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On the contributions of lattice theory to the study of persistent homology.
Description:  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 omnipotent 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.
Date:  2013-11-06
Start Time:   14:30
Speaker:  João Pita Costa (Josef Stefan Institute, Liubliana, Slovenia)
Institution:  Josef Stefan Institute, Liubliana, Eslovénia
Place:  Sala 5.5
Research Groups: -Geometry
-Algebra, Logic and Topology
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