Algebraic Methods in Combinatorics

Explore advanced algebraic techniques applied to combinatorial problems through this comprehensive workshop featuring 14 lectures from leading researchers. Delve into cutting-edge applications of algebraic methods that have led to breakthrough solutions for longstanding open problems in combinatorics, including the finite field Kakeya problem, Erdős' distinct distance problem, and the cap-set problem. Master the polynomial method through detailed examinations of its applications in Fourier analysis, sum-of-squares lower bounds, and subspace evasion techniques. Investigate geometric energies bridging discrete geometry and additive combinatorics, while studying submodular minimization and set-systems with restricted intersections. Analyze matrix theory applications including ranks of matrices with few distinct entries and intersection problems of linear subspaces. Examine removal lemmas for triangles and k-cycles, explore Ramsey numbers from both combinatorial and geometric perspectives, and study incidence geometry through cutting curves into segments. Learn about list decoding, dimension expanders, and polynomial identity testing instances, while discovering connections between few products and many sums in additive combinatorics. Gain insights into multiple crossings problems and unit distance challenges that demonstrate the power of algebraic methods in solving complex combinatorial questions.