Math 413/813 — Introduction to Algebraic Geometry

Minimum Requirements

Presentations Date Room
Schedule April 16/25 Jeff 422/319

Assessment and Deadlines: Project grades will be computed as follows:

Due Date Element Weight
2019-02-11 Outline 10%
2019-03-25 Rough Draft 10%
2019-04-01 Feedback on other's drafts 10%
2019-04-16/25 Presentation 30%
2019-04-16/25 Feedback on other's presentations 10%
2019-04-25 Final Paper 30%

Comments: By design this assignment is very open-ended. You are strongly encouraged to compute many examples. You are also encouraged to formulate, test, and prove your own conjectures.

Here is some advice on how to present mathematics.

Potential Topics


William Adams and Philippe Loustaunau, An introduction to Gröbner bases
Winfried Bruns and Joseph Gubeladze, Polytopes, rings, and K-theory, Monographs in Mathematics. Springer, 2009 ISBN 978-0-387-76355-2
David A. Cox, John B. Little, and Don O'Shea, Ideals, Varieties, and Algorithms, third edition, Springer, 2007 ISBN 978-0-387-35650-1
David A. Cox, John B. Little, and Don O'Shea, Using Algebraic Geometry, GTM 185, Springer, 2005 ISBN 978-0-387-20733-9
David Eisenbud, Commutative algebra with a view towards algebraic geometry, GTM 150. Springer, 1995 ISBN 0-387-94268-8
Gert-Martin Greuel and Gerhard Pfister, A Singular introduction to commutative algebra, 2nd edition, Springer, 2008 ISBN 978-3-540-73541-0
Brendan Hassett, Introduction to Algebraic Geometry, Cambridge University Press, 2007 ISBN 978-0-521-69141-3
Jürgen Herzog and Takayuki Hibi, Monomial ideals, GTM 260. Springer, 2011 ISBN 978-0-85729-105-9
Neal Koblitz, Elliptic Curve Cryptosystems, Math. Comp. 48 (1987), no. 177, 203–209
Franz Lemmermeyer, Conics — A poor man's elliptic curve
Sergei Lando and Alexander Zvonkin, Graphs on surfaces and their applications, Springer 2004 ISBN 978-3-540-38361-1
Ezra Miller and Bernd Sturmfels, Combinatorial commutative algebra, GTM 227. Springer, 2005 ISBN 0-387-22356-8
Bernd Sturmfels, Algorithms in invariant theory, Texts and Monographs in Symbolic Computation. Springer, 1993 ISBN 3-211-82445-6
Bernd Sturmfels, Gröbner bases and convex polytopes, University Lecture Series 8. American Mathematical Society, 1996 ISBN 0-8218-0487-1
Bernd Sturmfels, Solving systems of polynomial equations, CBMS 97, American Mathematical Society, 2002 ISBN 0-8218-3251-4
Terence Tao and Van H. Vu, Additive combinatorics, Cambridge University Press, 2010 ISBN 978-0-521-13656-3