The ACO Seminar (2023–2024)

Inspired by the classical random graph process introduced by Erdos and Renyi in 1960, we introduce two analogous processes for random representable matroids. In the talk we address the following questions, with answers to some already established in existing literature, while others stem from recent research findings:
How does the rank of the random matroid evolve in the process?
When does the first k-circuit appear for each integer k?
What is the length of the first circuit appearing in the process?
How does the connectivity of the matroid change?
What is the growth rate of the critical number (c.f. chromatic number of graphs) in the process?
When do given (small and large) matroid minors occur in the process?
How about the appearance of submatroids?