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We shall discuss the concept of sparse dominations of singular integral operators, in particular for those operators whose kernel do not satisfy any regularity estimate.
In the last fifteen years, the question of embedding metric spaces into “nice” Banach spaces has gathered researchers coming from very diverse origins.
Recent work of Kato and Kato-Naito-Sagaki has provided an improved understanding of the combinatorics of integrable level 0 representations of the affine Lie algebra.
This is joint work with Christian Le Merdy.
In 1964, Eells and Sampson asked whether a given smooth map can be deformed to a harmonic map in its homotopy class.
I will discuss what is known and conjectured regarding the problem of determining whether a curve defined over the rational numbers has any rational points.
A coarse embedding between metric spaces is, intuitively speaking, a map which preserves, in a weak sense, the geometry at large distances.
In this talk, I will discuss a problem which originates in complex analysis but is really a problem in non-linear elliptic PDE.
In order to adapt them to infinite dimensional vector spaces, a whole new theory needed to be developed.
Physicists have long been arguing that gauge theories at large rank should be related to topological string theories.
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