If you tell a physicist, «I give you a bunch of masses, what can you do?» He smiles and answers «I have Einstein’s equations, I can compute the geometry at every point of space-time».

If you tell us, ‘topdrimers’ «I give you a bunch of data with hidden relations, what can you do?» we smile and answer «We don’t have Maxwell’s or Einstein’s equations, nor any other equation, but we have topological invariants and we can construct a topological algorithmic field theory of data and perhaps we can extract a pretty faithful representation of those hidden patterns of correlated information».

Then you can tell us «Why you don’t use statistical methods together a machine learning approach?». Our answer will be «We want to explore massive data set which we don’t know much about, with global effects of relatively small interactions of many actors, going beyond the concept of network, and from these quivering simplicial complexes uncover the mystery of information: translate into algorithms the shape of relations in data space»

The meeting of two researchers with a different background but common intuition of the complexity of the problem, allowed to start working for a joint proposal that led to the FP7 FET-Proactive TOPDRIM project. While he believes that topology could lead to a new mathematics for understanding complex system, she imagines concurrent processes living in a world that is not flat, investigating new symmetries. Both of them were very curious to explore new ways of doing research looking forward to future emerging technologies.

In the three years of the project the six partners provided fundamental expertise, with a pretty demanding effort they succeeded in integrating their knowledge to achieve the project objectives, literally creating from scratch a new multidisciplinary research method and an exciting cross-fertilized environment. Throughout the timeline of the TOPDRIM project, 24 people, 16 of which were young researchers.

The participation of young people gave rise to a highly skilled figure of a new Data Scientist capable of continuing the development of topology driven methods yet being given the opportunity to create high-impact innovation by exploiting novel techniques, for example, to expand the market of big data analytics. One of the evidences is the Da.Re project led by the LOCCIONI group.

In 2012, young researchers involved in TOPDRIM were free to explore and define new algebraic and computational methods to discover new knowledge from data; the main result was the ambitious definition of a new methodology in data mining. Today, a group of scientists contaminated by the vision of TOPDRIM is inspiring new research methods in the life sciences: an unprecedented vision of the immune system or the bold pursue of the semantic functions of the connectome; the turbulent flow of the financial market or the intricacies of natural language processing, and so on and so forth. Others are still challenging basic crucial and conjectural questions, dreaming the birth of a real theory supporting the machine learning paradigm.

FET is the only program that supports the growth of interdisciplinary research groups and leaves them the freedom to brace themselves to face challenging hard research problems – perhaps the hardest.

At the end of the TOPDRIM project under the sponsorship of EATCS and CSS we organized the Young Researchers School. The contributes of worldwide outstanding scientists discussing how topology could help to understand the complexity and the concurrency in complex systems are collected in a white book.

In the continuation of the FET activities, during the European Researchers’ Night (27th of September 2019) we organized a Virtual Workshop to give the possibility to listen some young researchers speaking about research topics related to TOPDRIM and trying to overview several applications that in long term could change the life of many citizens and the organization of many companies.