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:20260422T212604Z UID:GASC/1 DESCRIPTION:Title: A c lassification of generic type 2 artinian rings\nby Oana Veliche (North eastern University) as part of Geometry\, Algebra\, Singularities\, and Co mbinatorics\n\n\nAbstract\nThe commutative local rings are usually placed in the following hierarchy\, based on the character of their singularity: regular\, hypersurface\, complete intersection\, and Gorenstein. These cl asses would be enough to describe all the rings of codepth 0 and 1. Howeve r\, a new class is needed to describe all the rings of codepth 2. This is the class of Golod rings\; an example of such a ring is the quotient of an y local ring by the square of the maximal ideal. Such a classification is still possible for all codepth 3 rings if one considers the multiplicativ e structure of the Tor-algebra of the ring. The Golod rings are exactly th e rings with trivial multiplication. \n\nIn a joint work with Lars W. Chri stensen we completely classify the Artinian compressed rings of type 2 of codepth 3 that are obtained from two compressed Gorenstein rings (rings 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\, namely the s ocle degrees of the two Gorenstein rings.\n LOCATION:https://researchseminars.org/talk/GASC/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jai Laxmi (TIFR Mumbai) DTSTART:20201005T161500Z DTEND:20201005T171500Z DTSTAMP:20260422T212604Z UID:GASC/2 DESCRIPTION:Title: Emb eddings of canonical modules\nby Jai Laxmi (TIFR Mumbai) as part of Ge ometry\, Algebra\, Singularities\, and Combinatorics\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GASC/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nasrin Altafi (KTH Stockholm) DTSTART:20201019T161500Z DTEND:20201019T171500Z DTSTAMP:20260422T212604Z UID:GASC/3 DESCRIPTION:Title: Hil bert functions of Gorenstein algebras with Lefschetz properties\nby N asrin Altafi (KTH Stockholm) as part of Geometry\, Algebra\, Singularities \, and Combinatorics\n\n\nAbstract\nIn 1995 T. Harima characterized Hilber t functions of Artinian Gorenstein algebras with\nthe weak Lefschetz prope rty and proved that they are\, in fact\, Stanley–Iarrobino (SI)-\nsequen ces. In this talk\, I will generalize T. Harima’s result and prove that SI-sequences\nclassify the Hilbert functions of Artinian Gorenstein algebr as with the strong Lefschetz\nproperty. The proof uses the Hessian criteri on by T. Maeno and J. Watanabe. Using this\ncriterion\, I will also provid e classes of Artinian Gorenstein algebras of codimension three\nsatisfying the strong Lefschetz property.\n LOCATION:https://researchseminars.org/talk/GASC/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Galetto (Cleveland State) DTSTART:20201026T161500Z DTEND:20201026T171500Z DTSTAMP:20260422T212604Z UID:GASC/4 DESCRIPTION:Title: Sta r configurations and symmetric shifted ideals\nby Federico Galetto (Cl eveland State) as part of Geometry\, Algebra\, Singularities\, and Combina torics\n\n\nAbstract\nThe ideals of so-called star configurations have bee n studied in connection to commutative\nalgebra and combinatorics. The pro blem of describing the Betti numbers of the symbolic\npowers of these idea ls was recently settled. I will present a solution to this problem obtaine d\nin joint work with Biermann\, De Alba\, Murai\, Nagel\, O’Keefe\, R ̈omer\, and Seceleanu. Our\nresults rely on the natural action of a symme tric group to study a larger class of ideals that\nwe call ’symmetric sh ifted ideals’.\n LOCATION:https://researchseminars.org/talk/GASC/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Man-Wei Cheung (Harvard) DTSTART:20201123T171500Z DTEND:20201123T181500Z DTSTAMP:20260422T212604Z UID:GASC/5 DESCRIPTION:Title: Cat egorification of infinite Grassmannians\nby Man-Wei Cheung (Harvard) a s part of Geometry\, Algebra\, Singularities\, and Combinatorics\n\n\nAbst ract\nJensen\, King\, and Su introduce the Grassmannian cluster categories . In the talk\, we will discuss the analogous of their construction to the Grassmannian of infinite rank. We show that there is a structure preservi ng bijection between the generically free rank one modules in a Grassmanni an category of infinite rank and the Plücker coordinates in a Grassmannia n cluster algebra of infinite rank. We developed a new combinatorial tool to determine when two k-subsets of integers are `non-crossing’\, i.e.\, when two Plücker coordinates of the Grassmannian cluster algebras of infi nite rank are compatible. This is a joint work with Jenny August\, Eleonor e Faber\, Sira Gratz\, and Sibylle Schroll.