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10:30 AM - 11:00 AM
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Coffee
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- Location
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- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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The Asymptotic Geometry of Genus-g Helicoids
Jacob Bernstein (Johns Hopkins University)
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- Location
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- Video
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- Abstract
- We discuss the problem of classifying the asymptotic geometry
of complete, properly embedded minimal surfaces in $R^3$ with finite
topology (i.e. topologically a finitely punctured compact surface).
The techniques needed to address this question are dramatically
different depending on whether there is one puncture or more than one.
The former has proven substantially more challenging, requiring very
deep results of Colding and Minicozzi, and will be the main focus of the
talk. Using very directly Colding and Minicozzi's work, we will sketch
a proof of the result - due to Meeks and Rosenberg - that the plane and helicoid
are the only such simply connected surfaces. We will then indicate how
this argument can be generalized to positive genus. That is, such
a surface is asymptotic to a helicoid and hence may be called a
"genus-g helicoid".
- Supplements
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--
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12:00 PM - 02:00 PM
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Lunch and Organizational Meeting
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- Location
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- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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The Seiberg-Witten equations and the dynamics of vector fields in dimension 3
Clifford Taubes (Harvard University)
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- Location
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- Video
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- Abstract
- I will describe how the gauge theory in the guise of the Seiberg-Witten equations can be used to give novel information about the dynamics that are generated by volume preserving vector fields on 3-dimensional manifolds.
- Supplements
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03:00 PM - 03:30 PM
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Coffee
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- Location
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- Video
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- Abstract
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- Supplements
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03:30 PM - 04:30 PM
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Generic spines as cut loci of Riemannian manifolds.
Hyam Rubinstein
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- Location
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- Video
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- Abstract
- This is joint work with Chris Goddard. In 1968 Alan Weinstein
showed that any smooth closed manifold M, except for the 2-sphere, admits
a Riemannian metric so that there are no conjugate points in the cut locus
from some base point. We extend this result to show that any generic spine
for M can be made into the cut locus, again so that there are no conjugate
points. Finally, the Riemannian distance function from some base point is
of Morse type and has the property that there is one critical point for
each face F of the spine and the index is the codimension of the face.
- Supplements
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