CS 860: Commutative Algebra with a view Towards Complexity Theory

General Information

  • Course Description: this course aims to study commutative algebra in the context of complexity theory. Topics include: quick review of complexity theory (with relevant complexity classes), Groebner bases, primary decomposition algorithms, computation of free resolutions, degree bounds for Nullstellensatz and for many other fundamental problems in commutative algebra, computational complexity of basic problems in commutative algebra and algebraic geometry, Koiran’s Nullstellensatz in PH, and more (time permitting). A more detailed description is given here.

  • Objectives: this course aims to introduce students to the rich interplay between commutative algebra and complexity theory, while exposing major results along with the several open questions at the interface of these areas.

Organization

Instructor: Rafael Oliveira,

  • Email: rafael.oliveira.teaching (at) gmail [dot] com
  • Office: DC 1313

Time and Place of lectures:

  • Mondays and Wednesdays, 10-11:20am
  • Location: DC 2568

General Student Drop-In Hours:

  • The best way to get your questions answered is via discussion on rocketchat. In case you want to meet in person, please send me a message on rocketchat to setup a time.

Grades:

  • 3 written assignments 60%
  • Scribe notes 20%
  • Lecture presentation 20%

Announcements

Announcements will be posted on rocketchat. Please create an account here and send me a message there so I can add you to the course channel.

Assignments

For detailed information on the assignments, please see this page

Midterm and Exam

There will be no exams for this class.

Lectures

Lecture notes will be posted after the lectures. References are mostly from the suggested supplemental resources.

Land Acknowledgment

The University of Waterloo is on lands that are deeply connected to Indigenous peoples who have historically lived and who currently live in this territory. We acknowledge that we live and work on the traditional territory of the Attawandaron (Neutral), Anishinaabeg, and Haudenosaunee peoples. The University of Waterloo is situated on the Haldimand Tract, the land promised to the Six Nations that includes ten kilometres on each side of the Grand River.

University Policies

Note for students who need accommodations: If you need accommodations, please let me know about them, and/or contact the AccessAbility office, so that we can provide the proper accommodations. If you feel uncomfortable letting me know about them, please contact the AccessAbility office as soon as you can so you can make the most out of the course.

The AccessAbility office, located in Needles Hall Room 1401, collaborates with all academic departments to arrange appropriate accommodations for students with special needs without compromising the academic integrity of the curriculum. If you require academic accommodations, please register with AccessAbility Services at the beginning of each academic term.

Academic Integrity: In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility. All members of the UW community are held to the highest standard of academic integrity in their studies, teaching, and research.

The Office of Academic Integrity’s website contains detailed information on UW policy for students and faculty. This site explains why academic integrity is important and how students can avoid academic misconduct. It also identifies resources available on campus for students and faculty to help achieve academic integrity in and out of the classroom.

Grievance: A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70 - Student Petitions and Grievances, Section 4. When in doubt please be certain to contact the department’s administrative assistant who will provide further assistance.

Discipline: A student is expected to know what constitutes academic integrity to avoid committing academic offenses, and to take responsibility for his/her actions. A student who is unsure whether an action constitutes an offense, or who needs help in learning how to avoid offenses (e.g., plagiarism, cheating) or about “rules” for group work/collaboration should seek guidance from the course professor, academic advisor, or the Undergraduate Associate Dean. When misconduct has been found to have occurred, disciplinary penalties will be imposed under Policy 71 – Student Discipline. For typical penalties check Guidelines for the Assessment of Penalties.

Appeals: A decision made or penalty imposed under Policy 70, Student Petitions and Grievances (other than a petition) or Policy 71, Student Discipline may be appealed if there is a ground. A student who believes he/she has a ground for an appeal should refer to Policy 72, Student Appeals.

Avoiding Academic Offences: we expect that students are aware of the line between acceptable and unacceptable academic behaviour, especially when discussing assignments with classmates and using the work of other students. For information on commonly misunderstood academic offences and how to avoid them, students should refer to the Faculty of Mathematics Academic Integrity Policy.

Intellectual Property: Students should be aware that this course contains the intellectual property of their instructor, TA, and/or the University of Waterloo. Intellectual property includes items such as:

  • Lecture content, spoken and written (and any audio/video recording thereof);
  • Lecture handouts, presentations, and other materials prepared for the course (e.g., PowerPoint slides);
  • Questions or solution sets from various types of assessments (e.g., assignments, quizzes, tests, final exams); and
  • Work protected by copyright (e.g., any work authored by the instructor or TA or used by the instructor or TA with permission of the copyright owner).

Course materials and the intellectual property contained therein, are used to enhance a student’s educational experience. However, sharing this intellectual property without the intellectual property owner’s permission is a violation of intellectual property rights. For this reason, it is necessary to ask the instructor, TA and/or the University of Waterloo for permission before uploading and sharing the intellectual property of others online (e.g., to an online repository). Permission from an instructor, TA or the University is also necessary before sharing the intellectual property of others from completed courses with students taking the same/similar courses in subsequent terms/years. In many cases, instructors might be happy to allow distribution of certain materials. However, doing so without expressed permission is considered a violation of intellectual property rights.

Please alert the instructor if you become aware of intellectual property belonging to others (past or present) circulating, either through the student body or online. The intellectual property rights owner deserves to know (and may have already given their consent).

Last updated on Feb 10, 2024

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