BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sean Sather-Wagstaff (Clemson University) DTSTART:20200502T160000Z DTEND:20200502T162000Z DTSTAMP:20260417T032147Z UID:DG_methods/1 DESCRIPTION:Title: Ascent of test modules\nby Sean Sather-Wagstaff (Clemson University ) as part of DG methods in commutative algebra and representation theory\n \n\nAbstract\nWe investigate modules for which vanishing of Tor-modules im plies finiteness of projective dimension. In particular\, we answer a ques tion of O. Celikbas and Sather-Wagstaff about ascent properties of such mo dules over residually algebraic flat local ring homomorphisms. To accompli sh this\, we consider ascent and descent properties over local ring homomo rphisms of finite flat dimension\, and for flat extensions of finite dimen sional differential graded algebras.\n LOCATION:https://researchseminars.org/talk/DG_methods/1/ END:VEVENT BEGIN:VEVENT SUMMARY:David Jorgensen (University of Texas Arlington) DTSTART:20200502T163000Z DTEND:20200502T165000Z DTSTAMP:20260417T032147Z UID:DG_methods/2 DESCRIPTION:Title: Asymptotic behavior of Ext over graded complete intersections - with Li ana Sega and Peder Thompson\nby David Jorgensen (University of Texas A rlington) as part of DG methods in commutative algebra and representation theory\n\n\nAbstract\nIt is well known that for a pair of modules over a c omplete intersection\, when all higher Ext modules have finite length\, th en the lengths of these higher Ext modules grow polynomially. In fact\, th e lengths are determined by two polynomials\, one giving the lengths of th e even Ext\, and one giving the lengths of the odd Ext. In this talk we wi ll discuss conditions when these two polynomials have the same leading coe fficient. This is equivalent to the vanishing of the Herbrand difference\, or Hochster’s Theta invariant\, a phenomenon studied by several authors in recent papers.\n LOCATION:https://researchseminars.org/talk/DG_methods/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Packauskas (SUNY Cortland) DTSTART:20200502T170000Z DTEND:20200502T172000Z DTSTAMP:20260417T032147Z UID:DG_methods/3 DESCRIPTION:Title: Quasi-polynomial growth of Betti sequences - with Luchezar Avramov and Nicholas Packauskas\nby Nicholas Packauskas (SUNY Cortland) as part of DG methods in commutative algebra and representation theory\n\n\nAbstract \nLet Q be a regular local ring and I an ideal generated by a regular sequ ence of c elements in the square of the maximal ideal. It is known that ov er the complete intersection R = Q/I that any finitely generated module M has Betti numbers eventually given by quasi-polynomial of degree less than c. That is\, there are integer-valued polynomial functions p M + and p M − with the same leading term such that β R 2i (M) = p M + (2i) and β R 2i+1(M) = p M − (2i + 1) for i sufficiently large. We will show that if q is the height of the ideal generated by the quadratic initial forms of I in the associated graded ring of Q\, then the degree of p M + − p M − is less than c − q − 1.\n LOCATION:https://researchseminars.org/talk/DG_methods/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Luigi Ferraro (Wake Forest University) DTSTART:20200502T173000Z DTEND:20200502T175000Z DTSTAMP:20260417T032147Z UID:DG_methods/4 DESCRIPTION:Title: The taylor resolution over a skew polynomial ring - with Frank Moore an d Desiree Martin\nby Luigi Ferraro (Wake Forest University) as part of DG methods in commutative algebra and representation theory\n\n\nAbstract \nLet I be a monomial ideal in the polynomial ring R = k[x1\, . . . \, xn] over a field k. In her thesis\, Taylor introduced a complex which provide s a multi-graded free resolution for R/I as an R-module. Later\, Gemeda pr ovided a differential graded structure on this complex while Avramov showe d that this DG algebra admits a divided power structure. We generalize the se results to monomial ideals J in a skew polynomial ring S. As an applica tion we show that if one fixes the number of generators of the ideal J\, t hen there are finitely many isomorphism classes for π ≥2 (S/J)\, where π(S/J) is the homotopy color Lie algebra of S/J\, an invariant which was introduced and studied by the first and last author in a different work. A s a result it follows that there are finitely many possibilities for the P oincar´e series of k over S/J\, if the number of generators of J is fixed .