\n LOCATION:https://researchseminars.org/talk/GASC/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Lei Yang (Northeastern University) DTSTART:20201102T171500Z DTEND:20201102T181500Z DTSTAMP:20260422T212604Z UID:GASC/6 DESCRIPTION:Title: Cox rings\, linear blow-ups and the generalized Nagata action\nby Lei Yan g (Northeastern University) as part of Geometry\, Algebra\, Singularities\ , and Combinatorics\n\n\nAbstract\nNagata gave the first counterexample to Hilbert's 14th problem on the finite generation of invariant rings by act ions of linear algebraic groups. His idea was to relate the ring of invari ants to a Cox ring of a projective variety. Counterexamples of Nagata's ty pe include the cases where the group is $\\mathbb{G}_a^m$ for $m$ greater than or equal to $3$. However\, for $m=2$\, the ring of invariants under t he Nagata action is finitely generated. It is still an open problem whethe r counterexamples exist for $m=2$.\n\nIn this talk we consider a generaliz ed version of Nagata's action by H. Naito. Mukai envisioned that the ring of invariants in this case can still be related to a cox ring of certain l inear blow-ups of $\\mathbb{P}^n$. We show that when $m=2$\, the Cox 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://researchseminars.org/talk/GASC/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jurij Volčič (Texas A&M) DTSTART:20201116T171500Z DTEND:20201116T181500Z DTSTAMP:20260422T212604Z UID:GASC/7 DESCRIPTION:Title: Pos itive polynomials in matrix variables\nby Jurij Volčič (Texas A&M) a s part of Geometry\, Algebra\, Singularities\, and Combinatorics\n\n\nAbst ract\nHilbert's 17th problem asked whether every positive polynomial can b e\nwritten as a quotient of sums of squares of polynomials. As many others \non Hilbert's famous list\, this problem and its affirmative resolution b y\nEmil Artin started a thriving mathematical discipline\, known as real\n algebraic geometry. At its core\, it studies the interplay between\npolyno mial inequalities and positivity (geometry) and sums of squares\ncertifyin g such positivity (algebra). Apart from its pure mathematics\nappeal\, thi s theory is the pillar of polynomial optimization\, since sums\nof squares can be efficiently traced via semidefinite programming.\n\nThis talk revi ews old and new results on positivity of noncommutative\npolynomials and t heir traces\, in terms of their matrix evaluations.\nThere are two natural setups to consider: positivity in matrix variables\nof a given fixed size \, and positivity in matrix variables of arbitrary\nsize. This talk compar es the sums-of-squares certificates of positivity\nacross these two setups \, their shortcomings and open ends.\n LOCATION:https://researchseminars.org/talk/GASC/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Shijie Zhu (University of Iowa) DTSTART:20201207T171500Z DTEND:20201207T181500Z DTSTAMP:20260422T212604Z UID:GASC/8 DESCRIPTION:Title: Hop f algebras of discrete co-representation type\nby Shijie Zhu (Universi ty of Iowa) as part of Geometry\, Algebra\, Singularities\, and Combinator ics\n\n\nAbstract\nHopf algebra is an important topic in geometric represe ntation theory. A basic algebra is of finite representation type if there are only finitely many non-isomorphic indecomposable representations. Basi c Hopf algebras of finite representation type have been classified by Liu and Li in 2004. As algebras\, they are just copies of Nakayama algebras. A pointed coalgebra is of discrete co-representation type\, if there are on ly finitely many non-isomorphic indecomposable co-representations for each dimension vector. We are trying to classify pointed Hopf algebras of dis crete co-representation type. We first classify their Ext-quivers as coalg ebras. Then we compute their algebra structures for each case. This is a j oint work with Miodrag Iovanov\, Emre Sen and Alexander Sistko.\n LOCATION:https://researchseminars.org/talk/GASC/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Keller VandeBogert (South Carolina) DTSTART:20201130T171500Z DTEND:20201130T181500Z DTSTAMP:20260422T212604Z UID:GASC/9 DESCRIPTION:Title: Gro bner Bases and Linear Strands of Determinantal Facet Ideals\nby Keller VandeBogert (South Carolina) as part of Geometry\, Algebra\, Singularitie s\, and Combinatorics\n\n\nAbstract\nDeterminantal facet ideals (DFI's) ar e a generalization of binomial edge ideals which were introduced by Ene\, Herzog\, Hibi\, and Mohammedi. The generating sets for such ideals come fr om matrix minors whose columns are parametrized by an associated simplicia l complex. In this talk\, we will discuss a generalized version of DFI's a nd give explicit conditions guaranteeing that the standard minimal generat ing set forms a reduced Grobner basis (with respect to the standard diagon al term order). Moreover\, we show that the linear strand of the initial i deal may be obtained as a "sparse" generalized Eagon-Northcott complex\, w hich may then be used to verify a conjecture relating the graded Betti num bers of a DFI to the graded Betti numbers of its initial ideal. This is jo int work with Ayah Almousa.\n LOCATION:https://researchseminars.org/talk/GASC/9/ END:VEVENT END:VCALENDAR