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BEGIN:VEVENT
SUMMARY:Spaces of riemannian metrics satisfying surgery stable curvature c
onditions
DTSTART;VALUE=DATE-TIME:20181108T094000Z
DTEND;VALUE=DATE-TIME:20181108T103000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4809@indico.scc.kit.edu
DESCRIPTION:Speakers: Jan-Bernhard Kordaß (Karlsruhe Institute of Technol
ogy (KIT))\nWe will introduce spaces of riemannian metrics on a smooth man
ifold satisfying a curvature condition given by a subset in the space of a
lgebraic curvature operators. Provided this condition is surgery stable\,
which is a notion based on the work of S. Hoelzel guaranteeing the conditi
on can be preserved under surgeries of a certain codimension\, we can gene
ralize several theorems from positive scalar curvature geometry to this se
tting. Notably\, we will comment on a generalization of a theorem of V. Ch
ernysh on the homotopy type of the space of psc metrics and point to cases
where we can distinguish connected components using invariants from spin
geometry.\n\nhttps://indico.scc.kit.edu/event/421/contributions/4809/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4809/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A rigidity theorem for the action of the diffeomorphism group on s
paces of psc metrics
DTSTART;VALUE=DATE-TIME:20181108T082000Z
DTEND;VALUE=DATE-TIME:20181108T091000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4808@indico.scc.kit.edu
DESCRIPTION:Speakers: Johannes Ebert ()\nFor a closed\, simply connected $
d$-dimensional manifold spin $M$\, we study the action of the (spin) diffe
omorphism group of $M$ on the space $\\mathcal{R}^+ (M)$ of psc metrics on
$M$. Our main result is that the homotopy class of the map $f^*: \\mathca
l{R}^+ (M) \\to \\mathcal{R}^+ (M)$ only depends on the cobordism class in
$\\Omega^{\\mathrm{Spin}}_{d+1}$ of the mapping torus of $f$. When proper
ly formulated\, the same result is true for manifolds with nontrivial fund
amental group.\n\nhttps://indico.scc.kit.edu/event/421/contributions/4808/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4808/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the topology of the Teichmüller space of negatively curved Rie
mannian metrics
DTSTART;VALUE=DATE-TIME:20181108T103500Z
DTEND;VALUE=DATE-TIME:20181108T112500Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4702@indico.scc.kit.edu
DESCRIPTION:Speakers: Gangotryi Sorcar (Einstein Institute of Mathematics\
, HUJI)\nThis talk is a survey on results concerning the space $T^{\n\nhtt
ps://indico.scc.kit.edu/event/421/contributions/4702/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4702/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non-negative Ricci curvature and harmonic maps
DTSTART;VALUE=DATE-TIME:20181109T082000Z
DTEND;VALUE=DATE-TIME:20181109T091000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4713@indico.scc.kit.edu
DESCRIPTION:Speakers: David Wraith ()\nTaking as our starting point the cl
assic paper of Eells and\nSampson\, we use harmonic maps as a tool to inve
stigate spaces and moduli spaces of Ricci non-negative metrics\, and also
to study concordances between such metrics. In the first case\, among othe
r things\, we recover some recent results of Tuschmann and Wiemeler. In th
e second case\, we uncover an interrelationship between concordance\, isot
opy and isometry for Ricci non-negative metrics\, which stands in contrast
to the situation for positive scalar curvature.\n\nhttps://indico.scc.kit
.edu/event/421/contributions/4713/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4713/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moduli spaces of non-negatively curved metrics on homotopy $RP^5$s
DTSTART;VALUE=DATE-TIME:20181109T104000Z
DTEND;VALUE=DATE-TIME:20181109T113000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4706@indico.scc.kit.edu
DESCRIPTION:Speakers: David González Álvaro (University of Fribourg)\nTh
e goal of this talk is to discuss the following result: for a manifold hom
otopy equivalent to $RP^5$\, the moduli space of metrics with non-negative
sectional (resp. with positive Ricci) curvature has infinitely many path
connected components. The proof involves various elements such as Brieskor
n spheres\, Grove-Ziller metrics\, reduced eta-invariants and fixed point
formulas. This is joint work with Anand Dessai.\n\nhttps://indico.scc.k
it.edu/event/421/contributions/4706/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4706/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Extra twisted connected sums and their $\\nu$-invariants
DTSTART;VALUE=DATE-TIME:20181108T131000Z
DTEND;VALUE=DATE-TIME:20181108T140000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4705@indico.scc.kit.edu
DESCRIPTION:Speakers: Sebastian Goette (University of Freiburg)\nJoyce’s
orbifold construction and the twisted connected sums by Kovalev and Corti
-Haskins-Nordström-Pacini provide many examples of compact Riemannian 7-m
anifolds with holonomy $G_2$. We would like to use this wealth of examples
to guess further properties of $G_2$-manifolds and to find obstructions a
gainst holonomy $G_2$\, taking into account the underlying topological $G_
2$-structures.\n\nThe Crowley-Nordström $\\nu$-invariant distinguishes to
pological $G_2$-structures. It vanishes for all twisted connected sums. By
adding an extra twist to this construction\, we show that the $\\nu$-inva
riant can assume all of its 48 possible values. This shows that $G_2$-bord
