collapsing sequence of R
iemannian manifolds with a uniform Ricci lower bound\, they proved that si
ngular strata of the limit space are rectifiable. Some of the key tools in
the proof include quantitative stratification\, which was first introduce
d in previous work of Cheeger-Naber\, and new related volume estimates\, t
ogether with a precise study of neck regions. After a brief review of Chee
ger-Colding theory\, the talk will focus on explaining the notions of quan
titative stratifications\, neck regions and their role in the proof.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Allen (University of Hartford)
DTSTART;VALUE=DATE-TIME:20200703T150000Z
DTEND;VALUE=DATE-TIME:20200703T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/5
DESCRIPTION:Title: Null Distance and Convergence of Warped Product Spacetimes\nby Bria
n Allen (University of Hartford) as part of mms&convergence\n\n\nAbstract\
nThe null distance was introduced by Christina Sormani and Carlos Vega as
a way of turning a spacetime into a metric space. This is particularly imp
ortant for geometric stability questions relating to spacetimes such as th
e stability of the positive mass theorem. In this talk\, we will describe
the null distance\, present properties of the metric space structure\, and
examine the convergence of sequences of warped product spacetimes equippe
d with the null distance. This is joint work with Annegret Burtscher.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Carron (Université de Nantes)
DTSTART;VALUE=DATE-TIME:20200904T150000Z
DTEND;VALUE=DATE-TIME:20200904T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/6
DESCRIPTION:Title: Euclidean heat kernel rigidity\nby Gilles Carron (Université de Na
ntes) as part of mms&convergence\n\n\nAbstract\nThis is joint work with D
avid Tewodrose (Cergy). I will explain that a metric measure space with Eu
clidean heat kernel are Euclidean. An almost rigidity result comes then fo
r free\, and this can be used to give another proof of Colding's almost r
igidity for complete manifold with non negative Ricci curvature and almos
t Euclidean growth.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danka Lučić (University of Jyväskylä)
DTSTART;VALUE=DATE-TIME:20200911T150000Z
DTEND;VALUE=DATE-TIME:20200911T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/7
DESCRIPTION:Title: Techniques for proving infinitesimal Hilbertianity\nby Danka Luči
ć (University of Jyväskylä) as part of mms&convergence\n\n\nAbstract\nA
metric space is said to be "universally infinitesimally Hilbertian" if\,
when endowed with any arbitrary Radon measure\, its associated 2-Sobolev s
pace is Hilbert. For instance\, all (sub)Riemannian manifolds and CAT(K) s
paces have this property. In this talk\, we will illustrate three differen
t strategies to prove the universal infinitesimal Hilbertianity of the Euc
lidean space\, which is the base case and where all the known approaches w
ork.\nThe motivations come\, among others\, from the study of rectifiable
metric measure spaces\, of metric-valued harmonic maps\, and of variationa
l problems (such as models representing low-dimensional elastic structures
).\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200925T150000Z
DTEND;VALUE=DATE-TIME:20200925T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/9
DESCRIPTION:Title: An optimal transport formulation of the Einstein equations of general r
elativity\nby Andrea Mondino (University of Oxford) as part of mms&con
vergence\n\n\nAbstract\nIn the seminar I will present a recent work joint
with S. Suhr (Bochum) giving an optimal transport formulation of the full
Einstein equations of general relativity\, linking the (Ricci) curvature o
f a space-time with the cosmological constant and the energy-momentum tens
or. Such an optimal transport formulation is in terms of convexity/concavi
ty properties of the Shannon-Bolzmann entropy along curves of probability
measures extremizing suitable optimal transport costs. The result\, togeth
er with independent work by McCann on lower bounds for Lorentzian Ricci Cu
rvature\, gives a new connection between general relativity and optimal tr
ansport\; moreover it gives a mathematical reinforcement of the strong lin
k between general relativity and thermodynamics/information theory that em
erged in the physics literature of the last years.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Flavia Santarcangelo (SISSA)
DTSTART;VALUE=DATE-TIME:20201002T150000Z
DTEND;VALUE=DATE-TIME:20201002T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/10
DESCRIPTION:Title: Independence of synthetic Curvature Dimension conditions on transport
distance exponent\nby Flavia Santarcangelo (SISSA) as part of mms&conv
ergence\n\n\nAbstract\nThe celebrated Lott-Sturm-Villani theory of metric
measure spaces furnishes synthetic notions of a Ricci curvature lower bou
nd $K$ joint with an upper bound $N$ on the dimension. \nTheir condition\
