November 6, 2009 at 2:30pm
Mary Gates Hall, Room 241 |
Bill Fulton
University of Michigan |
Character Formulas |
In this expository talk, we will give a simple formula, with a simple
proof, for the equivariant euler characteristic of an equivariant
vector bundle on on complete, smooth variety with a torus action.
On homogeneous varieties this gives Weyl's character formula, and
on toric varieties it gives Brion's formula for lattice points in
polytopes. This is based on ideas of George Quart in the 1970s and
recent conversations with Bill Graham.
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November 20, 2009 at 2:30pm
Mary Gates Hall, Room 241 |
Gunther Uhlmann
University of Washington |
Cloaking and Transformation Optics |
We describe recent theoretical and experimental progress on making objects
invisible to detection by electromagnetic waves, acoustic waves and quantum
waves. Maxwell's equations have transformation laws that allow for design of
electromagnetic materials that steer light around a hidden region, returning
it to its original path on the far side. Not only would observers be unaware
of the contents of the hidden region, they would not even be aware that
something was being hidden. The object, which would have no shadow, is said to
be cloaked. We recount some of the history of the subject and discuss some of
the mathematical issues involved.
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October 23, 2009 at 2:30pm
Mary Gates Hall, Room 241 |
Persi Diaconis
Stanford University |
Shuffling Cards and Adding Numbers |
When several large integers are added in the usual way 'carries' occur along the
way. It is natural to ask: 'About how many carries are there and how are they distributed
for typical numbers?' It turns out that these questions are intimately related to the
mathematics of the usual way we shuffle cards. I will explain the mathematics of
'carries' (they are cocycles!), shuffling and the connection. This is joint work with Jason Fulman.
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