ism presents no obstruction against holonomy $G_2$. We also exhibit exampl
es of 7-manifolds with disconnected $G_2$-moduli space. Our computation of
the $\\nu$-invariants involves integration of the Bismuth-Cheeger $\\eta$
-forms for families of tori\, which can be done either by elementary hyper
bolic geometry\, or using modular properties of the Dedekind $\\eta$-funct
ion.\n\nhttps://indico.scc.kit.edu/event/421/contributions/4705/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4705/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Positively curved manifolds with isometric torus actions
DTSTART;VALUE=DATE-TIME:20181109T133000Z
DTEND;VALUE=DATE-TIME:20181109T142000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4704@indico.scc.kit.edu
DESCRIPTION:Speakers: Michael Wiemeler (WWU Münster)\nThe classification
of positively (sectional) curved manifolds is a long standing open problem
in Riemannian geometry. So far it was a successful approach to consider t
he problem under the extra assumption of an isometric group action.\n\nIn
this talk I will report on recent joint work with Lee Kennard and Burkhard
Wilking in this direction. Among other things we show the following: Let
$M$ be a simply connected positively curved $n$-dimensional manifold with
$H^{odd} M\,\\mathbb{Q})=0$ and an isometric $T^8$-action. Then the ration
al cohomology ring of $M$ is isomorphic to the rational cohomology of one
of the CROSSes $S^n$\, $\\mathbb{C} P^{n/2}$ and $\\mathbb{H} P^{n/4}$.\n\
nhttps://indico.scc.kit.edu/event/421/contributions/4704/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4704/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Local flexibility of open partial differential relations
DTSTART;VALUE=DATE-TIME:20181109T143000Z
DTEND;VALUE=DATE-TIME:20181109T152000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4703@indico.scc.kit.edu
DESCRIPTION:Speakers: Bernhard Hanke (Augsburg University)\nIn his famous
book on partial differential relations Gromov formulates an exercise conce
rning local deformations of solutions to open partial differential relatio
ns. We will explain the content of this fundamental assertion and sketch a
proof.\n\nWe will illustrate this by various examples\, including the con
struction of $C^{1\,1}$-Riemannian metrics which are positively curved "al
most everywhere" on arbitrary manifolds.\n\nThis is joint work with Christ
ian Bär (Potsdam).\n\nhttps://indico.scc.kit.edu/event/421/contributions/
4703/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4703/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scalar curvature and the multiconformal class of a direct product
Riemannian manifold
DTSTART;VALUE=DATE-TIME:20181108T140500Z
DTEND;VALUE=DATE-TIME:20181108T145500Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4696@indico.scc.kit.edu
DESCRIPTION:Speakers: Saskia Roos (University of Potsdam)\nFor a closed\,
connected direct product Riemannian manifold $(M\,g) = (M_1 \\times \\ldot
s \\times M_l\, g_1 + \\ldots + g_l)$ we define its multiconformal class $
[\\![ g ]\\!]$ as the totality $\\lbrace f_1^2 g_1 + \\ldots + f_l^2 g_l \
\rbrace$ of all Riemannian metrics obtained from multiplying the metric $
g_i$ of each factor by a function $f_i^2:M \\rightarrow \\mathbb{R}_+$. In
this talk we discuss how constant scalar curvature metrics in a multiconf
ormal class are related with constant scalar curvature metrics on the fact
ors.\n\nhttps://indico.scc.kit.edu/event/421/contributions/4696/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4696/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Orbifolds all of whose geodesics are closed
DTSTART;VALUE=DATE-TIME:20181108T153000Z
DTEND;VALUE=DATE-TIME:20181108T162000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4695@indico.scc.kit.edu
DESCRIPTION:Speakers: Christian Lange (University of Cologne)\nManifolds a
ll of whose geodesics are closed have been studied a lot\, but there are o
nly few examples known. The situation is different if one allows in additi
on for orbifold singularities. In the talk we discuss such examples and th
eir properties. In particular\, we explain rigidity phenomena of the geode
sic length spectrum and of metrics with all geodesics closed in dimension
two.\n\nhttps://indico.scc.kit.edu/event/421/contributions/4695/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4695/
END:VEVENT
BEGIN:VEVENT
SUMMARY:$\\mathop{Spin}^c$ Dirac operators and the Kreck-Stolz s invariant
.
DTSTART;VALUE=DATE-TIME:20181109T094000Z
DTEND;VALUE=DATE-TIME:20181109T103000Z
DTSTAMP;VALUE=DATE-TIME:20240416T014641Z
UID:indico-contribution-421-4694@indico.scc.kit.edu
DESCRIPTION:Speakers: Jackson Goodman (University of Pennsylvania)\nWe use
the $\\mathop{Spin}^c$ Dirac operator to generalize a formula of Kreck an
d Stolz for the s invariant of $S^1$ invariant metrics with positive scala
r curvature. We then apply it to show that the moduli spaces of metrics wi
th nonnegative sectional curvature on certain 7-manifolds have infinitely
many path components. These include certain positively curved Eschenburg a
nd Aloff-Wallach spaces. Furthermore\, we use a $\\mathop{Spin}^c$ version
of the s invariant to discuss moduli spaces of metrics of positive scalar
and twisted scalar curvature on $\\mathop{Spin}^c$ manifolds.\n\nhttps://
indico.scc.kit.edu/event/421/contributions/4694/
LOCATION:University of Fribourg\, Switzerland
URL:https://indico.scc.kit.edu/event/421/contributions/4694/
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