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 2022 X-WR-CALDESC:Commutative Algebra Seminar at University of Utah Mathematics Department X-WR-TIMEZONE:America/Denver BEGIN:VEVENT UID:20220204T140000-uli-walther@math.utah.edu DTSTART;TZID=America/Denver:20220204T140000 DTEND;TZID=America/Denver:20220204T150000 DTSTAMP:20260830T125228Z SUMMARY:Lyubeznik and Cech-de Rham numbers DESCRIPTION:Speaker: Uli Walther\, Purdue University\n\nIf Y is an affine variety inside CC^n cut out by the ideal I inside, and m a distinguished maximal ideal of, CC[x_1,...,x_n], one can attach two sets of numbers to them, either by applying the de Rham functor the D-module H^t_I(R), or the D-module restriction functor for the inclusion Spec(R/m)\into … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-spring/ END:VEVENT BEGIN:VEVENT UID:20220318T140000-swaraj-pande@math.utah.edu DTSTART;TZID=America/Denver:20220318T140000 DTEND;TZID=America/Denver:20220318T150000 DTSTAMP:20260830T125228Z SUMMARY:Multiplicities of Jumping Numbers DESCRIPTION:Speaker: Swaraj Pande\, University of Michigan\n\nMultiplier ideals are refined invariants of singularities of algebraic varieties. They give rise to other numerical invariants, for example, the log canonical threshold and more generally, jumping numbers. This talk is about another related invariant, namely multiplicities of jumping numbers. For an … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-spring/ END:VEVENT BEGIN:VEVENT UID:20220325T140000-kevin-tucker@math.utah.edu DTSTART;TZID=America/Denver:20220325T140000 DTEND;TZID=America/Denver:20220325T150000 DTSTAMP:20260830T125228Z SUMMARY:The Theory of F-rational Signature DESCRIPTION:Speaker: Kevin Tucker\, University of Illinois at Chicago\n\nThere are a number of invariants defined via Frobenius in the study of singularities in characteristic. One such is the F-signature, which can be viewed as a quantitative measure of F-regularity - an important class of singularities central to the celebrated theory of tight closure pioneered by … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-spring/ END:VEVENT BEGIN:VEVENT UID:20220401T140000-alapan-mukhopadhyay@math.utah.edu DTSTART;TZID=America/Denver:20220401T140000 DTEND;TZID=America/Denver:20220401T150000 DTSTAMP:20260830T125228Z SUMMARY:Frobenius-Poincare Function and Hilbert-Kunz Multiplicity DESCRIPTION:Speaker: Alapan Mukhopadhyay\, University of Michigan\n\nWe shall discuss a natural generalization of the classical Hilbert-Kunz multiplicity theory when the underlying objects are graded. More precisely, given a graded ring $R$ and a finite co-length homogeneous ideal $I$ in a positive characteristic $p$ and for any complex number $y$, we shall show that … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-spring/ END:VEVENT BEGIN:VEVENT UID:20220422T140000-thomas-polstra@math.utah.edu DTSTART;TZID=America/Denver:20220422T140000 DTEND;TZID=America/Denver:20220422T150000 DTSTAMP:20260830T125228Z SUMMARY:Inversion of Adjunction of F-purity DESCRIPTION:Speaker: Thomas Polstra\, University of Virginia\n\nCritical to the inductive treatment of the complex minimal model program are theorems which compare the singularities of a complex variety with the singularities of a codimension $1$ subvariety. Such theorems, when viewed through the lens of reduction to prime characteristic, produce conjectures on … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-spring/ END:VEVENT BEGIN:VEVENT UID:20220429T140000-kriti-goel@math.utah.edu DTSTART;TZID=America/Denver:20220429T140000 DTEND;TZID=America/Denver:20220429T150000 DTSTAMP:20260830T125228Z SUMMARY:Hilbert-Kunz multiplicity of powers of an ideal DESCRIPTION:Speaker: Kriti Goel\, University of Utah\n\nWe provide suitable conditions under which the asymptotic limit of the Hilbert-Samuel coefficients of the Frobenius powers of an $m$-primary ideal exists in a Noetherian local ring $(R,m)$ with prime characteristic $p>0.$ This, in turn, gives an expression of the Hilbert-Kunz multiplicity of powers … LOCATION:LCB 222 URL:http://math.utah.edu/caseminar/2022-spring/ END:VEVENT END:VCALENDAR