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VIGRE seminar, spring 2002: Introduction to Computational Algebraic Geometry

Maurice Rojas
Students enrolled
Dale Curtis (undergraduate mathematics student); Marvin Decker, Xiang Fang, Edward Fuselier, Troy Henderson, Scott Johnson, Dimitrije Kostic (graduate mathematics students); Koji Ouchi, (graduate computer science student); Armando Solar Lezama (undergraduate computer science student)
Algebraic geometry was born over two millennia ago with the aim of understanding how to solve systems of polynomial equations. Ironically, algebraic geometry courses nowadays rarely talk about the most efficient way to solve a polynomial system. The need for robust and efficient algorithms for algebraic geometry is now motivated by numerous applications: even a short list would have to include: chemistry, signal processing, robotics, coding theory, optimization, mathematical biology, computer vision, game theory and statistics.
This course took a novel, albeit 2000 year old, approach by focusing on the mathematics most relevant to solving polynomial systems. The emphasis was on concrete constructions and algorithms, a strong algebraic background was not required. The course was integrated with the Frontiers lecture series by Bernd Sturmfels on polynomial system solving.