Prof Primoz Skraba

Primoz Skraba

Professor in Applied and Computational Topology

School of Mathematical Sciences
Queen Mary University of London
www.qmul.ac.uk/maths/profiles/skrabaprimoz.html
Centre for Probability, Statistics and Data Science
Centre for Fundamentals of AI and Computational Theory

Research

topology, geometry, algorithms

Interests

My research is in applied topology: mostly geometry, algebra, and recently stochastic topology -- along with other areas such as algorithms, computational geometry, and machine learning. A long time ago I also used to do signal processing.

Much of my research is on understanding persistent homology and its various aspects. Some of the areas include:

Stability: Persistence diagrams are the main invariant that is studied. We often try to understand spaces from finite samples, in which case, stability is important as it allows us to get quantitative control. I am very interested in stability statements and how they relate to classical objects such as exact sequences. In general there is a mixture of combinatorial and algebraic aspects to these type of questions.

Variants:There are several variants to persistence, such as zig-zag, robustness, and multiparameter. There are many open and interesting questions in this area. I have worked on some of these and have recently started working on multiparameter questions more concretely.

Algorithms: A key factor in persistent homology is that it can be computed quite efficiently (thanks to the hard work of many other people). I have worked on various complexity questions and there are still interesting questions here.

Stochastic topology: this is, roughly speaking, asking about the topology of a space which comes from a random process. In particular, I am interested in the homology group (and ultimately homotopy groups) of these spaces. The random models I am interested in are usually geometric (Poisson, Boolean, or some regular tiling).