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Erik Carlsson is a Professor in the Mathematics department at the University of California, Davis. His research interests encompass representation theory, algebraic geometry, algebraic combinatorics, and computational topology. He is particularly engaged in studying connections to the Goresky-Kottwitz-Macpherson (GKM) spaces and their applications to Macdonald theory in combinatorics. His work includes exploring potential applications of the unramified affine Springer fiber type conjecture and the analysis of signed Schur positivity through the nabla operator and modified Macdonald polynomials. Additionally, he has significantly contributed to the field of computational topology, focusing on persistent homology and the construction of alpha complexes in high dimensions through innovative mathematical optimization techniques. Carlsson has co-authored various publications that delve into these advanced topics, establishing himself as a key figure in contemporary mathematical research, especially in the intersection of algebra and geometry.
Department of Computer Science. GRE is NOT required.