معرفی
Jim Geelen is a Professor in the Department of Combinatorics and Optimization at the University of Waterloo, Faculty of Mathematics. His research focuses on matroid theory, particularly the Matroid Minors Project, which extends the Graph Minors Theory of Robertson and Seymour to matroids. Notably, he, Bert Gerards, and Geoff Whittle proved Rota's Conjecture, characterizing matroids representable over finite fields. His work also addresses extremal matroid theory, growth rates of minor-closed classes, and algorithmic applications.
He has advised doctoral students including Kerri Webb, Tony Huynh, Peter Nelson, Rohan Kapadia, and Benson Joeris. Geelen teaches advanced courses like CO749 on Graph Minors, offering video lectures. His research collaborations span matroid minors, excluded minors, and representation theory, with contributions to fields like combinatorics, Ramsey theory, and geometric density theorems.
His recent work explores the Erdős-Posa property in matroids, density Hales-Jewett theorems, and the structure of exponentially dense matroid classes. Geelen's publications include foundational papers on matroid connectivity, branch-width, and inequivalent representations, reflecting his deep engagement with foundational and applied aspects of combinatorial mathematics.
