# NCMW - Cohen Macaulay simplicial complexes in graph theory (2023)

## Venue: CMI, Kelambakkam

## Dates: 10 Jul 2023 to 15 Jul 2023

**Convener(s)**

Name: |
Priyavrat Deshpande | Anurag Singh |

Mailing Address: |
Assistant Professor, Chennai Mathematical Institute |
Assistant Professor, Indian Institute of Technology Bhilai |

Email: |
pdeshpande at cmi.ac.in | anurags at iitbhilai.ac.in |

The main aim of this workshop is to introduce participants with various methods and tools that are used to solve problems at the intersection of topological combinatorics and combinatorial commutative algebra. The

topics that we plan to explore are: Stanley-Reisner ring of a simplicial complex, Cohen-Macaulay conditions, edge and cover ideals of graphs, splitting monomial ideals and Fröberg’s theorem, component-wise linearity, simplicial complexes associated with graphs; like neighborhood complexes, independence complexes, matching complexes and their generalizations etc, discrete Morse theory and its applications. We also plan to discuss topological invariants of above men-tioned graph complexes and their connections to graph theory.**Pre-requisites:** First course in commutative algebra and algebraic topology with the understanding of homology and cohomology calculations.