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Short course: A Novice's Road Map of Research Trends in Contemporary Algebraic GeometryKaren E. Smith (Keeler Distinguished Professor, University of Michigan, Ann Arbor and Vieraileva Professori, University of Jyväskylä) Time and placeThe lectures will be held in Exactum (Kumpula, University of Helsinki) as follows: Scope2 credit points (lectures + extra course work). A set of Exercises for the extra course work is found here. Please note: it is not neccessary to complete all exercises in order to receive credits. LevelAdvanced studies AbstractAlgebraic geometry, the study of solutions sets for systems of polynomial equations, is one of the oldest branches of mathematics, beginning already with the Greeks' deep studies of conic sections. Yet is also one of the most central and active areas of modern mathematics, with connections and applications to many areas of mathematics and beyond. The lectures will introduce students to the basic definitions and questions of algebraic geometry, using many concrete examples. The main goal is to instill in the listener an understanding and appreciation of some of the main research directions in algebraic geometry today. Lecture 1: What is Algebraic Geometry? (Topics: Definition of algebraic variety, projective varieties, maps of varieties, many examples. The place of algebraic geometry in mathematics: Connections with algebra, differential geometry, applied math, representation theory, arithmetic geometry and number theory, complex geometry). Lecture 2: Research trends: resolution of singularities and birational geometry. Lecture 3: Moduli spaces |