Program

Wojciech Chachólski (KTH)

Geometry, Homology and Data

One of the key steps towards a successful analysis is to provide suitable representations of data  by objects  amenable for statistical and  ML methods.  

Since geometrical properties are often not amenable for such tools, one of the  most important contribution of Topological data analysis has been to provide strategies and algorithms of transforming geometrical information into objects for which statistical and ML methods can be applied to. During the last decade there has been an explosion of applications in which such representations of data played a significant role. In my talks I will  present one such strategy based on hierarchical stabilisation process leading to invariants called stable ranks.

I will use classical Wisconsin Breast Cancer data as one of examples when homological invariants can give interesting information.

Érika Roldán (MPI Leipzig)

Topology and Geometry of Random Cubical Complexes 

In this mini-course, we will explore the topology and local geometry of different random cubical complex models. In the first part, we explore two models of random subcomplexes of the regular cubical grid: percolation clusters (joint work with David Aristoff and Sayan Mukherjee), and the Eden Cell Growth model (joint work with Fedor Manin and Benjamin Schweinhart). In the second part, we study the fundamental group of random 2-dimensional subcomplexes of an n-dimensional cube; this model is analogous to the Linial-Meshulam model for simplicial complexes (joint work with Matt Kahle and Elliot Paquette).