CMI PhD Research Seminar
Date: Monday, 21 October 2024
Time: 10.30 - 11.30 AM
Venue: Seminar Hall
Vertex decomposable simplicial complexes and their Stanley-Reisner ideals
Rutuja Vilas Sawant
Chennai Mathematical Institute.
21-10-24

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Abstract

Stanley-Reisner theory provides one of the central link between combinatorics and commutative algebra. Pioneered in the 1970s, the correspondence between simplicial complexes and square-free monomial ideals contributed to substantial progress in both fields.

In this talk, I will discuss the one-to-one correspondence between square-free monomial ideals and simplicial complexes and highlight the crucial role of Alexander duality in the study of these ideals and complexes. The main focus of this talk is to prove that a simplicial complex is vertex decomposable if and only if the dual of the corresponding Stanley-Reisner ideal is vertex splittable.