6 papers
The generators of a colon ideal with an application to the weak Lefschetz property for monomial almost complete intersections in three variables
Matthew Davidson Booth, Adela Vraciu
Much progress has been made in classifying when the weak Lefschetz property holds for where and $I=(x^{d_{1}},y^{d_{2}},z^{d_{3}…
Lectures on singularity categories
Matt Booth
These are notes for a graduate-level introductory course on singularity categories.
Reflexive dg categories in algebra and topology
Matt Booth, Isambard Goodbody, Sebastian Opper
Reflexive dg categories were introduced by Kuznetsov and Shinder to abstract the duality between bounded and perfect derived categories. In particular this duality relates their Ho…
How to invert well-pointed endofunctors
Matt Booth
In this short note we observe that Kelly's transfinite construction of free algebras yields a way to invert well-pointed endofunctors. In enriched settings, this recovers construct…
On the weak Lefschetz property for ideals generated by powers of general linear forms
Matthew D. Booth, Pankaj Singh, Adela Vraciu
We provide a description of initial ideals for almost complete intersections generated by powers of general linear forms and prove that WLP in a fixed degree holds when the num…
Nonsmooth Calabi-Yau structures for algebras and coalgebras
Matt Booth, Joseph Chuang, Andrey Lazarev
We show that generalised Calabi-Yau dg (co)algebras are Koszul dual to generalised symmetric dg (co)algebras, without needing to assume any smoothness or properness hypotheses. Sim…