BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Susan Morey (Texas State University) DTSTART:20211119T130000Z DTEND:20211119T140000Z DTSTAMP:20260423T021054Z UID:VCAS/109 DESCRIPTION:Title: C ellular Resolutions and Powers of Monomial Ideals\nby Susan Morey (Tex as State University) as part of IIT Bombay Virtual Commutative Algebra Sem inar\n\n\nAbstract\nUsing combinatorial structures to obtain resolutions o f monomial ideals is an idea that traces back to Diana Taylor’s thesis\, where a simplex associated to the generators of a monomial ideal was used to construct a free resolution of the ideal. This concept has been expand ed over the years\, with various authors determining conditions under whic h simplicial or cellular complexes can be associated to monomial ideals in ways that produce a free resolution.  \nIn a research project initiated at a BIRS workshop “Women in Commutative Algebra” in Fall 2019\, the\n authors studied simplicial and cellular structures that produced resolutio ns of powers of monomial\nideals. The optimal structure to use depends upo n the structure of the monomial ideal. This talk will focus on powers of s quare-free monomial ideals of projective dimension one. Faridi and Hersey proved that a monomial ideal has projective dimension one if and only if t here is an associated tree (one dimensional acyclic simplicial complex) th at supports a free resolution of the ideal. The talk will show how\, for e ach power $r >\;1$\, to use the tree associated to a square-free monomia l ideal $I$ of projective dimension one to produce a cellular complex that supports a free resolution of $I^r$. Moreover\, each of these resolutions will be minimal resolutions. These cellular resolutions can also be viewe d as strands of the resolution of the Rees algebra of $I$. This talk will contain joint work with Susan Cooper\, Sabine El Khoury\, Sara Faridi\, Sa rah Mayes-Tang\, Liana Sega\, and Sandra Spiroff.\nChairperson - Takayuki Hibi\n LOCATION:https://researchseminars.org/talk/VCAS/109/ END:VEVENT END:VCALENDAR