Cohomology in algebra, geometry, physicsand statistics

Diffeological statistical models and diffeological Hausdorff measures

In my  talk I shall   first    explain  the concept  of diffeological  spaces  introduced by Souriau.   Then  I shall   explain  how to use   this  concept   to  endow  natural  smooth structures on  subsets of probability measures  on an arbitrary measurable   space.    I shall   discuss  the concept  of the diffeological   Fisher metric and the  resulting notion of the diffeological   Hausdorff measure   that are   categorically  natural, and meaningful for  statistical   estimations used in statistical physics and data  analysis.  
 My  talk  is based  on  my paper https://doi.org/10.3390/math8020167 and my joint paper  with  Alexei  Tuzhilin https://arxiv.org/abs/2011.13418
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