The Illinois Graduate Seminar in Algebraic Combinatorics is a student-run seminar for graduate students and advanced undergraduates interested in algebraic combinatorics and related areas.
The seminar focuses on expository and educational talks, with occasional presentations on recent research and ongoing work. It also provides participants with opportunities to learn new mathematics and practice mathematical exposition.
Advanced undergraduates and beginning graduate students are especially welcome.
Meeting time: Monday 4PM-5PM
Location: Loomis 136
SPEAKERS AND TITLES:
September 14 — Jaewon Min: What are Lie types?
Abstract: Reflection groups, Lie groups, Lie algebras and flag varieties share a common combinatorial classification, known as Lie types. Together, these objects constitute an important part of Lie theory. In this talk, we explore the relationships among them.
September 28 — Duy Phan: An Introduction to Schubert Calculus
Abstract: How many lines in P^3 meet four general lines? Starting from this classical question, we introduce Schubert calculus and explain how geometric counting problems become intersection computations on Grassmannians. Through concrete examples, we explore connections with Young tableaux, Schur functions, and the Littlewood–Richardson rule. No prior knowledge of Schubert calculus is assumed.
October 12 — Junseo Ko: A Combinatorial Approach to Representations of the Symmetric Group
Abstract: In this talk, we will introduce the Robinson–Schensted correspondence and discuss how it gives a combinatorial proof of a fundamental identity. We will also briefly discuss jeu de taquin and the hook-length formula, highlighting how combinatorial methods provide insight into representation-theoretic results.
October 26 — Anh-Thai Minh Le: Introduction to the Six-Vertex Model
Abstract: We introduce some ideas underlying the exact solvability of vertex models. Our focus will be the six-vertex model, its Yang-Baxter integrability, and its connections to algebraic combinatorics (e.g., alternating sign matrices, Schubert polynomials, etc.). No prior knowledge of statistical mechanics is assumed.
November 9 — Aaron Burnham-Schmidt: Hilbert Functions and Macaulay's Theorem
Abstract: Hilbert functions are ubiquitous in commutative algebra; one particular use of Hilbert functions is in studying the dimension of finitely generated graded algebras and modules. In 1927, Francis Macaulay proved that it is possible to characterize precisely which sequences of nonnegative integers can arise as Hilbert functions for quotients of finitely generated polynomial rings by homogeneous ideals. This talk will introduce Hilbert functions/polynomials through simple examples; we will then provide an overview of Macaulay's theorem and develop the necessary combinatorial machinery underpinning its proof.
November 16 — TBA
Abstract: TBA
December 7 — TBA
Abstract: TBA
Jaewon Min (email: jaewonm2@illinois.edu)
Duy Phan (email: duyphan2@illinois.edu)