Griffiths, PhillipPhillipGriffiths2019-10-302019-10-302018-05https://hdl.handle.net/20.500.12111/7866Lecture series by Phillip Griffiths given at the High School of Economics, Moscow on May 21, 22, 23 and June 7, 2018.Algebraic geometry is the study of the geometry of algebraic varieties, defined as the solutions of a system of polynomial equations over a field k. When k = C the earliest deep results in the subject were discovered using analysis, and analytic methods (complex function theory, PDEs and differential geometry) continue to play a central and pioneering role in algebraic geometry. The objective of these talks is to present an informal and illustrative account of some answers to the question in the title.en-USalgebraic geometryHodge TheoryLecture/speech