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Explore the intersection of algebra and geometry through computational methods in this graduate-level course taught by Professor Mike Stillman as part of the Fields Institute's Thematic Program in Commutative Algebra and Applications. Master fundamental algorithms and computational techniques used to solve problems in commutative algebra and algebraic geometry. Learn to apply computer algebra systems to investigate polynomial ideals, Gröbner bases, and their geometric interpretations. Develop skills in computational approaches to studying algebraic varieties, including primary decomposition, elimination theory, and dimension calculations. Gain hands-on experience with software tools commonly used in algebraic geometry research while building theoretical understanding of the underlying mathematical structures. The course spans 11 comprehensive lectures covering both foundational concepts and advanced computational methods essential for modern research in commutative algebra and algebraic geometry.
