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 2022 X-WR-CALDESC:Commutative Algebra Seminar at University of Utah Mathematics Department X-WR-TIMEZONE:America/Denver BEGIN:VEVENT UID:20220831T140000-matt-baker@math.utah.edu DTSTART;TZID=America/Denver:20220831T140000 DTEND;TZID=America/Denver:20220831T150000 DTSTAMP:20260823T110330Z SUMMARY:Non-archimedean and tropical geometry, algebraic groups, moduli spaces of matroids, and the field with one element DESCRIPTION:Speaker: Matt Baker\, Georgia Tech\n\nI will give an introduction to Oliver Lorscheid's theory of ordered blueprints - one of the more successful approaches to 'the field of one element' - and sketch its relationship to Berkovich spaces, tropical geometry, Tits models for algebraic groups, and moduli spaces of matroids. The basic idea … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20220909T140000-manuel-blickle@math.utah.edu DTSTART;TZID=America/Denver:20220909T140000 DTEND;TZID=America/Denver:20220909T150000 DTSTAMP:20260823T110330Z SUMMARY:Using the Riemann-Hilbert correspondence DESCRIPTION:Speaker: Manuel Blickle\, Universität Mainz\n\nWe will indicate how, using the Riemann-Hilbert correspondence, one can recover several results on local cohomology modules of polynomial rings. LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20220916T140000-seungsu-lee@math.utah.edu DTSTART;TZID=America/Denver:20220916T140000 DTEND;TZID=America/Denver:20220916T150000 DTSTAMP:20260823T110330Z SUMMARY:On the behavior of F-signature on the Nef cone DESCRIPTION:Speaker: Seungsu Lee\, University of Utah\n\nF-signature plays a crucial role when measuring singularities of varieties in positive characteristics. For example, if R is a local ring, s(R) = 1 implies R is regular, and 0 < s(R) < 1 implies R is strongly F-regular which is a char p analog of klt singularities. For a globally F-regular variety … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20220923T140000-keiichi-watanabe@math.utah.edu DTSTART;TZID=America/Denver:20220923T140000 DTEND;TZID=America/Denver:20220923T150000 DTSTAMP:20260823T110330Z SUMMARY:Elliptic ideals in 2 dimensional normal local rings DESCRIPTION:Speaker: Keiichi Watanabe\, Nihon University and Meiji University\n\nThis is a joint work in progress with Tomohiro Okuma and Ken-ichi Yoshida. Let (A, m) be a 2-dimensional excellent normal local ring. Let I be an integrally closed m-primary ideal, and let f : X -> Spec(A) be a resolution of singularity such that I O_X = O_X(-Z) is invertible. Also let Q be a … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20220930T140000-shiji-lyu@math.utah.edu DTSTART;TZID=America/Denver:20220930T140000 DTEND;TZID=America/Denver:20220930T150000 DTSTAMP:20260823T110330Z SUMMARY:Some properties of splinters and birational derived splinters DESCRIPTION:Speaker: Shiji Lyu\, Princeton University\n\nWe will discuss the notions of splinters and birational derived splinters. They are related to various interesting notions of singularities, but less are known about them. We will discuss some basic properties of those notions including behavior under limit and etale extensions. Then we will discuss … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20221003T140000-luis-n%C3%BA%C3%B1ez-betancourt@math.utah.edu DTSTART;TZID=America/Denver:20221003T140000 DTEND;TZID=America/Denver:20221003T150000 DTSTAMP:20260823T110330Z SUMMARY:Rees algebras of determinantal ideals DESCRIPTION:Speaker: Luis Núñez-Betancourt\, Centro de Investigación en Matemáticas (CIMAT)\n\nIn this talk we focus on Rees algebras and symbolic Rees algebras of determinantal ideals. In particular, we will show that they have mild singularities in prime characteristic. We will also discuss consequences for numerical invariants and initial ideals of the symbolic powers of these ideals. This … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20221007T140000-david-eisenbud@math.utah.edu DTSTART;TZID=America/Denver:20221007T140000 DTEND;TZID=America/Denver:20221007T150000 DTSTAMP:20260823T110330Z SUMMARY:Summands in high syzygies DESCRIPTION:Speaker: David Eisenbud\, UC Berkeley\n\nWork on infinite resolutions beyond the cases of complete intersections and Golod rings has tended to focus on the sequence of Betti numbers. Hai Long Dao and I have recently begun to study a question of a different kind, and I will report on this joint work: Let R = S/I be an Artinian quotient of a … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20221021T140000-jennifer-kenkel@math.utah.edu DTSTART;TZID=America/Denver:20221021T140000 DTEND;TZID=America/Denver:20221021T150000 DTSTAMP:20260823T110330Z SUMMARY:Lengths of local cohomology using some surprising Hilbert-Kunz functions DESCRIPTION:Speaker: Jennifer Kenkel\, University of Michigan\n\nWe investigate the lengths of certain local cohomology modules over polynomial rings. By fixing the degree component, and using the fact that the length of an Artinian ring is the same as that of its injective hull, we transform this into a question about rings of the form … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20221028T140000-sarasij-maitra@math.utah.edu DTSTART;TZID=America/Denver:20221028T140000 DTEND;TZID=America/Denver:20221028T150000 DTSTAMP:20260823T110330Z SUMMARY:Discussions on Berger's Conjecture DESCRIPTION:Speaker: Sarasij Maitra\, University of Utah\n\nIn this talk, we will discuss a conjecture of R. Berger dating back to around 1963. He conjectured that in a reduced one dimensional local complete algebra over a perfect field k, the torsion submodule of the module of differentials should capture information about the regularity of the algebra. We … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20221104T140000-trung-chau@math.utah.edu DTSTART;TZID=America/Denver:20221104T140000 DTEND;TZID=America/Denver:20221104T150000 DTSTAMP:20260823T110330Z SUMMARY:Barile-Macchia resolutions DESCRIPTION:Speaker: Trung Chau\, University of Utah\n\nResolving a monomial ideal over the polynomial ring is an easy task, but resolving it minimally isn't. In this talk we discuss Barile-Macchia resolutions, which is a new construction of free resolutions for all monomial ideals using discrete Morse theory, and point out important classes of ideals … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20221111T140000-peter-mcdonald@math.utah.edu DTSTART;TZID=America/Denver:20221111T140000 DTEND;TZID=America/Denver:20221111T150000 DTSTAMP:20260823T110330Z SUMMARY:Homological properties of the relative Frobenius map DESCRIPTION:Speaker: Peter McDonald\, University of Utah\n\nGiven a noetherian ring of positive characteristic, Kunz proved that the Frobenius endomorphism is flat if and only if the ring is regular. Radu and André established an analogue for homomorphisms of noetherian rings of positive characteristic, proving that such a map regular if and only if the … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT BEGIN:VEVENT UID:20221202T140000-jack-jeffries@math.utah.edu DTSTART;TZID=America/Denver:20221202T140000 DTEND;TZID=America/Denver:20221202T150000 DTSTAMP:20260823T110330Z SUMMARY:Bernstein's inequality and sandwich Bernstein-Sato polynomials DESCRIPTION:Speaker: Jack Jeffries\, University of Nebraska Lincoln\n\nRings of differential operators and their module theory have a number of important applications in Commutative Algebra. Much of the power of D-module theory stems from the fact that many "large" modules over polynomial rings exhibit striking finiteness properties as D-modules. The fountain of … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-fall/ END:VEVENT END:VCALENDAR