Joao Pita Costa: Heyting algebra over the persistence diagram

 
In the past 20 years Topological Data Analysis has been a vibrant area of 
research a lot due to the developments in applied and computational 
algebraic topology. Essentially it applies the qualitative methods of 
topology to problems of machine learning, data mining or computer vision. 
Under this topic, persistent homology is an area of mathematics interested 
in identifying a global structure by inferring high-dimensional structure 
from low-dimensional representations and studying properties of a often 
continuous space by the analysis of a discrete sample of it, assembling 
discrete points into global structure. Lattices are ever present in the 
everyday life of a working mathematician being distributive lattices some 
of the most important varieties of these algebras. A recent approach to the 
study of persistent homology using techniques of lattice theory is 
presented in this talk where we will also look at several algorithmic 
applications that imply the impact of these strategies.