\n LOCATION:https://researchseminars.org/talk/DG_methods/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Pablo Ocal (Texas A&M University) DTSTART:20200502T180000Z DTEND:20200502T182000Z DTSTAMP:20260417T032147Z UID:DG_methods/5 DESCRIPTION:Title: On the Gerstenhaber bracket in relative Hochschild cohomology of associ ative algebras\nby Pablo Ocal (Texas A&M University) as part of DG met hods in commutative algebra and representation theory\n\n\nAbstract\nWe wi ll begin by briefly presenting the inception of the Gerstenhaber bracket i n Hochschild cohomology\, which helped in capturing in an algebraic way th e infinitesimal information stored in the cohomology of the algebra. On th e first uses of the bracket by Gerstenhaber and Schack\, they essentially claimed that everything that can be done on Hochschild cohomology can also be done in relative Hochschild cohomology. However\, they required a sepa rability condition to obtain relative projective resolutions when working with diagrams of algebras. This additional requirement motivates contextua lizing our work to relative homological algebra. This is a less general co ntext but it has multiple advantages: we can remove the separability condi tion\, proofs are approachable\, computations can be carried out\, and an there is an interpretation of the bracket as a dg Lie algebra structure on a complex. We will also comment on recent results by Kaygun\, who constru cted a Jacobi-Zariski long exact sequence\, and by Cibils\, Lanzilotta\, M arcos\, Schroll\, and Solotar\, who described aspects of the Hochschild co homology of bounded quiver algebras using relative cohomological tools. Th is strongly suggests that this context may be adequate for a better unders tanding of the cohomology of associative algebras.\n LOCATION:https://researchseminars.org/talk/DG_methods/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Cris Negron (University of North Carolina) DTSTART:20200502T200000Z DTEND:20200502T202000Z DTSTAMP:20260417T032147Z UID:DG_methods/6 DESCRIPTION:Title: Support data for Hopf algebras via noncommutative hypersurfaces - with Julia Pevtsova\nby Cris Negron (University of North Carolina) as part of DG methods in commutative algebra and representation theory\n\n\nAbstra ct\nIn recent work with J. Pevtsova\, we develop an approach to support th eory for Hopf algebras via noncommutative hypersurfaces. As a starting poi nt\, one considers a Hopf algebra u which admits a smooth deformation U → u by a Noetherian Hopf algebra U of finite global dimension. One uses this deformation to produce a rank variety for u which takes values in an associated projective space. Our work is inspired by earlier contributions of Avramov and Buchweitz\, which concerned support for (commutative) loca l complete intersections. I will discuss some modular examples\, functions on finite group schemes and Drinfeld doubles of infinitesimal group schem es\, and also quantum groups over the complexes. I will discuss how one ca n use this hypersurface approach to address the tensor product property in certain “solvable” examples.\n LOCATION:https://researchseminars.org/talk/DG_methods/6/ END:VEVENT BEGIN:VEVENT SUMMARY:John Myers (SUNY Oswego) DTSTART:20200502T203000Z DTEND:20200502T205000Z DTSTAMP:20260417T032147Z UID:DG_methods/7 DESCRIPTION:Title: Three algebras and three definitions of Koszulness\nby John Myers ( SUNY Oswego) as part of DG methods in commutative algebra and representati on theory\n\n\nAbstract\nLet $R$ be a standard graded commutative algebra over a field $k$\, let $K$ be the Koszul complex on a minimal set of gener ators of the irrelevant ideal of $R$\, and let $H$ be the homology of $K$. Recall that $R$ is said to be \\textit{Koszul} if $k$ has a linear free r esolution over $R$. We adapt this definition to apply to $K$ (viewed as a DG algebra) and then to $H$ (viewed as a bigraded algebra). We describe ho w these three Koszul properties transfer back and forth between the three algebras $R$\, $K$\, and $H$\, and we give several examples of classes of algebras $R$ for which $H$ is Koszul.\n LOCATION:https://researchseminars.org/talk/DG_methods/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Walker (University of Nebraska-Lincoln) DTSTART:20200502T210000Z DTEND:20200502T212000Z DTSTAMP:20260417T032147Z UID:DG_methods/8 DESCRIPTION:Title: Lower bounds on the homology of dg-modules over exterior algebras\n by Mark Walker (University of Nebraska-Lincoln) as part of DG methods in c ommutative algebra and representation theory\n\n\nAbstract\nLet E be an ex terior algebra with n generators over a field\, and let P be a perfect dg- E-module that is not acyclic. In this talk I will discuss what is known ab out the smallest possible value of the dimension of the homology of P.