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SUMMARY:Andrea Mondino (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200921T133000Z
DTEND;VALUE=DATE-TIME:20200921T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T110512Z
UID:UofT_GandT/1
DESCRIPTION:Title: An optimal transport formulation of the Einstein equations of general r
elativity\nby Andrea Mondino (University of Oxford) as part of Univers
ity of Toronto Geometry & Topology seminar\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 of a space-time with the cosmological con
stant and the energy-momentum tensor. Such an optimal transport formulatio
n is in terms of convexity/concavity properties of the Shannon-Bolzmann en
tropy along curves of probability measures extremizing suitable optimal tr
ansport costs. The result\, together with independent work by McCann on lo
wer bounds for Lorentzian Ricci Curvature\, gives a new connection between
general relativity and optimal transport\; moreover it gives a mathematic
al reinforcement of the strong link between general relativity and thermod
ynamics/information theory that emerged in the physics literature of the l
ast years.\n\nThe talk will be via Zoom at: https://us02web.zoom.us/j/8113
3134160 passcode 507121\n
LOCATION:https://researchseminars.org/talk/UofT_GandT/1/
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SUMMARY:Qin Deng (University of Toronto)
DTSTART;VALUE=DATE-TIME:20201005T201000Z
DTEND;VALUE=DATE-TIME:20201005T210000Z
DTSTAMP;VALUE=DATE-TIME:20240329T110512Z
UID:UofT_GandT/2
DESCRIPTION:Title: Hölder continuity of tangent cones in RCD(K\,N) spaces and application
s to non-branching\nby Qin Deng (University of Toronto) as part of Uni
versity of Toronto Geometry & Topology seminar\n\n\nAbstract\nIt is known
by a result of Colding-Naber that for any two points in a Ricci limit spac
e\, there exists a minimizing geodesic where the geometry of small balls c
entred along the interior of the geodesic change in at most a H\\”older
continuous manner. This was shown using an extrinsic argument and had seve
ral key applications for the structure theory of Ricci limits. In this tal
k\, I will discuss how to generalize this result to the setting of metric
measure spaces satisfying the synthetic lower Ricci curvature bound condit
ion RCD(K\,N). As an application\, I will show that all RCD(K\,N) spaces a
re non-branching\, a fact which was previously unknown for Ricci limits.\n
LOCATION:https://researchseminars.org/talk/UofT_GandT/2/
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SUMMARY:Aleksandr Berdnikov (MIT)
DTSTART;VALUE=DATE-TIME:20201012T200000Z
DTEND;VALUE=DATE-TIME:20201012T210000Z
DTSTAMP;VALUE=DATE-TIME:20240329T110512Z
UID:UofT_GandT/3
DESCRIPTION:Title: Waists of maps measured via Urysohn width\nby Aleksandr Berdnikov (
MIT) as part of University of Toronto Geometry & Topology seminar\n\n\nAbs
tract\nUrysohn d-width is a measure for estimating how close a metric spac
e $X$ is to being $d$-dimensional. Specifically\, $UW_d(X)$ is the lower b
ound for the largest fiber of a projection of $X$ to a $d$-dimensional com
plex. However\, the dimension estimated in such a way is less well-behaved
than the usual dimension. We explore this discrepancy getting results lik
e the following:\n\n1. The topological projection $B^{f}\\times B^m\\to B^
m$ with $f\\sim mk$ can have a metric\, such that $UW_{m+k}(F)<\\varepsilo
n$ for all fibers $F$\, and yet the total space has $UW_{f-1}=O(1)$ (``alm
ost $m+k$ dimensional fibers over $m$-base build a $\\sim mk$-space'').\n\
n2. On the other hand\, for a map $X\\to Y^m$ the $UW_{m+1}(X)$ is bounde
d by $UW_1$ and $rk (H_1(\\cdot\,\\mathbb{Z}/2))$ of the fibers.\n\n Joint
with Alexey Balitskiy.\n\nhttps://utoronto.zoom.us/j/82235760196\n
LOCATION:https://researchseminars.org/talk/UofT_GandT/3/
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SUMMARY:Nick Salter (Columbia University)
DTSTART;VALUE=DATE-TIME:20201019T200000Z
DTEND;VALUE=DATE-TIME:20201019T210000Z
DTSTAMP;VALUE=DATE-TIME:20240329T110512Z
UID:UofT_GandT/4
DESCRIPTION:Title: The “what” and the “why” of framed mapping class groups\nby
Nick Salter (Columbia University) as part of University of Toronto Geomet
ry & Topology seminar\n\n\nAbstract\nGiven a family of Riemann surfaces\,
the monodromy representation\, valued in the mapping class group of the fi
