Combinatorial Algebraic Geometry

Welcome to the homepage of the Combinatorial Algebraic Geometry (CAG) group at McMaster University! Our members have research interests in a wide range of topics within combinatorial algebraic geometry and related areas.

Current group members (2022-2023)

Faculty:

• Dr. Megumi Harada

• Dr. Jenna Rajchgot

• Dr. Adam Van Tuyl

Postdoctoral fellows:

• Dr. Thanh Thai Nguyen

Graduate students:

• Büşra Atar (MSc)

• Kieran Bhaskara (MSc)

• Adrian Cook (MSc)

• Mike Cummings (MSc)

• Craig Kohne (PhD)

• Illya Kierkosz (MSc)

• Runyue Wang (MSc)

More detailed information on the research of our current and past group members can be found on our research page.

Information for prospective students

We are always interested in recruiting motivated students. To find out if our group is right for you, please read on, and view our research page!

General information for prospective graduate students

• We are a collaborative group; prospective graduate students will have the opportunity to interact with all CAG group members.

• Students and postdocs will meet with their mentors on a weekly basis.

• We expect CAG students to attend our biweekly McMaster Algebra and Algebraic Geometry seminar, the Algebra, Geometry, and Combinatorics online seminar, and all McMaster Math & Stats colloquia. In addition, we expect our students to attend research workshops and conferences for which they have an opportunity to attend.

Prerequisite knowledge for prospective graduate students

We expect our incoming graduate students to have taken the standard undergraduate mathematics courses. In particular, students should be comfortable with

• basic abstract algebra, to the level of a first sequence of courses in groups, rings, and fields.

Reading: "Abstract Algebra: Theory and Applications" by Thomas W. Judson

• some advanced linear algebra

Reading: "Linear Algebra Done Right" by Sheldon Axler

• basic topology

Reading: Ch. 1-3 of "Topology" by James R. Munkres

We expect our students to learn the following material shortly after arriving. Students are encouraged to start this reading in the summer.

• Ch. 1-5, 8 of "Ideals, Varieties, and Algorithms" by David Cox, John Little, Donal O'Shea

• Ch. 1-4, 7 of "Introduction to Commutative Algebra" by M. F. Atiyah and I.G. MacDonald

• "An Invitation to Algebraic Geometry" by Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, and William Traves

Students should be motivated to learn much more once they arrive at McMaster. Specific subject areas will depend on the research direction, but may include topics from the following books (among others):

• "Lectures on Symplectic Geometry" by Ana Cannas Da Silva

• "Combinatorial Commutative Algebra" by Ezra Miller and Bernd Sturmfels

• "Young Tableaux" by William Fulton

• "Toric Varieties" by David Cox, John Little, and Hal Schenck

• "Graded Syzygies" by Irena Peeva

• "Monomial Algebras" by Rafael H. Villarreal

Prospective undergraduate students

We often have research opportunities available for advanced undergraduate students. If you are interested in undergraduate research, please contact one of the CAG faculty members.