Lectures: Tuesday and Thursday 1:00pm-2:30pm 3866 East Hall
Instructor: Thomas Lam, tfylam@umich.edu
Office Hours: Tuesday 2:30pm-4:15pm and Thursday 11:30pm-12:20pm in EH2834.
Course description:
This is an introductory course in Schubert calculus, a branch of enumerative geometry with deep connections to combinatorics and representation theory. A typical problem in Schubert calculus is: fix four lines in three-dimensional space; how many other lines intersect all four? Some of the topics we may study include: cohomology of Grassmannians and flag varieties, Schur functions, Schubert polynomials, Littlewood-Richardson rules, equivariant Schubert calculus, K-theory Schubert calculus, affine Schubert calculus, quantum Schubert calculus, back stable Schubert calculus.
Prerequesites: Familiarity with linear algebra is essential. Experience with combinatorics, algebraic geometry, and/or algebraic topology is helpful.
Grading:
There will be several problem sets throughout the semester. There will be no exams.
Grades will be calculated from: Problem Sets (98%) and evidence of completion of course evaluation (2%).
References:
[Fulton] W. Fulton, Young tableaux, Cambridge University Press, 1997.
[Man] L. Manivel, Symmetric functions, Schubert polynomials and degeneracy loci, AMS, 2001.
[Tym] Tymoczko, An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and Macpherson
[AF] Anderson and Fulton, Equivariant Cohomology in Algebraic Geometry
Homework policy:
Homework must be written in LaTeX and is due at the start of class. Homework can be emailed to me, or submitted in person. Late homework is generally not accepted.
You are allowed (and encouraged) to work with other students on the problem sets, but you must write the solutions yourself and include the names of those you worked with when you hand in your homework. You are not allowed to post homework problems on question websites such as mathoverflow or stackexchange. You are allowed to use AI tools to help you to understand a problem but you are responsible for the entirety of the homework submission. If you use material from AI, a book, online, or elsewhere, you must acknowledge the source.
If the situation arises, you are expected to be able to explain (in detail) your homework solution to me.
Problem Sets:
Pset 1 (Due Tuesday Sep 29)
Academic Misconduct: The University of Michigan community functions best when its members treat one another with honesty, fairness, respect, and trust. The college promotes the assumption of personal responsibility and integrity, and prohibits all forms of academic dishonesty and misconduct. All cases of academic misconduct will be referred to the LSA Office of the Assistant Dean for Undergraduate Education. Being found responsible for academic misconduct will usually result in a grade sanction, in addition to any sanction from the college. For more information, including examples of behaviors that are considered academic misconduct and potential sanctions, please see lsa.umich.edu/lsa/academics/academic-integrity.html.
Disabilities:
If you think you need an accommodation for a disability, please let me know as soon as possible. In particular, a Verified Individualized Services and Accommodations (VISA) form must be provided to me at least two weeks prior to the need for a test/quiz accommodation.
The University of Michigan recognizes disability as an integral part of diversity and is committed to creating an inclusive and equitable educational environment for students with disabilities.
Students who are experiencing a disability-related barrier should contact Services for Students with Disabilities https://ssd.umich.edu/; 734-763-3000 or [email protected]). For students who are connected with SSD, accommodation requests can be made in Accommodate. If you have any questions or concerns please contact your SSD Coordinator or visit SSD’s Current Student webpage. SSD considers aspects of the course design, course learning objects and the individual academic and course barriers experienced by the student. Further conversation with SSD, instructors, and the student may be warranted to ensure an accessible course experience.
List of lectures (tentative):