This seminar will cover basic algebraic geometry with a view towards applications, including (but not limited to) algebraic group theory and differential algebra. Each semester we work through a specific textbook in algebraic geometry or some related subject, at times bringing in outside material in the forms of more advanced textbook material or research-level topics. Any student working in a field that makes use of algebraic geometry may benefit from participating in this seminar, and anyone who decides to attend the seminar will be welcome to give talks in his or her area of research.
In past semesters we have read through "Algebraic Groups and Differential Galois Theory" by Teresa Crespo and Zbigniew Hajto, which covered the basic theory of algebraic varieties, algebraic groups, and their applications to differential Galois theory; and Chapter 1 of David Mumford's "The Red Book of Varieties and Schemes," focusing on some more advanced topics in the study of varieties.
In the Spring 2016 semester, we will continue our focus on algorithmic components of algebraic geometry. We will be reading "Ideals, Varieties, and Algorithms" by David Cox, John Little, and Donal O'Shea. In the Fall 2015 semester, we covered Groebner bases, elimination and extension theory, and the algebra-geometry duality. This semester, we will study Chapters 8-10, focusing on projective varieties, dimension theory, and advanced techniques in Groebner basis theory.
All meetings in the Spring 2016 semester will be on Fridays from 2:00-4:00 PM in Room 5212, unless otherwise stated.
Organizers:
Eli Amzallag: eamzallag1989@yahoo.com
Richard Gustavson: rgustavson@gradcenter.cuny.edu
Peter Thompson: pthompso@u.rochester.edu
References:
"Algebraic Groups and Differential Galois Theory" by Teresa Crespo and Zbigniew Hajto
"Algebraic Geometry" by Robin Hartshorne (the standard book on algebraic geometry)
"Introduction to Affine Group Schemes" by William C. Waterhouse (a great source for understanding the connection between algebraic groups and Hopf algebras)
"Ideals, Varieties, and Algorithms" by David Cox, John Little, and Donal O'Shea
"The Red Book of Varieties and Schemes" by David Mumford
"Linear Algebraic Groups" by James E. Humphreys (a good source for the connections between algebraic groups and their Lie algebras)