, called the Curvature-Dimension condition and denoted by $\\mathsf{CD}(K
\,N)$\, is formulated in terms of a modified displacement convexity of an
entropy functional along $W_{2}$-Wasserstein geodesics. In a joint work
with A. Akdemir\, F. Cavalletti\, A. Colinet and R. McCann\, we show tha
t the choice of the squared-distance function as transport cost does not i
nfluence the theory. In particular\, by denoting with $\\mathsf{CD}_{p}
(K\,N)$ the analogous condition but with the cost given by the $p^{th}$ p
ower of the distance\, we prove that $\\CD_{p}(K\,N)$ are all equivalent
conditions for any $p>1$ --- at least in spaces whose geodesics do not br
anch. \nFollowing the strategy introduced in the work by Cavalletti-Milman
\, we also establish the local-to-global property of $\\mathsf{CD}_{p}(
K\,N)$ spaces. \n\nFinally\, we will present a result obtained in collabo
ration with F. Cavalletti and N. Gigli that\, combined with the one previ
ously described\, allows to conclude that for any $p\\geq1$\, all the $
\\mathsf{CD}_{p}(K\,N)$ conditions\, when expressed in terms of displacem
ent convexity\, are equivalent\, provided the space $X$ satisfies the appr
opriate essentially non-branching condition.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Semola (Scuola Normale Superiore)
DTSTART;VALUE=DATE-TIME:20201009T150000Z
DTEND;VALUE=DATE-TIME:20201009T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/11
DESCRIPTION:Title: Rectifiability of RCD(K\,N) spaces via delta-splitting maps\nby Da
niele Semola (Scuola Normale Superiore) as part of mms&convergence\n\n\nAb
stract\nThe theory of metric measure spaces verifying the Riemannian-Curva
ture-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 o
f Riemannian manifolds with Ricci curvature bounded from below by K and di
mension bounded from above by N.\n\nIn this talk\, after providing some ba
ckground and motivations\, I will describe a simplified approach to the st
ructure theory of these spaces relying on the so-called delta-splitting ma
ps. This tool\, developed by Cheeger-Colding in the study of Ricci limits\
, has revealed to be extremely powerful also more recently in the study of
RCD spaces. \n\nThe seminar is based on a joint work with Elia Brue' and
Enrico Pasqualetto.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Chun Lee (The Chinese University of Hong Kong (CUHK) Mathemati
cs)
DTSTART;VALUE=DATE-TIME:20211001T150000Z
DTEND;VALUE=DATE-TIME:20211001T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
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 Hon
g Kong (CUHK) Mathematics) as part of mms&convergence\n\n\nAbstract\nIn th
is talk\, we consider Riemannian manifolds with almost non-negative scalar
curvature and Perelman entropy. We establish an\nepsilon-regularity theor
em showing that such a space must be close to Euclidean space in a suitabl
e sense. We will illustrate examples showing that\nthe result is false wit
h respect to the Gromov-Hausdorff and Intrinsic Flat distances\, and more
generally the metric space structure is not\ncontrolled under entropy and
scalar lower bounds. We will introduce the notion of the d_p distance betw
een (in particular) Riemannian manifolds\,\nwhich measures the distance be
tween W^{1\,p} Sobolev spaces\, and it is with respect to this distance th
at the epsilon regularity theorem holds. This\nis joint work with A. Naber
and R. Neumayer.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qin Deng (Massachusetts Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210917T150000Z
DTEND;VALUE=DATE-TIME:20210917T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/13
DESCRIPTION:Title: Hölder continuity of tangent cones in RCD(K\,N) spaces and applicatio
ns to non-branching\nby Qin Deng (Massachusetts Institute of Technolog
y) as part of mms&convergence\n\n\nAbstract\nIt is known by a result of Co
lding-Naber that for any two points in a Ricci limit space\, there exists
a minimizing geodesic where the geometry of small balls centred along the
interior of the geodesic change in at most a Hölder continuous manner. Th
is was shown using an extrinsic argument and had several key applications
for the structure theory of Ricci limits. In this talk\, I will discuss ho
w to overcome the use of smooth structure in the Colding-Naber argument in
order to generalize this result to the setting of metric measure spaces s
atisfying the synthetic lower Ricci curvature bound condition RCD(K\,N). A
s an application\, I will show that all RCD(K\,N) spaces are non-branching
\, a result which was previously unknown for Ricci limit spaces.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Farinelli (SISSA)
DTSTART;VALUE=DATE-TIME:20211008T150000Z
DTEND;VALUE=DATE-TIME:20211008T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
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 mms&conve
rgence\n\n\nAbstract\nUpper and lower bounds of the Hausdorff measure of n
odal sets of Laplace eigenfunctions have been largely studied in the cont
