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Multi angle  Parametrizing with Guy
Toro, Tatiana (Auteur de la Conférence) | CIRM (Editeur )

Over the past 20 years we have been interested in finding good parameterizations for sets that are well approximated by nice sets. In this talk we will discuss the meanings of good and nice. We will recall some the results from the past and present new results concerning the regularity of sets that can be well approximated by Lipschitz graphs.

28A75 ; 49Q05 ; 49Q20 ; 49Kxx

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I will review several relaxations of the classical Monge Optimal Transport problem using a dynamic “time” extension and discuss the corresponding available numerical methods. They also apply to some instances of variational mean field games.

49Q20 ; 49M25 ; 35J70 ; 65M60 ; 35J96

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Multi angle  Isoperimetry with density
Morgan, Frank (Auteur de la Conférence) | CIRM (Editeur )

In 2015 Chambers proved the Log-convex Density Conjecture, which says that for a radial density f on $R^n$, spheres about the origin are isoperimetric if and only if log f is convex (the stability condition). We discuss recent progress and open questions for other densities, unequal perimeter and volume densities, and other metrics.

49Q20 ; 53C17 ; 49N60

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