BEGIN:VCALENDAR VERSION:2.0 PRODID:-//University of Utah Math Department//Commutative Algebra Seminar//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-WR-CALNAME:Commutative Algebra Seminar - Fall 2019 X-WR-CALDESC:Commutative Algebra Seminar at University of Utah Mathematics Department X-WR-TIMEZONE:America/Denver BEGIN:VEVENT UID:20190830T143000-elo%C3%ADsa-grifo@math.utah.edu DTSTART;TZID=America/Denver:20190830T143000 DTEND;TZID=America/Denver:20190830T153000 DTSTAMP:20260825T100349Z SUMMARY:A stable version of Harbourne's Conjecture DESCRIPTION:Speaker: Eloísa Grifo\, University of California, Riverside\n\nThe n-th power of an ideal is easy to compute, though difficult to describe geometrically; in contrast, symbolic powers are difficult to compute while having a natural geometric description. In trying to compare symbolic and ordinary powers, Harbourne conjectured that a famous containment by … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20190906T143000-bangere-purnaprajna@math.utah.edu DTSTART;TZID=America/Denver:20190906T143000 DTEND;TZID=America/Denver:20190906T153000 DTSTAMP:20260825T100349Z SUMMARY:Deformation of canonical morphisms and moduli spaces DESCRIPTION:Speaker: Bangere Purnaprajna\, University of Kansas, Lawrence\n\nIn this talk we will deal with the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we show a criterion that determines when a finite map can be deformed to a one--to--one map. We use this … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20190913T143000-josh-pollitz@math.utah.edu DTSTART;TZID=America/Denver:20190913T143000 DTEND;TZID=America/Denver:20190913T153000 DTSTAMP:20260825T100349Z SUMMARY:Cohomological support of a local ring DESCRIPTION:Speaker: Josh Pollitz\, University of Utah\n\nDuring this talk, we will discuss a theory of cohomological support defined for pairs of DG modules over a Koszul complex. These specialize to the support varieties of Avramov and Buchweitz defined over a complete intersection ring. Moreover, the support sets introduced in this talk can be used to … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20190920T143000-marcus-robinson@math.utah.edu DTSTART;TZID=America/Denver:20190920T143000 DTEND;TZID=America/Denver:20190920T153000 DTSTAMP:20260825T100349Z SUMMARY:BCM Test Ideals of Mixed Characteristic Toric Schemes DESCRIPTION:Speaker: Marcus Robinson\, University of Utah\n\nAbstract - In this talk we will give a brief introduction to the topic of big Cohen-Macaulay test ideals, a mixed characteristic analogue of the multiplier/test ideals defined in equal/positive characteristic. We will provide a formula to compute the BCM test ideal in the case of monomial ideals of … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20190927T143000-luigi-ferraro@math.utah.edu DTSTART;TZID=America/Denver:20190927T143000 DTEND;TZID=America/Denver:20190927T153000 DTSTAMP:20260825T100349Z SUMMARY:Differential graded algebra over quotients of skew polynomial rings by normal elements DESCRIPTION:Speaker: Luigi Ferraro\, Wake Forest University\n\nDifferential graded algebra techniques have played a crucial role in the development of homological algebra, especially in the study of homological properties of commutative rings carried out by Serre, Tate, Gulliksen, Avramov, and others. In this article, we extend the construction of the Koszul … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191004T143000-kyle-maddox@math.utah.edu DTSTART;TZID=America/Denver:20191004T143000 DTEND;TZID=America/Denver:20191004T153000 DTSTAMP:20260825T100349Z SUMMARY:F-singularities and Frobenius closure of ideals DESCRIPTION:Speaker: Kyle Maddox\, University of Missouri, Columbia\n\nThe canonical Frobenius map defined for any prime characteristic ring can both reveal and obscure an incredible amount of data about the ring. In this talk, we will first discuss a closure operation (Frobenius closure) on ideals defined in terms of the Frobenius map, then outline a similar map (a … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191015T140000-hugh-geller@math.utah.edu DTSTART;TZID=America/Denver:20191015T140000 DTEND;TZID=America/Denver:20191015T150000 DTSTAMP:20260825T100349Z SUMMARY:DG-Algebra resolutions for products of ideals DESCRIPTION:Speaker: Hugh Geller\, Clemson University\n\nResolutions possessing DG-algebra structures are powerful tools. In 2019, Avramov, Iyengar, Nasseh, and Sather-Wagstaff show how the existence of a DG-algebra structure on a minimal resolution can be used to prove a strong Tor-rigidity result. We investigate when minimal resolutions do in fact … LOCATION:LCB 219 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191018T143000-robert-laudone@math.utah.edu DTSTART;TZID=America/Denver:20191018T143000 DTEND;TZID=America/Denver:20191018T153000 DTSTAMP:20260825T100349Z SUMMARY:Representation stability for 0-Hecke modules DESCRIPTION:Speaker: