Maximum Cardinality Matching in n^2 Time

I will present a combinatorial n^2-time algorithm for the maximum matching problem, improving over the classical matrix multiplication based algorithms. The first half of the talk will review the theory of skew-symmetric flow problems and how it captures the maximum matching problem. The second half of the talk sketches how we can generalize the techniques from combinatorial max flow algorithms to skew-symmetric flows to solve max matching in n^2 time.