This is the homepage of the Algebra and Algebraic Geometry Seminar at McMaster University. This seminar is primarily intended for McMaster University graduate students, postdocs, and faculty with an interest in algebra, algebraic geometry, number theory, or related areas. If you are interested in giving a talk, please contact one of the faculty members affiliated with the seminar: Cam Franc, Megumi Harada, Jenna Rajchgot, or Adam Van Tuyl,
During Fall 2026, talks take place Tuesdays at 10:30-11:20am (Eastern) at HH 312.
Abstract: The Hilbert series of a homogeneous algebra reflects various algebraic properties of the algebra through the h-polynomial appearing in its numerator. In this talk, I will give an overview of the relationship between Hilbert series and ring-theoretic properties, e.g., the Cohen–Macaulay and Gorenstein properties, and explain some fundamental results on h-polynomials, including Macaulay’s criterion. I will also discuss Stanley–Reisner rings, which play an important role in the study of h-polynomials of homogeneous algebras. Finally, I will present some recent results from joint work with Kenta Ueyama and Takumi Yanagida on homogeneous algebras whose h-polynomials are products of cyclotomic polynomials.
Abstract: Hessenberg varieties are subvarieties of the flag variety Flags(\C^n) and have a rich geometry which intersects with the theory of combinatorial commutative algebra, Schubert geometry and Schubert calculus, and geometric representation theory, among other areas. The cohomology rings of Hessenberg varieties have been studied extensively due to their connections with the theory of quasisymmetric functions. I will give a curated introduction to this circle of ideas, with a focus on a selection of recent developments.
Abstract: Edge ideals of graphs provide a fertile ground for uncovering combinatorial expressions for algebraic invariants of squarefree monomial ideals. In fact, many algebraic invariants of these edge ideals directly reflect combinatorial properties of their underlying graphs. In this talk, I will discuss how the independence polynomial P_G(x), the generating function for independent sets of a graph G, encodes surprisingly rich information about the Hilbert series of the corresponding edge ideal I(G). In particular, I will explain how P_G(x) determines both the top coefficient and the degree of the h-polynomial. I will then demonstrate the results through familiar examples and a simple suspension construction that lets us track these invariants cleanly.
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We will share with our Dean some narratives of our activities and our research.
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During Winter 2027, talks take place Tuesdays at 10:30-11:20am (Eastern) at HH ??? (to be confirmed).
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