\n LOCATION:https://researchseminars.org/talk/DG_methods/8/ END:VEVENT BEGIN:VEVENT SUMMARY:James Cameron (UCLA) DTSTART:20200502T213000Z DTEND:20200502T215000Z DTSTAMP:20260417T032147Z UID:DG_methods/9 DESCRIPTION:Title: Stratification for cochain algebras on Borel constructions of G-spaces< /a>\nby James Cameron (UCLA) as part of DG methods in commutative algebra and representation theory\n\n\nAbstract\nFor G a compact Lie group and X a finite G-CW complex I will discuss how the the Borel equivariant cohomolo gy ring of X with Fp coefficients controls the structure of the derived ca tegory of the cochain algebra of the Borel construction on X.\nI will also indicate how generalizing from finite groups to compact Lie groups and G- spaces allows one to study some of the categories that appear in modular r epresentation theory via categories that have structure that doesn’t app ear at the purely algebraic level.\n LOCATION:https://researchseminars.org/talk/DG_methods/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Pevtsova (University of Washington) DTSTART:20200502T220000Z DTEND:20200502T222000Z DTSTAMP:20260417T032147Z UID:DG_methods/10 DESCRIPTION:Title: Support theory for Elementary supergroups - with Dave Benson\, Srikant h Iyengar and Henning Krause\nby Julia Pevtsova (University of Washing ton) as part of DG methods in commutative algebra and representation theor y\n\n\nAbstract\nElementary supergroup schemes arise as a detecting family in the theory of supports for finite supergroup schemes. As such\, they p lay a similar role to finite supergroup schemes as elementary abelian p-gr oups play for finite groups\, as known from the classical work of Quillen and Chouinard. In this talk I’ll describe the theory of varieties\, the calculation of the Balmer spectrum and the Benson-Iyengar-Krause stratific ation for the singularity category of an elementary supergroup scheme. An interesting and novel feature of the theory is that it combines the π-poi nt approach of Friedlander-Pevtsova with the hypersurface approach of Avra mov-Iyengar as an attempt to construct Carlson’s rank varieties in the s uper context.\n LOCATION:https://researchseminars.org/talk/DG_methods/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Hamid Rahmati (University of Nebraska-Lincoln) DTSTART:20200503T163000Z DTEND:20200503T165000Z DTSTAMP:20260417T032147Z UID:DG_methods/11 DESCRIPTION:Title: Transferring algebra structures on complexes\, part 1 - with Claudia M iller\nby Hamid Rahmati (University of Nebraska-Lincoln) as part of DG methods in commutative algebra and representation theory\n\n\nAbstract\nW e discuss a homological method for transferring algebra structures on comp lexes along suitably nice homotopy equivalences. We also show how one can get such homotopy equivalencies\, from old ones\, using a homological tool called the perturbation lemma.\n LOCATION:https://researchseminars.org/talk/DG_methods/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Miller (Syracuse University) DTSTART:20200503T170000Z DTEND:20200503T172000Z DTSTAMP:20260417T032147Z UID:DG_methods/12 DESCRIPTION:Title: Transferring algebra structures on complexes\, part 2 - with Hamid Rah mati\nby Claudia Miller (Syracuse University) as part of DG methods in commutative algebra and representation theory\n\n\nAbstract\nWe discuss h ow to use the homotopy on the tautological Koszul complex given by the wei ghted de Rham map to build a concrete permutation invariant dg-algebra str ucture on a well-known resolution.\n LOCATION:https://researchseminars.org/talk/DG_methods/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Mohsen Gheibi (University of Texas at Arlington) DTSTART:20200503T173000Z DTEND:20200503T175000Z DTSTAMP:20260417T032147Z UID:DG_methods/13 DESCRIPTION:Title: Quasi-projective dimension - with David A. Jorgensen and Ryo Takahashi \nby Mohsen Gheibi (University of Texas at Arlington) as part of DG me thods in commutative algebra and representation theory\n\n\nAbstract\nIn t his talk\, I will introduce a homological invariant namely quasi-projectiv e dimension\, which is a generalization of the projective dimension. I wil l discuss the basic properties of the quasi-projective dimension and compa re it with other homological dimensions. In particular\, I will show that the modules with finite quasi-projective dimension\, in many cases\, behav e similarly as modules of finite complete intersection dimension. I also w ill address some open problems about the quasi-projective dimension.