In recent years, there have been more and more applications of algebraic geometry. Scholars in fields ranging from electrical engineering to operations research have found themselves learning about ideals, varieties, and the algorithms used to compute with these objects. However, the applications of algebraic geometry, though varied and of great interest, do not convey the full depth of the field. What do algebraic geometers consider to be the heart of their subject? This is the central question of the tutorial.
It follows that the tutorial will have an unusual focus. The talks will not concentrate on applications; rather, the emphasis will be on having experts explain some of the central ideas of algebraic geometry to an audience who knows only basic facts about polynomials and varieties.
The topics covered will include intersection theory, Grassmannians, singularities, toric varieties, curve and surface theory, commutative algebra, and real algebraic geometry. While this list has many omissions (such as arithmetic algebraic geometry and Hodge theory), the hope is that the tutorial will give an accessible and compelling introduction to the richness of algebraic geometry.