Math 512, Modern Algebraic Geometry, Fall 2015
MWF, 9-9:50 a.m., 441 Altgeld Hall
357 Altgeld Hall
nevins AT illinois DOT edu
Office hours: Mondays, 11-11:50am and 3-3:50pm; Fridays 1-1:50pm.
Algebraic Geometry (click title to access on-line!),
R. Hartshorne, Springer-Verlag, 1977. Another excellent reference is Ravi Vakil's
Foundations of Algebraic Geometry; I will assign reading from it (though this reading is largely optional), and some problems from it.
Homework, grades, etc.:
Students will be expected to do some reading outside of class. The course will focus on training students to use the language and toolkit of schemes; hence we will discuss, and work through, many problems together. You should do whatever work for the course you think will help you as you become a mathematician. Since this is an advanced graduate course, grades are a non-issue.
Algebraic geometry is the geometric study of solution sets of systems of polynomial equations. In recent decades it has become a subject of
tremendous breadth as well as depth. It plays a central role in numerous developments in analytic and differential geometry, number theory, representation theory, combinatorics, string theory, and integrable systems, among others.
This will be an introduction to
the language and tools of modern algebraic geometry, namely, schemes and sheaf cohomology, with sample applications.
Class summaries and homework assignments
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