BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Oana Veliche (Northeastern University) DTSTART:20200921T161500Z DTEND:20200921T171500Z DTSTAMP:20260404T094428Z UID:GASC/1 DESCRIPTION:Title: A classification of generic type 2 artinian rings\nby Oana Veliche (Northeastern University) as part of Geometry\, Algebra\, Singularities\, and Combinatorics\n\n\nAbstract\nThe commutative local rings are usually placed in the following hierarchy\, based on the character of their singu larity: regular\, hypersurface\, complete intersection\, and Gorenstein. T hese classes would be enough to describe all the rings of codepth 0 and 1. However\, a new class is needed to describe all the rings of codepth 2. T his is the class of Golod rings\; an example of such a ring is the quotien t of any local ring by the square of the maximal ideal. Such a classificat ion is still possible for all codepth 3 rings if one considers the multip licative structure of the Tor-algebra of the ring. The Golod rings are exa ctly the rings with trivial multiplication. \n\nIn a joint work with Lars W. Christensen we completely classify the Artinian compressed rings of typ e 2 of codepth 3 that are obtained from two compressed Gorenstein rings (r ings of type 1). We prove that the class of all generic Artinian rings of type 2 is exactly determined by only two easily computable numbers\, namel y the socle degrees of the two Gorenstein rings.\n LOCATION:https://stable.researchseminars.org/talk/GASC/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jai Laxmi (TIFR Mumbai) DTSTART:20201005T161500Z DTEND:20201005T171500Z DTSTAMP:20260404T094428Z UID:GASC/2 DESCRIPTION:Title: Embeddings of canonical modules\nby Jai Laxmi (TIFR Mumbai) as par t of Geometry\, Algebra\, Singularities\, and Combinatorics\n\nAbstract: T BA\n LOCATION:https://stable.researchseminars.org/talk/GASC/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nasrin Altafi (KTH Stockholm) DTSTART:20201019T161500Z DTEND:20201019T171500Z DTSTAMP:20260404T094428Z UID:GASC/3 DESCRIPTION:Title: Hilbert functions of Gorenstein algebras with Lefschetz properties\nby Nasrin Altafi (KTH Stockholm) as part of Geometry\, Algebra\, Singul arities\, and Combinatorics\n\n\nAbstract\nIn 1995 T. Harima characterized Hilbert functions of Artinian Gorenstein algebras with\nthe weak Lefschet z property and proved that they are\, in fact\, Stanley–Iarrobino (SI)-\ nsequences. In this talk\, I will generalize T. Harima’s result and prov e that SI-sequences\nclassify the Hilbert functions of Artinian Gorenstein algebras with the strong Lefschetz\nproperty. The proof uses the Hessian criterion by T. Maeno and J. Watanabe. Using this\ncriterion\, I will also provide classes of Artinian Gorenstein algebras of codimension three\nsat isfying the strong Lefschetz property.\n LOCATION:https://stable.researchseminars.org/talk/GASC/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Galetto (Cleveland State) DTSTART:20201026T161500Z DTEND:20201026T171500Z DTSTAMP:20260404T094428Z UID:GASC/4 DESCRIPTION:Title: Star configurations and symmetric shifted ideals\nby Federico Gale tto (Cleveland State) as part of Geometry\, Algebra\, Singularities\, and Combinatorics\n\n\nAbstract\nThe ideals of so-called star configurations h ave been studied in connection to commutative\nalgebra and combinatorics. The problem of describing the Betti numbers of the symbolic\npowers of the se ideals was recently settled. I will present a solution to this problem obtained\nin joint work with Biermann\, De Alba\, Murai\, Nagel\, O’Keef e\, R ̈omer\, and Seceleanu. Our\nresults rely on the natural action of a symmetric group to study a larger class of ideals that\nwe call ’symmet ric shifted ideals’.\n LOCATION:https://stable.researchseminars.org/talk/GASC/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Man-Wei Cheung (Harvard) DTSTART:20201123T171500Z DTEND:20201123T181500Z DTSTAMP:20260404T094428Z UID:GASC/5 DESCRIPTION:Title: Categorification of infinite Grassmannians\nby Man-Wei Cheung (Har vard) as part of Geometry\, Algebra\, Singularities\, and Combinatorics\n\ n\nAbstract\nJensen\, King\, and Su introduce the Grassmannian cluster cat egories. In the talk\, we will discuss the analogous of their construction to the Grassmannian of infinite rank. We show that there is a structure p reserving bijection between the generically free rank one modules in a Gra ssmannian category of infinite rank and the Plücker coordinates in a Gras smannian cluster algebra of infinite rank. We developed a new combinatoria l tool to determine when two k-subsets of integers are `non-crossing’\, i.e.\, when two Plücker coordinates of the Grassmannian cluster algebras of infinite rank are compatible. This is a joint work with Jenny August\, Eleonore Faber\, Sira Gratz\, and Sibylle Schroll.