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 2017 X-WR-CALDESC:Commutative Algebra Seminar at University of Utah Mathematics Department X-WR-TIMEZONE:America/Denver BEGIN:VEVENT UID:20170901T143000-aaron-bertam@math.utah.edu DTSTART;TZID=America/Denver:20170901T143000 DTEND;TZID=America/Denver:20170901T153000 DTSTAMP:20260823T110330Z SUMMARY:Unstable syzygies DESCRIPTION:Speaker: Aaron Bertam\, University of Utah\n\nA stability condition gives a measure of the instability of a complex of vector bundles via its Harder-Narasimhan filtration. There is a canonical Euler stability condition on projective space that we can use in this way to measure the instability of free resolutions of Gorenstein rings. This has … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20170908T143000-pham-hung-quy@math.utah.edu DTSTART;TZID=America/Denver:20170908T143000 DTEND;TZID=America/Denver:20170908T153000 DTSTAMP:20260823T110330Z SUMMARY:Applications of filter regular sequences to some positive characteristic problems DESCRIPTION:Speaker: Pham Hung Quy\, FPT University, Vietnam\n\nWe use the notion of filter regular sequence to study some singularities and invariant defined by Frobenius action on local cohomology. LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20170915T143000-roger-wiegand@math.utah.edu DTSTART;TZID=America/Denver:20170915T143000 DTEND;TZID=America/Denver:20170915T153000 DTSTAMP:20260823T110330Z SUMMARY:Betti tables over short Gorenstein algebras DESCRIPTION:Speaker: Roger Wiegand\, University of Nebraska\n\nLet k be a field and R a short, standard-graded Gorenstein k-algebra with embedding dimension e > 2. (Thus the Hilbert series of R is 1+es+s^2 .) The category of finitely generated graded R-modules has wild representation type, but much of the representation theory of the category is revealed by the … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20170922T143000-henning-krause@math.utah.edu DTSTART;TZID=America/Denver:20170922T143000 DTEND;TZID=America/Denver:20170922T153000 DTSTAMP:20260823T110330Z SUMMARY:The what, where, and why of endofinite modules DESCRIPTION:Speaker: Henning Krause\, Bielefeld University, Germany\n\nThe notion of an endofinite module was introduced some 25 years ago by Crawley-Boevey. In my talk I'll explain what it is (a natural finiteness condition), where it comes from (representation theory of algebras), and why it is useful also in many other contexts (e.g. in homotopy theory or the study … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20171019T143000-jonathan-montano@math.utah.edu DTSTART;TZID=America/Denver:20171019T143000 DTEND;TZID=America/Denver:20171019T153000 DTSTAMP:20260823T110330Z SUMMARY:Local cohomology of powers of ideals and modules DESCRIPTION:Speaker: Jonathan Montano\, University of Kansas\n\nLet R be a Noetherian local ring of dimension d. In this work, our first goal is to study the behavior of the sequence of lengths of local cohomology modules of powers of ideals. For homogeneous ideals, we are able to show that after restricting the lower degrees to a linear bound, the sequence does … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20171020T143000-alex-tchernev@math.utah.edu DTSTART;TZID=America/Denver:20171020T143000 DTEND;TZID=America/Denver:20171020T153000 DTSTAMP:20260823T110330Z SUMMARY:Determinantal hypersurfaces and representations of Coxeter groups DESCRIPTION:Speaker: Alex Tchernev\, SUNY, Albany\n\nLet ( A_1, .... , A_m ) be a tuple of n by n matrices with complex coefficients. We consider the hypersurface in complex affine m-space given by the equation det( - I + x_1 A_1 + ... + x_m A_m ) = 0 where I is the identity matrix. Motivated by questions arising from functional analysis of operators … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20171103T143000-benjamin-briggs@math.utah.edu DTSTART;TZID=America/Denver:20171103T143000 DTEND;TZID=America/Denver:20171103T153000 DTSTAMP:20260823T110330Z SUMMARY:Long exact sequences for the homotopy Lie algebra and the L.S. category of a homomorphism DESCRIPTION:Speaker: Benjamin Briggs\, University of Toronto\n\nThe minimal model of a local map $\phi: R\ to S$ presents a graded Lie algebra $\pi^*(\phi)$, known as the homotopy Lie algebra of $\phi$. While $\pi^*(\phi)$ produces sensible results from the perspective of Koszul duality, it has poor formal properties. In particular, one would like a long exact … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20171103T143000-vincent-galinas@math.utah.edu DTSTART;TZID=America/Denver:20171103T143000 DTEND;TZID=America/Denver:20171103T153000 DTSTAMP:20260823T110330Z SUMMARY:The A-infinity structure on the Ext algebra of a commutative ring DESCRIPTION:Speaker: Vincent Galinas\, University of Toronto\n\nLet R be a Noetherian k-algebra, and for simplicity assume that R is augmented of finite type over k of characteristic zero. The minimal semifree model of R is given by the Chevalley-Eilenberg construction of a Lie(-infinity) coalgebra whose dual is the homotopy Lie algebra $\pi$ of R. Taking the … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20171110T143000-ilya-smirnov@math.utah.edu DTSTART;TZID=America/Denver:20171110T143000 DTEND;TZID=America/Denver:20171110T153000 DTSTAMP:20260823T110330Z SUMMARY:Lech's inequality and its improvements DESCRIPTION:Speaker: Ilya Smirnov\, University of Michigan\n\nIn 1960 Lech proved a simple inequality relating the multiplicity and the colength of an m-primary ideal in a local ring. His proof also shows that the inequality is never sharp if dimension is at least two. I will describe two possible ways to refine Lech's inequality and fix this problem. This is … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20171201T143000-jon-carlson@math.utah.edu DTSTART;TZID=America/Denver:20171201T143000 DTEND;TZID=America/Denver:20171201T153000 DTSTAMP:20260823T110330Z SUMMARY:p-Divisible Modules DESCRIPTION:Speaker: Jon Carlson\, University of Georgia, Athens\n\nAssume that G is a finite group and that k is a field of characteristic p. A p-divisible module is one whose absolutely indecomposable direct summands all have dimension divisible by p and whose support variety equals the full spectrum of the cohomology ring. These modules (tensor) generate the … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20171208T143000-dan-smolkin@math.utah.edu DTSTART;TZID=America/Denver:20171208T143000 DTEND;TZID=America/Denver:20171208T153000 DTSTAMP:20260823T110330Z SUMMARY:Cartier algebras, Subadditivity, and symbolic powers DESCRIPTION:Speaker: Dan Smolkin\, University of Utah\n\nIn 2000, Ein, Lazarsfeld, and Smith found a uniform bound for the size of symbolic powers of ideals in a regular ring. Their original proof, in characteristic zero, uses multiplier ideals, though the same proof works in positive characteristic using test ideals instead. The main reason for the … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT BEGIN:VEVENT UID:20171208T143000-lukas-katthaen@math.utah.edu DTSTART;TZID=America/Denver:20171208T143000 DTEND;TZID=America/Denver:20171208T153000 DTSTAMP:20260823T110330Z SUMMARY:Multiplicative structures on minimal free resolutions of monomial ideals DESCRIPTION:Speaker: Lukas Katthaen\, University of Minnesota\n\nThe minimal free resolution of a quotient of the polynomial ring admits a (generally non-associative) multiplication which satisfies the Leibniz rule. This multiplication is far from being unique and in favorable cases it can be chosen to be associative, which turns the resolution into a DGA. In … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2017-fall/ END:VEVENT END:VCALENDAR