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 2016 X-WR-CALDESC:Commutative Algebra Seminar at University of Utah Mathematics Department X-WR-TIMEZONE:America/Denver BEGIN:VEVENT UID:20160825T151000-jimmy-seiner@math.utah.edu DTSTART;TZID=America/Denver:20160825T151000 DTEND;TZID=America/Denver:20160825T161000 DTSTAMP:20260823T110330Z SUMMARY:On lower bounds for Betti numbers DESCRIPTION:Speaker: Jimmy Seiner\, University of Michigan\n\nWe will examine new and old results concerning lower bounds for Betti numbers of modules over a polynomial ring. We will be centering around several questions inspired by Horrocks' conjecture that the Betti numbers should be bounded below by certain binomial coefficients. Lots of examples will be … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20160826T151000-billy-sanders@math.utah.edu DTSTART;TZID=America/Denver:20160826T151000 DTEND;TZID=America/Denver:20160826T161000 DTSTAMP:20260823T110330Z SUMMARY:A pointless approach to supports in categories DESCRIPTION:Speaker: Billy Sanders\, Norwegian University of Science and Technology\n\nIn this talk, we will discuss the following question: when are the thick subcategories of the bounded derived category of a commutative ring parameterizable by the specialization closed subsets of a Noetherian scheme. To do this, we will use pointless topology to construct a space and a notion of … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20160902T151000-ryo-takahashi@math.utah.edu DTSTART;TZID=America/Denver:20160902T151000 DTEND;TZID=America/Denver:20160902T161000 DTSTAMP:20260823T110330Z SUMMARY:Balmer spectra of right bounded derived categories of commutative rings DESCRIPTION:Speaker: Ryo Takahashi\, Nagoya University, Japan\n\nLet T be a tensor triangulated category, that is, a triangulated category with symmetric monoidal structure. The Balmer spectrum of T is by definition the set of thick tensor ideals of T which are prime. This set has a topology similar to the Zariski topology for the spectrum of a commutative ring. … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20160930T151000-javier-carvajal-rojas@math.utah.edu DTSTART;TZID=America/Denver:20160930T151000 DTEND;TZID=America/Denver:20160930T161000 DTSTAMP:20260823T110330Z SUMMARY:Fundamental groups of F-regular singularities via F-signature DESCRIPTION:Speaker: Javier Carvajal-Rojas\, University of Utah\n\nWe will talk about the algebraic fundamental group of a strongly F-regular singularity. More concretely, via a new transformation rule for the F-signature under certain sort of mildly ramified finite extensions of rings, we will discuss the finiteness of these groups, analogous to results of Xu and … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161007T151000-jugal-k.-verma@math.utah.edu DTSTART;TZID=America/Denver:20161007T151000 DTEND;TZID=America/Denver:20161007T161000 DTSTAMP:20260823T110330Z SUMMARY:Ideals of joint reduction number zero DESCRIPTION:Speaker: Jugal K. Verma\, IIT Bombay, India\n\nWe will present some old and new results on ideals of joint reduction number zero in a Noetherian ring. Complete ideals in two dimensional rational singularities and zero dimensional monomial ideals in polynomial rings are examples of such ideals. A local cohomological characterization of such … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161007T151000-pace-nielsen@math.utah.edu DTSTART;TZID=America/Denver:20161007T151000 DTEND;TZID=America/Denver:20161007T161000 DTSTAMP:20260823T110330Z SUMMARY:Using free constructions to answer questions in algebra DESCRIPTION:Speaker: Pace Nielsen\, Brigham Young University\n\nIt is not difficult to construct a commutative ring R with R isomorphic to R[x]. But is it possible to have R isomorphic to R[x,y] and yet R not isomorphic to R[x]? Similarly, it is easy to show that if R is a commutative ring, and M,N are two right R-modules with the ascending chain condition on … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161021T151000-bhargav-bhatt@math.utah.edu