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Special ColloquiumExport this event to calendar

Friday, November 22, 2019 — 4:00 PM EST

Kiumars Kaveh, University of Pittsburg,

"Valuations in algebraic geometry and applications"
 
We start by an overview of the basic notion of a valuation (on an algebra) and construction of convex polytopes and convex bodies in algebraic geometry via valuations. This is in the heart of general theory of Newton-Okounkov bodies. The main theorem is an elegant formula for the number of intersection points of hypersurfaces in a projective variety in terms of volume of convex bodies. In symplectic geometry this gives strong results about Hamiltonian torus actions on projective varieties and constructing symplectic ball embeddings. The above concerns study of "line bundles" on varieties. We then consider extending these ideas to more general bundles such as "vector bundles" and "principal bundles" and state our very recent results on classifying toric principal bundles. This is a fruitful interaction of ideas from algebraic geometry, building theory and tropical geometry. For the most part the talk should be accessible to anybody with basic knowledge of algebra and geometry.
 
MC 5479
 
Refreshments will be served at 5:00pm in MC 5403
 

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