ext of smooth Riemannian manifolds.\nIn the talk we will investigate this
problem in the setting of singular metric measure spaces satisfying a synt
hetic curvature condition. In particular we prove a lower bound for the me
asure of the nodal set. We follow an approach introduced by Steinerberger
in the smooth case\, which uses an indeterminacy estimate involving optima
l transport. Further exploring the relation between eigenfunctions and opt
imal transport\, we will also present a lower bound for the Wasserstein di
stance between the positive part and the negative part of an eigenfunction
\, conjectured by Steinerberger. These are joint works with Fabio Cavallet
ti and Nicolò De Ponti.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Pasqualetto (Scuola Normale Superiore)
DTSTART;VALUE=DATE-TIME:20210924T150000Z
DTEND;VALUE=DATE-TIME:20210924T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/15
DESCRIPTION:Title: The role of test plans in metric measure geometry\nby Enrico Pasqu
aletto (Scuola Normale Superiore) as part of mms&convergence\n\n\nAbstract
\nA test plan on a metric measure space is a probability measure on curves
having bounded compression and finite kinetic energy\; the former means t
hat it does not concentrate mass at any time\, the latter that the metric
speed functional satisfies a suitable integral bound with respect to the t
est plan.\nIn the first part of the talk\, I will discuss the prominent ro
le that test plans played in the development of Sobolev and BV calculus on
metric measure spaces\, as well as their strong connections (on spaces wi
th lower Ricci bounds) with Optimal Transport and the theory of Regular La
grangian Flows.\nIn the second part of the talk\, I will report on some re
cent results concerning "master test plans": roughly speaking\, these resu
lts say that under suitable assumptions on the underlying space\, smaller
classes of test plans are still sufficient to entirely recover the Sobolev
and BV calculus. As a consequence\, I will show that on finite-dimensiona
l RCD spaces the reduced boundaries of finite perimeter sets have constant
dimension.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Kopfer (IAM Universität Bonn)
DTSTART;VALUE=DATE-TIME:20211015T130000Z
DTEND;VALUE=DATE-TIME:20211015T140000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/16
DESCRIPTION:Title: Optimal transport and homogenization\nby Eva Kopfer (IAM Universit
ät Bonn) as part of mms&convergence\n\n\nAbstract\nWe consider discrete d
ynamical transport costs on periodic network graphs and compute the limit
cost as the mesh size of the graphs is getting finer and finer. A prominen
t example is given by the\nBenamou-Brenier formulation of the Wasserstein
distance.\n\nNotice the unusual time.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattia Fogagnolo (Scuola Normale Superiore)
DTSTART;VALUE=DATE-TIME:20211022T150000Z
DTEND;VALUE=DATE-TIME:20211022T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/17
DESCRIPTION:Title: Minkowski inequalities in manifolds with nonnegative Ricci curvature\nby Mattia Fogagnolo (Scuola Normale Superiore) as part of mms&converge
nce\n\n\nAbstract\nWe provide\, in manifolds with nonnegative Ricci curvat
ure\, a sharp estimate of the total curvature of a hypersurface in terms o
f a power of the perimeter of is minimizing hull.\nIn particular\, it yiel
ds a new sharp Minkowski inequality for outward minimizing sets. The proof
relies on full monotonicity formulas along the level sets of p-harmonic f
unctions\nand on the sharp iso-p-capacitary inequality derived from the re
cent Brendle's isoperimetric inequality.\nThese results are obtained in a
joint work with L. Benatti and L. Mazzieri.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Hallgren (Cornell University)
DTSTART;VALUE=DATE-TIME:20211029T150000Z
DTEND;VALUE=DATE-TIME:20211029T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/18
DESCRIPTION:Title: Ricci Flow with a Lower Bound on Ricci Curvature\nby Max Hallgren
(Cornell University) as part of mms&convergence\n\n\nAbstract\nIn this tal
k\, we will investigate the possible singularity behavior of closed soluti
ons of Ricci flow whose Ricci curvature is uniformly bounded below\, and w
hose volume does not go to zero. In four dimensions\, we will see that onl
y orbifold singularities can arise\, and prove integral curvature estimate
s on time slices. We will also see a rough picture of singularity formatio
n in higher dimensions.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Violo (University of Jyväskylä (JYU))
DTSTART;VALUE=DATE-TIME:20211105T160000Z
DTEND;VALUE=DATE-TIME:20211105T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/19
DESCRIPTION:Title: Rigidity and almost-rigidity of the Sobolev inequality under lower Ric
ci curvature bounds\nby Ivan Violo (University of Jyväskylä (JYU)) a
s part of mms&convergence\n\n\nAbstract\nIn this seminar we will present a
