slideshow 3

Cohomology in algebra, geometry, physicsand statistics

The cohomological characterization of information functions >

Speaker’s name: 
Juan Pablo Vigneaux
Speaker’s affiliation: 
Max-Planck-Institute for Mathematics in Sciences

 

Place: 
in konirna seminar room, IM front building, ground floor
Date: 
Wednesday, 11. December 2019 - 11:30 to 12:30
Abstract: 
Information structures are categorical objects that serve as models of systems of measurements in physics and
analog concepts in  computer science and logic. "Information cohomology" is a homological invariant naturally attached to the presheaves on them along the lines of SGA IV. Several functions appear as cocycles (for adapted modules of coefficients): Shannon entropy and some of its generalizations, the multinomial coefficients and their generalizations, the determinant of gaussian covariant matrices, the dimension of affine subspaces... The  cocycle conditions encode remarkable recurrence relations of these functions, and some of them can be put in correspondence (e.g. the multiplicative relations among multinomial coefficients imply the  chain rule for the corresponding entropy). These are the first steps  towards a general "topology of statistical systems" in the vein of topos theory.