Student Probability Seminar

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Bipartite Matching: Past and Present

Speaker: Jacob Shkrob, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, April 7, 2025, 11 a.m.

Synopsis:

We will introduce the matching problem, one of many combinatorial optimization problems such as the traveling salesman problem, and go over foundational results achieved by Aldous and Ambrossio et. al. The first result pertains to the case of Exponential edge weights and uses local weak convergence. The second result is more specific to the quadratic matching problem on the 2-dimensional torus, but has inspired subsequent followup works trying to achieve the optimal constants for d > 2 with general densities. If time permits, we will go through both techniques in detail.