\n LOCATION:https://researchseminars.org/talk/DG_methods/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Diethorn (University of Utah) DTSTART:20200503T180000Z DTEND:20200503T182000Z DTSTAMP:20260417T032147Z UID:DG_methods/14 DESCRIPTION:Title: Generators of Koszul homology\nby Rachel Diethorn (University of U tah) as part of DG methods in commutative algebra and representation theor y\n\n\nAbstract\nOne approach to understanding Koszul homology is to find the generators. In the first part of this talk\, I will provide explicit f ormulas for the generators of Koszul homology on the minimal generators of an ideal J with coefficients in what we call a J-closed module. This gene ralizes work of Herzog and of Corso\, Goto\, Huneke\, Polini\, and Ulrich. In the second part of the talk I will demonstrate the utility of such for mulas. In particular\, I will discuss an application to the Koszul homolog y algebra of quotients by certain edge ideals\, and I will give an answer\ , for such rings\, to a question of Avramov about the Koszul homology alge bra of a Koszul algebra.\n LOCATION:https://researchseminars.org/talk/DG_methods/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugh Roberts Geller (Clemson University) DTSTART:20200503T200000Z DTEND:20200503T202000Z DTSTAMP:20260417T032147Z UID:DG_methods/15 DESCRIPTION:Title: DG-structures for fiber products\nby Hugh Roberts Geller (Clemson University) as part of DG methods in commutative algebra and representatio n theory\n\n\nAbstract\nA construction of Tate shows that every algebra ov er a ring R possess a DG-algebra resolution over R. These resolutions are not always minimal and Avramov even shows that certain algebras cannot hav e a minimal resolution with a DG-algebra structure. This talk gives an exp licit construction of a DG-structure for certain fiber products and criter ia for determining when the structure is a DG-module\, DG-algebra\, or min imal DG-algebra.\n LOCATION:https://researchseminars.org/talk/DG_methods/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Pinches Dirnfeld (University of Utah) DTSTART:20200503T203000Z DTEND:20200503T205000Z DTSTAMP:20260417T032147Z UID:DG_methods/16 DESCRIPTION:Title: Base change along the Frobenius endomorphism and the Gorenstein proper ty\nby Pinches Dirnfeld (University of Utah) as part of DG methods in commutative algebra and representation theory\n\n\nAbstract\nLet R be a lo cal ring of positive characteristic and X a complex with nonzero finitely generated homology and finite injective dimension. We prove that if derive d base change of X via the Frobenius (or more generally\, via a contractin g) endomorphism has finite injective dimension then R is Gorenstein.\n LOCATION:https://researchseminars.org/talk/DG_methods/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Lars Winther Christensen (Texas Tech University) DTSTART:20200503T210000Z DTEND:20200503T212000Z DTSTAMP:20260417T032147Z UID:DG_methods/17 DESCRIPTION:Title: Dimension and codimension of homologically finite complexes - with Iye ngar\nby Lars Winther Christensen (Texas Tech University) as part of D G methods in commutative algebra and representation theory\n\n\nAbstract\n In local algebra\, the quotient of the bounded derived category by the sub category of perfect complexes is often referred to as the singularity cate gory. The quotient is trivial for a regular local ring\, and for a Gorenst ein ring it is triangulated equivalent the stable category of Gorenstein p rojective modules or\, if one prefers that point of view\, to the homotopy category of totally acyclic complexes of projective modules. I will discu ss an ongoing project in which we extend these ideas to sheaves and reconc ile them with other categorical measures of the Gorenstein property.\n LOCATION:https://researchseminars.org/talk/DG_methods/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Liana Şega (University of Missouri) DTSTART:20200503T213000Z DTEND:20200503T215000Z DTSTAMP:20260417T032147Z UID:DG_methods/18 DESCRIPTION:Title: Free resolutions over compressed artinian level algebras of socle degr ee three - with Rasoul Ahangari Maleki\nby Liana Şega (University of Missouri) as part of DG methods in commutative algebra and representation theory\n\n\nAbstract\nWe will discuss rationality of Poincar´e series and linearity of free resolutions in the case of compressed artinian level al gebras of socle degree three.\n LOCATION:https://researchseminars.org/talk/DG_methods/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Tamaroff (Trinity College Dublin) DTSTART:20200503T160000Z DTEND:20200503T162000Z DTSTAMP:20260417T032147Z UID:DG_methods/19 DESCRIPTION:Title: The non-commutative calculus of fields and forms through dg-resolution s\nby Pedro Tamaroff (Trinity College Dublin) as part of DG methods in commutative algebra and representation theory\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DG_methods/19/ END:VEVENT END:VCALENDAR