ber\, is a key invariant that encodes a great deal of information about th
e topological and algebraic structure of the family. Many natural families
\, including families of translation surfaces\, smooth sections of line bu
ndles on surfaces (e.g. plane curves)\, and the family of Milnor fibers of
a plane curve singularity\, are equipped with the additional data of a pr
eferred section of a line bundle (e.g. a holomorphic 1-form). In such circ
umstances\, the monodromy group is valued in a special subgroup known as t
he framed mapping class group. I will discuss some new tools to understand
framed mapping class groups\, and the sorts of insight they can bring to
the study of the families listed above. This encompasses joint work with A
aron Calderon and Pablo Portilla Cuadrado.\n
LOCATION:https://researchseminars.org/talk/UofT_GandT/4/
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BEGIN:VEVENT
SUMMARY:Yi Lai (UC Berkley)
DTSTART;VALUE=DATE-TIME:20201026T200000Z
DTEND;VALUE=DATE-TIME:20201026T210000Z
DTSTAMP;VALUE=DATE-TIME:20240329T110512Z
UID:UofT_GandT/5
DESCRIPTION:Title: A family of 3d steady gradient solitons that are flying wings\nby Y
i Lai (UC Berkley) as part of University of Toronto Geometry & Topology se
minar\n\n\nAbstract\nA family of 3d steady gradient solitons that are flyi
ng wings\nAbstract: We found a family of $\\mathbb{Z}_2\\times O(2)$-symme
tric 3d steady gradient Ricci solitons. We show that these solitons are al
l flying wings. This confirms a conjecture by Hamilton.\n\nhttps://us02web
.zoom.us/j/89431825216 Passcode: 569079\n
LOCATION:https://researchseminars.org/talk/UofT_GandT/5/
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SUMMARY:Zhichao Wang (University of Toronto Mississauga)
DTSTART;VALUE=DATE-TIME:20201102T210000Z
DTEND;VALUE=DATE-TIME:20201102T220000Z
DTSTAMP;VALUE=DATE-TIME:20240329T110512Z
UID:UofT_GandT/6
DESCRIPTION:Title: Multiplicity one for min-max theory in compact manifolds with boundary
and its applications\nby Zhichao Wang (University of Toronto Mississau
ga) as part of University of Toronto Geometry & Topology seminar\n\n\nAbst
ract\nIn this talk\, we introduce the multiplicity one theorem for min-max
free boundary minimal hypersurfaces in compact manifolds with boundary of
dimension between 3 and 7 for generic metrics. To approach this\, we deve
loped the min-max theory for free boundary h-hypersurfaces and proved the
generic properness for free boundary minimal hypersurfaces. The applicatio
n includes the construction of new free boundary minimal hypersurfaces in
the unit balls in Euclidean spaces and self-shrinkers of the mean curvatur
e flow with arbitrarily large entropy. This is a joint work with A. Sun an
d X. Zhou.\n\nZoom link: https://utoronto.zoom.us/j/84117185836\n
LOCATION:https://researchseminars.org/talk/UofT_GandT/6/
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SUMMARY:Freid Tong (Columbia University)
DTSTART;VALUE=DATE-TIME:20201109T210000Z
DTEND;VALUE=DATE-TIME:20201109T220000Z
DTSTAMP;VALUE=DATE-TIME:20240329T110512Z
UID:UofT_GandT/7
DESCRIPTION:Title: Asymptotically conical Calabi-Yau metrics with singularities\nby Fr
eid Tong (Columbia University) as part of University of Toronto Geometry &
Topology seminar\n\n\nAbstract\nAsymptotically conical Calabi-Yau manifol
ds are a special class of complete Ricci-flat Kähler manifold that are as
ymptotic to a cone at infinity. Their importance lies in the fact that the
y often appear as blow-up models for degenerations of non-collapsed Kahler
-Einstein metrics near a singular limit. The first general construction of
asymptotically conical Calabi-Yau manifolds using analytic techniques goe
s back to the work of Tian-Yau in the 90s\, and the analytic theory was su
bsequently refined and is now very well developed. In this talk\, I will f
irst review the theory of asymptotically conical Calabi-Yau metrics\, then
I will discuss some work on the study of degenerations of asymptotically
conical Calabi-Yau metrics and applications to constructing asymptotically
conical Calabi-Yau metrics with singularities. This is joint work with Tr
istan Collins and Bin Guo.\n\nThe talk will be on Zoom at https://utoronto
.zoom.us/j/81789338490 Passcode: 257573\n
LOCATION:https://researchseminars.org/talk/UofT_GandT/7/
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