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TZID:America/Chicago
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DTSTART:20231105T020000
TZOFFSETFROM:-0500
TZOFFSETTO:-0600
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DTSTART:20240310T020000
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BEGIN:VEVENT
UID:calendar.25843.field_event_date_2.0@math.wustl.edu
CREATED:20230901T193800Z
DESCRIPTION:Abstract: We will discuss various situations where a certain pe
rturbation of the Dirac operator on spin manifolds can be used to obtain d
istance estimates from lower scalar curvature bounds. A first situation co
nsists in an area non-decreasing map from a Riemannian spin manifold with
boundary X into the round sphere under the condition that the map is local
ly constant near the boundary and has nonzero degree. Here a positive lowe
r bound of the scalar curvature is quantitatively related to the distance
from the support of the differential of f and the boundary of X. A second
situation consists in estimating the distance between the boundary compone
nts of Riemannian “bands” M × [−1,1] where M is a closed manifold that do
es not carry positive scalar curvature. Both situations originated from qu
estions asked by Gromov. In the final part, I will compare the Dirac meth
od with the minimal hypersurface method and show that if N is a closed man
ifold such that the cylinder N x R carries a complete metric of positive s
calar curvature, then N also carries a metric of positive scalar curvatur
e. This answers a question asked by Rosenberg and Stolz.\n\nThis talk is b
ased on joint work with Daniel Räde and Rudolf Zeidler.\n\nHost: Yanli Son
g
DTSTART;TZID=America/Chicago:20231110T160000
DTEND;TZID=America/Chicago:20231110T170000
LAST-MODIFIED:20231101T151430Z
SUMMARY:Geometry and Topology Seminar: Metric inequalities with positive sc
alar curvature
URL;TYPE=URI:https://math.wustl.edu/events/geometry-and-topology-seminar-me
tric-inequalities-positive-scalar-curvature
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