# Special Seminar in Computing and Mathematical Sciences

*,*Electrical Engineering

*,*Technion -- Israel Institute of Technology

*,*

Omer Bobrowski received his undergraduate degree in Mathematics and Computer Science at the Open University in Israel, and his PhD at the Technion – Israel Institute of Technology in 2012. He did his postdoctoral research in the Department of Mathematics at Duke University during the years 2012-2016, and subsequently joined the Faculty of Electrical Engineering at the Technion as an Assistant Professor, where he is currently based. Omer Bobrowski’s main research interests lie in the area of random topology and its applications. In particular, he is interested in limiting theorems and phase transitions related to the topology of random structures. In addition, he studies various statistical aspects bridging between random topology and the field of Topological Data Analysis, including inference problems and noise modeling.

Connectivity and percolation (the formation of "giant" components) are two well-studied phenomena in random graphs. In recent years, there has been an ongoing effort to generalize these phenomena to higher dimensions using random simplicial complexes. Simplicial complexes are a natural generalization of graphs that consist of vertices, edges, triangles, tetrahedra, and higher dimensional simplexes. The generalized notions of connectivity and percolation are based on the language of homology - an algebraic-topological structure representing cycles of varying dimensions.

In this talk we will mainly focus on random geometric complexes. Such complexes are generated from vertices given by a random point process, with simplexes added according to their geometric configuration. We will discuss recent results analyzing phase transitions (i.e. rapid changes) related to these topological phenomena. We will also discuss the relevance of these results in the field of Topological Data Analysis (TDA).