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 2016 X-WR-CALDESC:Commutative Algebra Seminar at University of Utah Mathematics Department X-WR-TIMEZONE:America/Denver BEGIN:VEVENT UID:20160129T151000-graeme-milton@math.utah.edu DTSTART;TZID=America/Denver:20160129T151000 DTEND;TZID=America/Denver:20160129T161000 DTSTAMP:20260823T110330Z SUMMARY:Superfunctions and the algebra of subspace collections DESCRIPTION:Speaker: Graeme Milton\, University of Utah\n\nA natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of subspace collections. Operations on subspace collections are … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160205T151000-amnon-neeman@math.utah.edu DTSTART;TZID=America/Denver:20160205T151000 DTEND;TZID=America/Denver:20160205T161000 DTSTAMP:20260823T110330Z SUMMARY:Grothendieck duality via Hochschild homology DESCRIPTION:Speaker: Amnon Neeman\, Australian National University\n\nHochschild cohomology was introduced in a 1945 paper by Hochschild, and Grothendieck duality dates back to the early 1960s. The fact that the two have some relation with each other is very new - it came up in papers by Avramov and Iyengar [2008], Avramov, Iyengar, and Lipman [2010] and Avramov, … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160212T151000-julia-pevtsova@math.utah.edu DTSTART;TZID=America/Denver:20160212T151000 DTEND;TZID=America/Denver:20160212T161000 DTSTAMP:20260823T110330Z SUMMARY:Varieties for elementary subalgebras of modular Lie algebras DESCRIPTION:Speaker: Julia Pevtsova\, University of Washington\n\nMotivated by questions in modular representation theory, Carlson, Friedlander and the speaker instigated the study of projective varieties of abelian p-nilpotent subalgebras of a fixed dimension r for a p-Lie algebra g. These varieties are closely related to the much studied class of varieties of … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160304T151000-ian-shipman@math.utah.edu DTSTART;TZID=America/Denver:20160304T151000 DTEND;TZID=America/Denver:20160304T161000 DTSTAMP:20260823T110330Z SUMMARY:From representation varieties to Cohen-Macaulay modules DESCRIPTION:Speaker: Ian Shipman\, University of Utah\n\nAn important tool in the study of algebras is the representation variety, which parameterizes representations of a fixed dimension. These varieties are useful for organizing the representation theory of wild algebras and also raise interesting geometric questions themselves. It turns out that it is … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160311T151000-kazuma-shimomoto@math.utah.edu DTSTART;TZID=America/Denver:20160311T151000 DTEND;TZID=America/Denver:20160311T161000 DTSTAMP:20260823T110330Z SUMMARY:F-singularities and non Cohen-Macaulay rings DESCRIPTION:Speaker: Kazuma Shimomoto\, Nihon University, Tokyo\n\nThis is a report on joint work with P.H. Quy (Hanoi). I will talk about recent progress on the connection between F-singularities and non CM rings, using the Frobenius action on local cohomology modules. I will also discuss open problems. LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160311T151000-lars-winther-christensen@math.utah.edu DTSTART;TZID=America/Denver:20160311T151000 DTEND;TZID=America/Denver:20160311T161000 DTSTAMP:20260823T110330Z SUMMARY:Generic local rings interpolate between Gorenstein and Golod DESCRIPTION:Speaker: Lars Winther Christensen\, Texas Tech., Lubbock\n\nLet Q be a power series ring, for example $\mathbb{Q}[\![x,y,z]\!]$, and let I be an ideal in Q. If the drop in depth from Q to the quotient R=Q/I is at most 3, then R can be classified based on a multiplicative structure on the finite free resolution of R as a Q-module. The identification of the … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160325T151000-brooke-ullery@math.utah.edu DTSTART;TZID=America/Denver:20160325T151000 DTEND;TZID=America/Denver:20160325T161000 DTSTAMP:20260823T110330Z SUMMARY:Constructing ideals with high Castelnuovo-Mumford regularity DESCRIPTION:Speaker: Brooke Ullery\, University of Utah\n\nThe Castelnuovo-Mumford regularity of a module is a homological invariant that roughly measures complexity. Though straightforward to define, it is difficult to find ideals in polynomial rings with high Castelnuovo-Mumford regularity. I will demonstrate a method that takes as input well-understood … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160401T151000-henning-krause@math.utah.edu DTSTART;TZID=America/Denver:20160401T151000 DTEND;TZID=America/Denver:20160401T161000 DTSTAMP:20260823T110330Z SUMMARY:Auslander-Reiten duality for Grothendieck abelian categories DESCRIPTION:Speaker: Henning Krause\, University of Bielefeld\n\nA duality for representations of artin algebras was introduced in the 1970s by Auslander and Reiten. One can think of this as an analogue of Serre duality for projective varieties. The talk will present a version of Auslander-Reiten duality for Grothendieck abelian categories. This makes it possible … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160406T151000-thomas-polstra@math.utah.edu DTSTART;TZID=America/Denver:20160406T151000 DTEND;TZID=America/Denver:20160406T161000 DTSTAMP:20260823T110330Z SUMMARY:Global Hilbert-Kunz Multiplicity DESCRIPTION:Speaker: Thomas Polstra\, University of Missouri\n\nThis talk will be a report on some results from a joint work in progress with Alessandro De Stefani and Yongwei Yao. Hilbert-Kunz multiplicity is a classical numerical invariant of study attached to local rings of prime characteristic. In this talk we will discuss how to naturally extend this … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160422T151000-rankeya-datta@math.utah.edu DTSTART;TZID=America/Denver:20160422T151000 DTEND;TZID=America/Denver:20160422T161000 DTSTAMP:20260823T110330Z SUMMARY:Valuations and Frobenius DESCRIPTION:Speaker: Rankeya Datta\, University of Michigan\n\nWe examine some usual notions of singularities in characteristic p > 0 such as F-finiteness, F-splitting, F-purity etc., for valuation rings. The novelty of this approach stems from the fact that most of the characteristic p notions of singularities have been extensively studied in the Noetherian … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160429T151000-dylan-zwick@math.utah.edu DTSTART;TZID=America/Denver:20160429T151000 DTEND;TZID=America/Denver:20160429T161000 DTSTAMP:20260823T110330Z SUMMARY:Symmetric bicolored trees and symmetric tropical ranks DESCRIPTION:Speaker: Dylan Zwick\n\nIn this talk I will define and investigate symmetric bicolored trees, the symmetric versions of the bicolored trees studied by Markwig and Yu. In particular, I'll show that a special subset of these symmetric bicolored trees, those with an "unbranched stem", form a pure-dimensional simplicial … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT BEGIN:VEVENT UID:20160506T151000-claudiu-raicu@math.utah.edu DTSTART;TZID=America/Denver:20160506T151000 DTEND;TZID=America/Denver:20160506T161000 DTSTAMP:20260823T110330Z SUMMARY:The syzygies of some thickenings of determinantal varieties DESCRIPTION:Speaker: Claudiu Raicu\, University of Notre Dame\n\nThe space of m x n matrices admits a natural action of the group GL_m x GL_n via row and column operations on the matrix entries. The invariant closed subsets are the determinantal varieties defined by the (reduced) ideals of minors of the generic matrix. The minimal free resolutions of these ideals … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2016-spring/ END:VEVENT END:VCALENDAR