Speaker: Anna Weigandt, Massachusetts Institute of TechnologyTitle: Combinatorial Aspects of Determinantal VarietiesDate: 01/09/2023Time: 4:10 PM - 5:00 PMPlace: C304 Wells Hall (Virtual Meeting Link)Contact: Sabrina M Walton (waltons3@msu.edu)

Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as “how many lines meet four fixed lines in three-space?” These problems can be recast as questions about the structure of cohomology rings of geometric spaces such as flag varieties. Borel’s isomorphism identifies the cohomology of the complete flag variety with a simple quotient of a polynomial ring. Lascoux and Schützenberger (1982) defined Schubert polynomials, which are coset representatives for the Schubert basis of this ring. However, it was not clear if this choice was geometrically natural. Knutson and Miller (2005) provided a justification for the naturality of Schubert polynomials via antidiagonal Gröbner degenerations of matrix Schubert varieties, which are generalized determinantal varieties. Furthermore, they showed that pre-existing combinatorial objects called pipe dreams govern this degeneration. In this talk, we study the dual setting of diagonal Gröbner degenerations of matrix Schubert varieties, interpreting these limits in terms of the “bumpless pipe dreams” of Lam, Lee, and Shimozono (2021). We then use the combinatorics of K-theory representatives for Schubert classes to compute the Castelnuovo-Mumford regularity of matrix Schubert varieties, which gives a bound on the complexity of their coordinate rings.

Department of Mathematics

Michigan State University

619 Red Cedar Road

C212 Wells Hall

East Lansing, MI 48824

Phone: (517) 353-0844

Fax: (517) 432-1562

- People
- All
- Regular Faculty
- Postdocs
- Fixed Term/Visiting Faculty
- Specialists and Instructors
- Adjunct Faculty
- Emeriti
- Graduate Students
- Teaching Assistants
- Staff
- Administration
- Diversity, Equity, Inclusiveness
- Faculty Honors

- Research
- Faculty Research Interests
- Seminars
- Seminars by Week
- Topology RTG
- MCIAM
- MathSciNet
- Institute of Mathematical Physics
- Math Library
- Phillips Lecture

- Undergraduate
- Undergraduate Program
- Class Pages
- Student Portal
- Webwork
- Math Learning Center
- Actuarial Science
- Advising Information
- Override Request
- Math Placement Service
- Herzog Competition
- Scholarships
- Exchange Program
- Sample Finals
- Multicultural Center Feasibility