Past Geometry and Analysis Seminar

26 November 2012
14:15
Michael Monastyrsky
Abstract
The lecture will discuss some applications of topology to a number of interesting physical systems: 1. Classifications of Phases, 2. Classifications of one-dimensional textures in Nematics and Superfluid HE-3, 3. Classification of defects, 4. Phase transition in Liquid membranes. The solution of these problems leads to interesting mathematics but the talk will also include some historical remarks.
  • Geometry and Analysis Seminar
19 November 2012
14:15
Jeff Giansiracusa
Abstract
Motived by the desire to study geometry over the 'field with one element', in the past decade several authors have constructed extensions of scheme theory to geometries locally modelled on algebraic objects more general than rings. Semi-ring schemes exist in all of these theories, and it has been suggested that schemes over the semi-ring T of tropical numbers should describe the polyhedral objects of tropical geometry. We show that this is indeed the case by lifting Payne's tropicalization functor for subvarieties of toric varieties to the category of T-schemes. There are many applications such as tropical Hilbert schemes, tropical sheaf theory, and group actions and quotients in tropical geometry. This project is joint work with N. Giansiracusa (Berkeley).
  • Geometry and Analysis Seminar

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