\n LOCATION:https://stable.researchseminars.org/talk/GASC/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Lei Yang (Northeastern University) DTSTART:20201102T171500Z DTEND:20201102T181500Z DTSTAMP:20260404T094428Z UID:GASC/6 DESCRIPTION:Title: Cox rings\, linear blow-ups and the generalized Nagata action\nby Lei Yang (Northeastern University) as part of Geometry\, Algebra\, Singula rities\, and Combinatorics\n\n\nAbstract\nNagata gave the first counterexa mple to Hilbert's 14th problem on the finite generation of invariant rings by actions of linear algebraic groups. His idea was to relate the ring of invariants to a Cox ring of a projective variety. Counterexamples of Naga ta's type include the cases where the group is $\\mathbb{G}_a^m$ for $m$ g reater than or equal to $3$. However\, for $m=2$\, the ring of invariants under the Nagata action is finitely generated. It is still an open problem whether counterexamples exist for $m=2$.\n\nIn this talk we consider a ge neralized version of Nagata's action by H. Naito. Mukai envisioned that th e ring of invariants in this case can still be related to a cox ring of ce rtain linear blow-ups of $\\mathbb{P}^n$. We show that when $m=2$\, the Co x rings of this type of linear blow-ups are still finitely generated\, and we can describe their generators. This answers the question by Mukai.\n LOCATION:https://stable.researchseminars.org/talk/GASC/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jurij Volčič (Texas A&M) DTSTART:20201116T171500Z DTEND:20201116T181500Z DTSTAMP:20260404T094428Z UID:GASC/7 DESCRIPTION:Title: Positive polynomials in matrix variables\nby Jurij Volčič (Texas A&M) as part of Geometry\, Algebra\, Singularities\, and Combinatorics\n\ n\nAbstract\nHilbert's 17th problem asked whether every positive polynomia l can be\nwritten as a quotient of sums of squares of polynomials. As many others\non Hilbert's famous list\, this problem and its affirmative resol ution by\nEmil Artin started a thriving mathematical discipline\, known as real\nalgebraic geometry. At its core\, it studies the interplay between\ npolynomial inequalities and positivity (geometry) and sums of squares\nce rtifying such positivity (algebra). Apart from its pure mathematics\nappea l\, this theory is the pillar of polynomial optimization\, since sums\nof squares can be efficiently traced via semidefinite programming.\n\nThis ta lk reviews old and new results on positivity of noncommutative\npolynomial s and their traces\, in terms of their matrix evaluations.\nThere are two natural setups to consider: positivity in matrix variables\nof a given fix ed size\, and positivity in matrix variables of arbitrary\nsize. This talk compares the sums-of-squares certificates of positivity\nacross these two setups\, their shortcomings and open ends.\n LOCATION:https://stable.researchseminars.org/talk/GASC/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Shijie Zhu (University of Iowa) DTSTART:20201207T171500Z DTEND:20201207T181500Z DTSTAMP:20260404T094428Z UID:GASC/8 DESCRIPTION:Title: Hopf algebras of discrete co-representation type\nby Shijie Zhu (U niversity of Iowa) as part of Geometry\, Algebra\, Singularities\, and Com binatorics\n\n\nAbstract\nHopf algebra is an important topic in geometric representation theory. A basic algebra is of finite representation type if there are only finitely many non-isomorphic indecomposable representation s. Basic Hopf algebras of finite representation type have been classified by Liu and Li in 2004. As algebras\, they are just copies of Nakayama alge bras. A pointed coalgebra is of discrete co-representation type\, if there are only finitely many non-isomorphic indecomposable co-representations f or each dimension vector. We are trying to classify pointed Hopf algebras of discrete co-representation type. We first classify their Ext-quivers a s coalgebras. Then we compute their algebra structures for each case. This is a joint work with Miodrag Iovanov\, Emre Sen and Alexander Sistko.\n LOCATION:https://stable.researchseminars.org/talk/GASC/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Keller VandeBogert (South Carolina) DTSTART:20201130T171500Z DTEND:20201130T181500Z DTSTAMP:20260404T094428Z UID:GASC/9 DESCRIPTION:Title: Grobner Bases and Linear Strands of Determinantal Facet Ideals\nby Keller VandeBogert (South Carolina) as part of Geometry\, Algebra\, Singu larities\, and Combinatorics\n\n\nAbstract\nDeterminantal facet ideals (DF I's) are a generalization of binomial edge ideals which were introduced by Ene\, Herzog\, Hibi\, and Mohammedi. The generating sets for such ideals come from matrix minors whose columns are parametrized by an associated si mplicial complex. In this talk\, we will discuss a generalized version of DFI's and give explicit conditions guaranteeing that the standard minimal generating set forms a reduced Grobner basis (with respect to the standard diagonal term order). Moreover\, we show that the linear strand of the in itial ideal may be obtained as a "sparse" generalized Eagon-Northcott comp lex\, which may then be used to verify a conjecture relating the graded Be tti numbers of a DFI to the graded Betti numbers of its initial ideal. Thi s is joint work with Ayah Almousa.\n LOCATION:https://stable.researchseminars.org/talk/GASC/9/ END:VEVENT END:VCALENDAR