Robert Laudone\, University of California, San Diego\n\nThe category FI and its variants have been of great interest recently. Being a finitely generated FI-module implies many desirable properties about sequences of symmetric group representations, in particular representation stability. We define a new combinatorial category analogous to FI for the … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191025T143000-pinches-dirnfeld@math.utah.edu DTSTART;TZID=America/Denver:20191025T143000 DTEND;TZID=America/Denver:20191025T153000 DTSTAMP:20260825T100349Z SUMMARY:Base change along the Frobenius Endomorphism and the Gorenstein property DESCRIPTION:Speaker: Pinches Dirnfeld\, University of Utah\n\nLet R be a local ring of positive characteristic and X a complex with finitely generated nonzero homology and finite injective dimension. We prove that if derived base change of X via the Frobenius (or more generally, via a contracting) endomorphism has finite injective dimension then R is … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191101T143000-agn%C3%A8s-beaudry@math.utah.edu DTSTART;TZID=America/Denver:20191101T143000 DTEND;TZID=America/Denver:20191101T153000 DTSTAMP:20260825T100349Z SUMMARY:Invertibility in Chromatic Homotopy Theory DESCRIPTION:Speaker: Agnès Beaudry\, University of Colorado, Boulder\n\nFor a symmetric monoidal category C, the invertible objects with respect to the symmetric monoidal product often give rise to a group called the Picard group of C. This group contains important information about C, in particular, about its self-equivalences. An important symmetric monoidal category … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191101T153000-stephen-h.-mckean@math.utah.edu DTSTART;TZID=America/Denver:20191101T153000 DTEND;TZID=America/Denver:20191101T163000 DTSTAMP:20260825T100349Z SUMMARY:Enriching Bézout’s Theorem DESCRIPTION:Speaker: Stephen H. McKean\, Duke University\n\nClassically, Bézout’s Theorem counts the number of intersections of two generic algebraic curves over an algebraically closed field. Using tools from A^1-homotopy theory and building on the work of Jesse Kass and Kirsten Wickelgren, we give an enrichment of Bézout’s Theorem over any perfect field. … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191108T143000-linquan-ma@math.utah.edu DTSTART;TZID=America/Denver:20191108T143000 DTEND;TZID=America/Denver:20191108T153000 DTSTAMP:20260825T100349Z SUMMARY:Fedder's criterion and symbolic power containment for singular rings DESCRIPTION:Speaker: Linquan Ma\, Purdue University\n\nWe extend Fedder's criterion for F-purity to singular ambient rings. As applications, we discuss several generalizations of Grifo-Huneke's result on symbolic power containments (Harbourne's conjecture) in regular rings to singular rings, either when the ideal has finite projective dimension or when … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191115T143000-laure-flapan-special-seminar@math.utah.edu DTSTART;TZID=America/Denver:20191115T143000 DTEND;TZID=America/Denver:20191115T153000 DTSTAMP:20260825T100349Z SUMMARY:Fano Lagrangian submanifolds of hyperkahler manifolds DESCRIPTION:Speaker: Laure Flapan (Special Seminar)\, M.I.T.\n\nFor any polarized hyperkahler manifold of K3 type whose dimension is divisible by 8, we produce a Lagrangian submanifold which is Fano arising as a connected component of the fixed locus of an involution on the hyperkahler manifold. This is joint work with E. Macrì, K. O’Grady, and G. Sacca. LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191122T143000-zhan-jiang@math.utah.edu DTSTART;TZID=America/Denver:20191122T143000 DTEND;TZID=America/Denver:20191122T153000 DTSTAMP:20260825T100349Z SUMMARY:Closure operations on complete local rings of mixed characteristic DESCRIPTION:Speaker: Zhan Jiang\, University of Michigan\n\nClosure operations are important tools in commutative algebra. The most well-known closure operation is tight closure introduced by Hochster and Huneke, which turns out to be very powerful and fruitful. Other examples are epf and r1f closures defined by Heitmann for rings of mixed characteristics. … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT BEGIN:VEVENT UID:20191206T143000-austyn-simpson@math.utah.edu DTSTART;TZID=America/Denver:20191206T143000 DTEND;TZID=America/Denver:20191206T153000 DTSTAMP:20260825T100349Z SUMMARY:Hilbert-Kunz multiplicity of fibers and Bertini theorems DESCRIPTION:Speaker: Austyn Simpson\, University of Illinois, Chicago\n\nThe Hilbert-Kunz multiplicity is a prime characteristic numerical invariant that detects regularity. In this talk, I discuss a type of Bertini theorem for equidimensional (quasi)projective schemes which says that the measure of singularity given by Hilbert-Kunz does not get worse upon taking general … LOCATION:LCB 225 URL:http://math.utah.edu/caseminar/2019-fall/ END:VEVENT END:VCALENDAR