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 - Spring 2019 X-WR-CALDESC:Commutative Algebra Seminar at University of Utah Mathematics Department X-WR-TIMEZONE:America/Denver BEGIN:VEVENT UID:20190125T143000-sudhir-ghorpade@math.utah.edu DTSTART;TZID=America/Denver:20190125T143000 DTEND;TZID=America/Denver:20190125T153000 DTSTAMP:20260825T100349Z SUMMARY:Number of zeros of polynomials over finite fields DESCRIPTION:Speaker: Sudhir Ghorpade\, IIT Bombay\n\nIt is elementary and well-known that a polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. An analogue of this for homogeneous polynomials is that a homogeneous polynomial in two variables of degree d with coefficients in F has at most d non-proportional … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190201T143000-claudia-miller@math.utah.edu DTSTART;TZID=America/Denver:20190201T143000 DTEND;TZID=America/Denver:20190201T153000 DTSTAMP:20260825T100349Z SUMMARY:Betti numbers of the Frobenius powers of the maximal ideal over generic hypersurfaces in 3 variables DESCRIPTION:Speaker: Claudia Miller\, Syracuse University\n\nWe discuss the conjectured curious behavior of the Betti numbers of the Frobenius powers of the maximal ideal in hypersurfaces k[x,y,z]/(f), where k is an infinite field of any positive characteristic p, such as 1000000000000066600000000000001. Indeed, if f is chosen generically, then high enough … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190208T143000-patricia-klein@math.utah.edu DTSTART;TZID=America/Denver:20190208T143000 DTEND;TZID=America/Denver:20190208T153000 DTSTAMP:20260825T100349Z SUMMARY:Lech's inequality and the Stückrad-Vogel conjecture DESCRIPTION:Speaker: Patricia Klein\, University of Kentucky\n\nLet (R, m) be a Noetherian local ring, and let M be a finitely generated R-module of dimension d. Let e(I,M) denote the Hilbert-Samuel multiplicity of M on the ideal I. Lech's inequality states that the set {length(R/I)/e(I,R)}, as I runs through all m-primary ideals, is bounded below by 1/d!e(m,R). … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190215T143000-tba@math.utah.edu DTSTART;TZID=America/Denver:20190215T143000 DTEND;TZID=America/Denver:20190215T153000 DTSTAMP:20260825T100349Z SUMMARY:TBA DESCRIPTION:Speaker: TBA\n\nTBA LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190222T143000-adam-boocher@math.utah.edu DTSTART;TZID=America/Denver:20190222T143000 DTEND;TZID=America/Denver:20190222T153000 DTSTAMP:20260825T100349Z SUMMARY:Using Boij-Soederberg theory to bound Betti numbers DESCRIPTION:Speaker: Adam Boocher\, University of San Diego\n\nSuppose that I is a homogeneous ideal of height c in a polynomial ring. Such ideals have at least c minimal generators, and that is about all we can say in this generality. If however we impose bounds on the regularity of the ideal then there are surprising constraints on the number of generators … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190301T143000-john-zhang@math.utah.edu DTSTART;TZID=America/Denver:20190301T143000 DTEND;TZID=America/Denver:20190301T153000 DTSTAMP:20260825T100349Z SUMMARY:Polynomial rings over triangulated categories-an introduction to derivators DESCRIPTION:Speaker: John Zhang\, UCLA\n\nI will discuss an analogue of taking categories of (possibly graded) modules over a polynomial ring as a purely categorical construction. This requires the formalism of derivators, but in return this allows us to expand the construction to other areas of mathematics. These constructions satisfy some … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190308T143000-janina-letz@math.utah.edu DTSTART;TZID=America/Denver:20190308T143000 DTEND;TZID=America/Denver:20190308T153000 DTSTAMP:20260825T100349Z SUMMARY:Local to global principles for generation time over commutative rings DESCRIPTION:Speaker: Janina Letz\, University of Utah\n\nIn the derived category of modules over a noetherian ring a complex G is said to generate a complex X if the latter can be obtained from the former by taking finitely many summands and cones. The number of cones needed in this process is the generation time of X. In this talk I will present some … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190315T143000-speaker@math.utah.edu DTSTART;TZID=America/Denver:20190315T143000 DTEND;TZID=America/Denver:20190315T153000 DTSTAMP:20260825T100349Z SUMMARY:Spring Break DESCRIPTION:Speaker: speaker\n\n LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190319T153000-jonathan-campbell@math.utah.edu DTSTART;TZID=America/Denver:20190319T153000 DTEND;TZID=America/Denver:20190319T163000 DTSTAMP:20260825T100349Z SUMMARY:Bicategorical duality theory with applications to topology and algebra DESCRIPTION:Speaker: Jonathan Campbell\, Vanderbilt University\n\nIn this talk I'll describe how a bicategorical gadget, called the shadow, allows one to extract many interesting algebraic and topological invariants. For example, in algebraic bicategories, one easily recovers group characters, and in certain topological categories, one recovers the Lefschetz … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190329T143000-ian-aberbach@math.utah.edu DTSTART;TZID=America/Denver:20190329T143000 DTEND;TZID=America/Denver:20190329T153000 DTSTAMP:20260825T100349Z SUMMARY:Local cohomology bounds and test ideals DESCRIPTION:Speaker: Ian Aberbach\, University of Missouri, Columbia\n\nLet R be a local ring of positive prime characteristic p. The notion of tight closure, developed by Hochster and Huneke, is a powerful tool in understanding Noetherian rings, and is also of intrinsic interest. In particular, we can classify singularities in terms of the “amount” of tight closure … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT BEGIN:VEVENT UID:20190419T143000-vesna-stojanoska@math.utah.edu DTSTART;TZID=America/Denver:20190419T143000 DTEND;TZID=America/Denver:20190419T153000 DTSTAMP:20260825T100349Z SUMMARY:Dualizing spheres for p-adic analytic groups with applications to chromatic homotopy theory DESCRIPTION:Speaker: Vesna Stojanoska\, University of Illinois, Urbana-Champaign\n\nI will describe a Linearization Conjecture that identifies the spectral dualizing module of a p-adic analytic group in terms of a representation sphere built from its Lie algebra. We can prove this when the action is restricted to certain small finite subgroups. These results are enough to determine … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2019-spring/ END:VEVENT END:VCALENDAR