Lectures related to Matching Polynomials: Real-Rootedness and Signings

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Interlacing Families and Ramanujan Graphs

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Ramanujan Graphs: Constructions and Similarities

Explores Ramanujan graphs' constructions, matching polynomials, perfect matchings, and universal covers, along with quantitation and qualitative aspects.

Linear Programming Duality

Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.

Greedy Change-Making Algorithm: Optimality and Stability

Explores the optimality of the greedy change-making algorithm and the stability of maximum matching.

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Matroids: Matroid Intersection

Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.

Algorithms & Growth of Functions

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Algorithms: Stable Matchings

Covers the concept of stable matchings and the Gale-Shapley algorithm.

Algorithms: Stable Matchings

Covers the concept of stable matchings and the Gale-Shapley algorithm.

Recent Advances in the Dimer Model and Its Applications

Covers recent advancements in the dimer model, emphasizing its applications in probability and conformal field theory.

Graph Matching Entropy

Explores the relationship between matchings, entropy, and Bethe free entropy in random graphs.

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Matching Polynomials: Real-Rooted Property

Explores matching polynomials, emphasizing their real-rooted property and related bounds.

Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

Discusses the Ford-Fulkerson method and strongly connected components in graph algorithms.

Max-flow Min-cut Theorem

Explores the Max-flow Min-cut theorem, integral capacities, Ford-Fulkerson method, bipartite matching, and edge-disjoint paths.

Algorithms: Union Find and Minimum Spanning Trees

Discusses Union-Find data structures and Minimum Spanning Trees, covering algorithms and their applications in network design and optimization.

Max-flow and Disjoint Sets

Explores the Ford-Fulkerson method, max-flow, applications of max-flow, and the disjoint-set data structure.

Interlacing Families and Ramanujan Graphs

Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.