Your final project should consist of an expository paper and a poster presentation on June 8. You may work in groups of 1-3 students. More details and suggested topics are below. To propose a topic and group, send me an email with all group members cc'ed with a topic, at least one reference, and list of all group members.

Important Dates

Friday, May 22 -- Have finalized project and group, approved by instructor by email
Monday, June 8 -- Poster Session 2:30-4:20pm in IEB 205
Monday, June 8 -- Submit final paper on Gradescope by the end of the day

Description

The project (both paper and poster) should be on a topic related to computational algebraic geometry. Some suggested topics and references are below. Both should be understandable to someone familiar with Chapters 1-4 of the text book, in particular, to a fellow member of the class. You should give a brief description of the topic along with relevant definitions, ideas, and results, but you do not need to include proofs. Your exposition should include at least one example that is not in the source material and at least one theorem (that can be from the source material). The paper should be about 3-5 pages long.

Use of LaTeX for typesetting is encouraged but not required. See, for instance, the following tutorial for more details. Overleaf is a popular online editor.

I will provide posterboards the last week of classes that can be used for the final poster session. This will be an opportunity to tell the other students in the class about your topic.


Grading
The projects will be graded on the following criteria.

Content -- Demonstrate that you have understood and digested the main concepts from your chosen topic and their connection with the course content. There should be an example that is not directly from the source you are working from. In particular you should answer: What is the goal? How is it achieved? How is material you learned from this course relevant?

Mathematical Accuracy -- Correctly state and explain the main mathematical content. You should use correctly, where relevant, technical content from the course (Grobner bases, ideals, varieties, etc.).

Paper Communication -- Use definitions/theorems/examples/text to effectively explain your topic. You can directly cite theorems and definitions (with references), but the exposition should be your own.

Poster Visual Communication -- Use pictures/examples/text to explain your topic. It should be possible to understand the content of your poster without you being there to explain it.

Poster Session Oral Communication -- Clearly communicate the content of your project to other students in the class, both in accurate technical language and informally summarizing the main ideas.

Format -- You should cite all references used. Your paper should start with an introduction of a paragraph (or more) introducing readers to your topic and the relevant motivation and context.


Suggested topics

Below is a list of possible final projects topics with references. Some references are provided as a starting point, but you may find it helpful to consult other texts, articles, or websites. Remember to cite your sources appropriately. You are welcome to suggest your own topics if there is another area or application you are interested in, so please feel free to discuss your ideas with me.

Topic	Reference
Robotics and Automatic Geometric Theorem Proving (**taken**)	CLO Chapter 6
Invariant Theory of Finite Groups (**taken**)	CLO Chapter 7
The Projective Algebra-Geometry Dictionary	CLO Section 8.3
Bezout's Theorem (**taken**)	CLO Section 8.7
The Dimension of a Variety(**taken**)	CLO Chapter 9
Additional Groebner Basis Algorithms	CLO Chapter 10
The Complexity of the Ideal Membership Problem	See Appendix D of CLO, Project 1
Computer Graphics and Vision (**taken**)	See Appendix D of CLO, Project 8
Algebraic Statistics (**taken**)	See Appendix D of CLO, Project 13
Groebner Bases for Graph Coloring and Sudoku (**taken**)	See Appendix D of CLO, Project 14
Toric Varieties	See Appendix D of CLO, Projects 15 and 16
Integer Programming and Combinatorics (**taken**)	Using Algebraic Geometry by Cox, Little, and O'Shea, Sections 8.1, 8.2
Grobner Fans/The Grobner Walk (**taken**)	Using Algebraic Geometry by Cox, Little, and O'Shea, Sections 8.4, 8.5
Algebraic Coding Theory (**taken**)	Using Algebraic Geometry by Cox, Little, and O'Shea, Chapter 9
Stanley Reisner Ideals	Combinatorial Commutative Algebra by Miller and Sturmfels, Sections 1.1, 1.2
Sums of squares and the real Nullstellensatz	Solving Systems of Polynomial Equations by Sturmfels, Chapter 7
Universal Groebner Bases	Groebner bases and convex polytopes by Sturmfels, Chapter 7
The Combinatorial Nullstellensatz (**taken**)	Combinatorial Nullstellensatz by Noga Alon