PhD. Thesis Defense: Elshani Kamberi, HOMOLOGICAL INVARIANTS OF SQUAREFREE POWERS OF SIMPLICIAL TREES
HOMOLOGICAL INVARIANTS OF SQUAREFREE POWERS OF SIMPLICIAL TREES
Elshani Kamberi
Mathematics, PhD Dissertation, 2025
Thesis Jury
Asst. Prof. Dr. Ayesha Asloob Qureshi(Thesis Advisor)
Asst. Prof. Dr. Nurdagül Anbar
Asst. Prof. Dr. Süha Orhun Mutluergil
Prof. Dr. Seher Tutdere Kavut
Assoc. Prof. Dr. Giancarlo Rinaldo
Date & Time: 17th, July 2025 – 12:30 PM
Place: FENS L055
Zoom Link: https://sabanciuniv.zoom.us/
Keywords : Squarefree power, simplicial forest, linear resolution, linearly related, Castelnuovo-Mumford regularity, path ideals.
Abstract
In this thesis, we study the squarefree powers of facet ideals associated with simplicial trees. Specifically, we examine the linearity of their minimal free resolution and their regularity. Additionally, we investigate when the first syzygy module of squarefree powers of facet ideal of a simplicial tree is generated by linear relations. Finally, we provide a combinatorial formula for the regularity of the squarefree powers of $t$-path ideals of path graphs.