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Embeddability is a natural geometric criteria for CR structures. In dimensions higher than three, there is local integrability condition that implies embeddability. In this dimension, this condition is vacuous and is replaced by a global condition on the sign of the Paneitz operator…
In dimensions four and higher, the Ricci flow may encounter singularities modelled on cones with nonnegative scalar curvature. It may be possible to resolve such singularities and continue the flow using expanding Ricci solitons asymptotic to these cones, if they exist. I will discuss joint…
Abstract
The question of whether a smooth complex variety with a positive first Chern class, called a Fano variety, has a Kahler-Einstein metric has been a major topic in complex geometry since the 1980s. In the last decade, algebraic geometry, or more specifically…
Abstract
Interpolation for Brill--Noether Curves
Abstract: In this talk, we determine when there is a Brill--Noether curve of given degree and given genus that passes through a given number of general points in any projective space.
I will report on recent developments of the theory of monodromy groups of convergent and overconvergent F-isocrystals. These algebraic groups have been defined by Crew using the Tannakian formalism. After quickly recalling the definitions, I will explain the main ideas of the proof of Crew's …