
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: [
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.

Apr. 13 
Sergei Gukov (UCSB)
Audio [ mp3,
wma ];
Lecture notes.

Apr. 20 
Xiaodong Cao (MSRI and Cornell Univeristy)
(joint meeting with Differential Geometry Seminar)
Recently, Chow and Hamilton introduced the cross curvature flow on
threemanifolds, 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 threemanifolds with negative sectional
curvature. In this talk, we will study the cross curvature flow on
locally homogenous threemanifolds. 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 SaloffCoste.
Audio [ mp3,
wma ];
Lecture notes.

Apr. 27 
No meeting

May 4 
No meeting

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 ChristdoulouKlainerman theorem on stability of
Minkowski spacetime.
Audio [ mp3,
wma ];
Lecture notes.

May 18 
No meeting.

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.

May 25 
Paolo Cascini (UCSB)
H. D. Cao introduced the KählerRicci 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 KählerEinstein metrics on
manifolds with c_{1} < 0.
More in general, the KählerRicci 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.

June 1 
James M^{c}Kernan (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 P^{1}bundles is an example of such a link, and the
Sarkisov program provides a natural framework to prove that the
birational automorphism group of P^{2} 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.


