Recent work of Nisse-Sottile, Hrushovski-Loeser, Ducros, and Giansiracusa-Giansiracusa has demonstrated that valuation rings of rank >1 play an important role in the geometry of analytic and tropical varieties over non-Archimedean valued fields of rank 1.
Algebraic Geometry Seminar
The Algebraic Geometry Seminar features talks on all branches of algebraic geometry, as well as related research fields including, and not limited to: number theory, complex geometry, and differential geometry.
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University of Michigan
There has been much progress in recent years on the LMMP for 3-folds in characteristic p>5. In this talk I will discuss the proof of the base point free theorem and how it leads to termination of the LMMP with scaling and the existence of Mori fibre spaces.
University of Cambridge
University of Illinois at Chicago