DTSTART;TZID=America/Denver:20161021T151000 DTEND;TZID=America/Denver:20161021T161000 DTSTAMP:20260823T110330Z SUMMARY:The direct summand conjecture and its derived variant DESCRIPTION:Speaker: Bhargav Bhatt\, University of Michigan\n\n LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161028T151000-alessandro-de-stefani@math.utah.edu DTSTART;TZID=America/Denver:20161028T151000 DTEND;TZID=America/Denver:20161028T161000 DTSTAMP:20260823T110330Z SUMMARY:Global F-signature DESCRIPTION:Speaker: Alessandro De Stefani\, KTH, Sweden\n\nThe F-signature of a local ring is a numerical invariant that was formally introduced by Huneke and Leuschke, and it was shown to always exist by Tucker. Roughly speaking, it provides an asymptotic measurement for the number of splittings of the Frobenius endomorphism on a ring of prime … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161104T151000-winfried-bruns@math.utah.edu DTSTART;TZID=America/Denver:20161104T151000 DTEND;TZID=America/Denver:20161104T161000 DTSTAMP:20260823T110330Z SUMMARY:Castelnuovo-Mumford regularity of power products DESCRIPTION:Speaker: Winfried Bruns\, Universität Osnabrück\n\nWe show that the Castelnuovo-Mumford regularity and related invariants of products of powers of ideals in a standard graded polynomial ring are affine-linear in the exponents if these are large enough, provided that each ideal is generated by elements of constant degree. A counterexample shows that … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161111T151000-ray-heitmann@math.utah.edu DTSTART;TZID=America/Denver:20161111T151000 DTEND;TZID=America/Denver:20161111T161000 DTSTAMP:20260823T110330Z SUMMARY:A question of Lyubeznik DESCRIPTION:Speaker: Ray Heitmann\, University of Texas at Austin\n\nHochster and Huneke proved that if *R* is an excellent local domain of charac- teristic *p*, then the absolute integral closure *R+* of *R* is a big Cohen-Macaulay module. This result is certainly not true in characteristic zero or mixed characteristic. However, Gennady Lyubeznik suggested an analog … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161116T151000-rachel-pries@math.utah.edu DTSTART;TZID=America/Denver:20161116T151000 DTEND;TZID=America/Denver:20161116T161000 DTSTAMP:20260823T110330Z SUMMARY:Galois action on homology of Fermat curves DESCRIPTION:Speaker: Rachel Pries\, Colorado State University\n\nWe prove a result about the Galois module structure of the Fermat curve using commutative algebra, number theory, and algebraic topology. Specifically, we extend work of Anderson about the action of the absolute Galois group of a cyclotomic field on a relative homology group of the Fermat curve. By … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161118T151000-john-myers@math.utah.edu DTSTART;TZID=America/Denver:20161118T151000 DTEND;TZID=America/Denver:20161118T161000 DTSTAMP:20260823T110330Z SUMMARY:Homological criteria for minimal multiplicity DESCRIPTION:Speaker: John Myers\, University of Nebraska, Lincoln\n\nThere are well-known lower bounds on the Hilbert-Samuel multiplicity of a Noetherian local ring, depending on what type of ring is under consideration (e.g., complete intersection, Gorenstein, Cohen-Macaulay). Rings for which these lower bounds are achieved are known to have nice properties, … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT BEGIN:VEVENT UID:20161202T151000-jake-levinson@math.utah.edu DTSTART;TZID=America/Denver:20161202T151000 DTEND;TZID=America/Denver:20161202T161000 DTSTAMP:20260823T110330Z SUMMARY:Boij-Söderberg theory for Grassmannians DESCRIPTION:Speaker: Jake Levinson\, University of Michigan\n\nBoij-Söderberg theory is a structure theory for syzygies of graded modules: a near-classification of the possible Betti tables of such modules (which record the degrees of generators in a minimal free resolution). One of the surprises of the theory was the discovery of a "dual" classification of … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2016-fall/ END:VEVENT END:VCALENDAR