new rigidity principle related to the value of the optimal constant in t
he Sobolev inequality\, for n-dimensional Riemannian manifolds with Ricci
curvature bounded below by n-1. The analysis will be carried out in the mo
re general class of (non-smooth) RCD-spaces\, which will allow us to get a
lso an almost-rigidity result.\n\nThe arguments are based on a Euclidean
Polya-Szego inequality on metric measure spaces and on a version of Lions'
concentration-compactness principle under varying ambient space. This is
joint work with Francesco Nobili.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Creutz (University of Cologne)
DTSTART;VALUE=DATE-TIME:20211203T160000Z
DTEND;VALUE=DATE-TIME:20211203T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/20
DESCRIPTION:Title: Area minimizing surfaces for singular boundary values\nby Paul Cre
utz (University of Cologne) as part of mms&convergence\n\n\nAbstract\nFix
a nonnegative integer g and a finite configuration of \ndisjoint Jordan c
urves in Euclidean space. Then\, by a classical result \nof Douglas\, the
re is an area minimizer among all surfaces of genus at \nmost g which spa
n the given curve configuration. In the talk I will \ndiscuss a generaliz
ation of this theorem to singular configurations of \npossibly non-disjoi
nt or self-intersecting curves. The proof relies on \nan existence result
for minimal surfaces in singular metric spaces and \ndoes not seem amena
ble by classical smooth techniques. This is joint \nwork with M. Fitzi.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Bate (University of Warwick)
DTSTART;VALUE=DATE-TIME:20211112T160000Z
DTEND;VALUE=DATE-TIME:20211112T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
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\nAbstrac
t\nWe characterise rectifiable subsets of a complete metric space $X$ in t
erms of local approximation\, with respect to the Gromov--Hausdorff distan
ce\, 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 pr
ove that it is sufficient that\, at almost every point and each sufficient
ly small scale\, $E$ is approximated by a bi-Lipschitz image of Euclidean
space.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathias Braun (IAM Universität Bonn)
DTSTART;VALUE=DATE-TIME:20211119T160000Z
DTEND;VALUE=DATE-TIME:20211119T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/22
DESCRIPTION:Title: Vector calculus for tamed Dirichlet spaces\nby Mathias Braun (IAM
Universität Bonn) as part of mms&convergence\n\n\nAbstract\nWe outline th
e construction of a first order calculus on a \ntopological Lusin measure
space $(M\, \\mathfrak{m})$ carrying a \nquasi-regular\, strongly local Di
richlet form $\\mathcal{E}$ in the language \nof $L^\\infty$-modules propo
sed by Gigli. Furthermore\, we show how to develop \na second order calcul
us if $(M\,\\mathcal{E}\,\\mathfrak{m})$ is tamed by a \nsigned measure in
the extended Kato class in the sense of Erbar\, Rigoni\, \nSturm and Tama
nini. These types of Ricci bounds typically arise on spaces \ne.g. with si
ngularities of unbounded curvature or with nonconvex boundary. \nThis proc
edure allows us to define e.g. Hessians\, covariant and exterior \nderivat
ives\, Ricci curvature\, and second fundamental form.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jikang Wang (Rutgers University)
DTSTART;VALUE=DATE-TIME:20211126T160000Z
DTEND;VALUE=DATE-TIME:20211126T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/23
DESCRIPTION:Title: Ricci limit spaces are semi-locally simply connected\nby Jikang Wa
ng (Rutgers University) as part of mms&convergence\n\n\nAbstract\nIn this
talk\, we will discuss local topology of a Ricci limit space $(X\,p)$\, wh
ich is the pointed Gromov-Hausdorff limit of a sequence of complete $n$-ma
nifolds with a uniform Ricci curvature lower bound. I will show that $(X\,
p)$ 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 cont
ractible in $X$. We will also discuss a slice theorem for pseudo-group act
ions on the Ricci limit space and how to use this slice theorem to constru
ct a homotopy map on the limit space. Partial material of this talk is joi
nt work with Jiayin Pan.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guofang Wei (UC Santa Barbara)
DTSTART;VALUE=DATE-TIME:20211210T160000Z
DTEND;VALUE=DATE-TIME:20211210T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071747Z
UID:mmsANDconv/24
DESCRIPTION:Title: Examples of Ricci limit spaces with non-integer Hausdorff dimension\nby Guofang Wei (UC Santa Barbara) as part of mms&convergence\n\n\nAbstr
act\nWe give the first examples of collapsing Ricci limit spaces on which
the Hausdorff dimension of the singular set exceeds that of the regular se
t\; moreover\, the Hausdorff dimension of these spaces can be non-integers
. This answers a question of Cheeger-Colding about collapsing Ricci limit
spaces. This is a joint work with Jiayin Pan.\n
LOCATION:https://researchseminars.org/talk/mmsANDconv/24/
END:VEVENT
END:VCALENDAR