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Geometry, Topology, and Physics Seminar, Spring 2007
Organizers:
Sergei Gukov
and Dave Morrison.
Meets 3:30 - 5:00 p.m. Fridays in South Hall 6635.
Various topics relating geometry, topology, and physics.
Other Quarters: [
Fall, 2021;
Winter, 2020;
Fall, 2019;
Spring, 2018;
Winter, 2018;
Fall, 2017;
Spring, 2017;
Wnter, 2017;
Fall, 2016;
Spring, 2016;
Winter, 2016;
Fall, 2015;
Spring, 2015;
Winter, 2014;
Fall, 2013;
Fall, 2012;
Fall, 2011;
Winter, 2011;
Spring, 2010;
Winter, 2010;
Fall, 2009;
Spring, 2009;
Winter, 2009;
Fall, 2008;
Spring, 2008;
Winter, 2008;
Fall, 2007;
Spring, 2007;
Winter, 2007;
Fall, 2006
]
| Apr. 6 |
Dave Morrison (UCSB)
Organizational meeting.
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| Apr. 13 |
Sergei Gukov (UCSB)
Audio [ mp3,
wma ];
Lecture notes.
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| Apr. 20 |
Recently, Chow and Hamilton introduced the cross curvature flow on
three-manifolds, which is a weakly parabolic partial differential
equation system when the sectional curvatures have a definite sign.
They also conjectured the long time existence and convergence of cross
curvature flow on closed three-manifolds with negative sectional
curvature. In this talk, we will study the cross curvature flow on
locally homogenous three-manifolds. We will describe the long time
behavior of the cross curvature flow for each case. This is a joint
work with Yilong Ni and Laurent Saloff-Coste.
Audio [ mp3,
wma ];
Lecture notes.
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| Apr. 27 |
No meeting
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| May 4 |
No meeting
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| May 11 |
Mike Anderson (SUNY, Stony Brook)
MEETS AT 4 PM THIS WEEK.
A discussion of the
wide open question: is AdS spacetime dynamically stable?
This is basically a hyperbolic PDE problem, a
bit analogous to Christdoulou-Klainerman theorem on stability of
Minkowski spacetime.
Audio [ mp3,
wma ];
Lecture notes.
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| May 18 |
No meeting.
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| May 21 |
John Lott (MSRI and University of Michigan)
South Hall 4607, 3:30 p.m.
(Differential Geometry Seminar; note unusual day and location)
Lecture notes.
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| May 25 |
Paolo Cascini (UCSB)
H. D. Cao introduced the Kähler-Ricci flow for canonical metrics
on manifolds with definite first Chern class. In particular he obtained a new
proof of Calabi's conjecture on the existence of Kähler-Einstein metrics on
manifolds with c1 < 0.
More in general, the Kähler-Ricci flow is expected to provide a deeper
understanding of the geometry of the underlying manifold. We will survey on
some of its property and applications.
Audio, part 1 [ mp3,
wma ],
audio, part 2 [ mp3,
wma ];
Lecture notes.
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| June 1 |
James McKernan (UCSB)
MEETS AT 4 PM THIS WEEK.
The conjectural output of the minimal model program is
either a minimal model or a Mori fibre space. Unfortunately
the output in neither case is unique.
Kawamata has recently shown that any two minimal models are connected
by a sequence of flops. The Sarkisov program aims to factorise any
birational map between two Mori fibre spaces into a sequence of
elementary links. In the case of surfaces, an elementary
transformation of P1-bundles is an example of such a link, and the
Sarkisov program provides a natural framework to prove that the
birational automorphism group of P2 is generated by a Cremona
transformation and PGL(3).
We describe recent work with Christopher Hacon where we extend the
Sarkisov program to all dimensions.
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