Continuous combinatorics

Combinatorics was conceived, and then developed over centuries as a discipline about finite structures. In the modern world, however, its applications increasingly pertain to structures that, although finite, are extremely large: statistical physics, the Internet network, social networks, to name just a few. Moreover, the numerical characteristics researchers are normally interested in are “continuous” in the sense that small perturbations in the structure do not change the output very much. This makes it very natural to try to think of the “limit theory” of such objects by pretending that “very large” actually means “infinite”. It turns out that this mathematical abstraction is very useful and instructive and leads to unexpected connections with many other things, both in mathematics and computer science.
“Continuous Combinatorics” is an unifying term for several directions (like graph limits or flag algebras) bound together by this principle, and in our presentation we will try to review as much of it as time permits.