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SUMMARY:Oana Veliche (Northeastern University)
DTSTART;VALUE=DATE-TIME:20200921T161500Z
DTEND;VALUE=DATE-TIME:20200921T171500Z
DTSTAMP;VALUE=DATE-TIME:20201029T110532Z
UID:GASC/1
DESCRIPTION:Title: A classification of generic type 2 artinian rings\nby O
ana Veliche (Northeastern University) as part of Geometry\, Algebra\, Sing
ularities\, and Combinatorics\n\n\nAbstract\nThe commutative local rings a
re usually placed in the following hierarchy\, based on the character of
their singularity: regular\, hypersurface\, complete intersection\, and Go
renstein. These classes would be enough to describe all the rings of codep
th 0 and 1. However\, a new class is needed to describe all the rings of c
odepth 2. This is the class of Golod rings\; an example of such a ring is
the quotient of any local ring by the square of the maximal ideal. Such a
classification is still possible for all codepth 3 rings if one considers
the multiplicative structure of the Tor-algebra of the ring. The Golod ri
ngs are exactly the rings with trivial multiplication. \n\nIn a joint work
with Lars W. Christensen we completely classify the Artinian compressed r
ings of type 2 of codepth 3 that are obtained from two compressed Gorenste
in rings (rings of type 1). We prove that the class of all generic Artinia
n rings of type 2 is exactly determined by only two easily computable numb
ers\, namely the socle degrees of the two Gorenstein rings.\n
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BEGIN:VEVENT
SUMMARY:Jai Laxmi (TIFR Mumbai)
DTSTART;VALUE=DATE-TIME:20201005T161500Z
DTEND;VALUE=DATE-TIME:20201005T171500Z
DTSTAMP;VALUE=DATE-TIME:20201029T110532Z
UID:GASC/2
DESCRIPTION:Title: Embeddings of canonical modules\nby Jai Laxmi (TIFR Mum
bai) as part of Geometry\, Algebra\, Singularities\, and Combinatorics\n\n
Abstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nasrin Altafi (KTH Stockholm)
DTSTART;VALUE=DATE-TIME:20201019T161500Z
DTEND;VALUE=DATE-TIME:20201019T171500Z
DTSTAMP;VALUE=DATE-TIME:20201029T110532Z
UID:GASC/3
DESCRIPTION:Title: Hilbert functions of Gorenstein algebras with Lefschet
z properties\nby Nasrin Altafi (KTH Stockholm) as part of Geometry\, Algeb
ra\, Singularities\, and Combinatorics\n\n\nAbstract\nIn 1995 T. Harima ch
aracterized Hilbert functions of Artinian Gorenstein algebras with\nthe we
ak Lefschetz property and proved that they are\, in fact\, Stanley–Iarro
bino (SI)-\nsequences. In this talk\, I will generalize T. Harima’s resu
lt and prove that SI-sequences\nclassify the Hilbert functions of Artinian
Gorenstein algebras with the strong Lefschetz\nproperty. The proof uses t
he Hessian criterion by T. Maeno and J. Watanabe. Using this\ncriterion\,
I will also provide classes of Artinian Gorenstein algebras of codimension
three\nsatisfying the strong Lefschetz property.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Galetto (Cleveland State)
DTSTART;VALUE=DATE-TIME:20201026T161500Z
DTEND;VALUE=DATE-TIME:20201026T171500Z
DTSTAMP;VALUE=DATE-TIME:20201029T110532Z
UID:GASC/4
DESCRIPTION:Title: Star configurations and symmetric shifted ideals\nby Fe
derico Galetto (Cleveland State) as part of Geometry\, Algebra\, Singulari
ties\, and Combinatorics\n\n\nAbstract\nThe ideals of so-called star confi
gurations have been studied in connection to commutative\nalgebra and comb
inatorics. The problem of describing the Betti numbers of the symbolic\npo
wers of these ideals was recently settled. I will present a solution to th
is problem obtained\nin joint work with Biermann\, De Alba\, Murai\, Nagel
\, O’Keefe\, R ̈omer\, and Seceleanu. Our\nresults rely on the natural
action of a symmetric group to study a larger class of ideals that\nwe cal
l ’symmetric shifted ideals’.\n
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BEGIN:VEVENT
SUMMARY:Mandy Cheung (Harvard)
DTSTART;VALUE=DATE-TIME:20201123T171500Z
DTEND;VALUE=DATE-TIME:20201123T181500Z
DTSTAMP;VALUE=DATE-TIME:20201029T110532Z
UID:GASC/5
DESCRIPTION:by Mandy Cheung (Harvard) as part of Geometry\, Algebra\, Sing
ularities\, and Combinatorics\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Yang (Northeastern University)
DTSTART;VALUE=DATE-TIME:20201102T171500Z
DTEND;VALUE=DATE-TIME:20201102T181500Z
DTSTAMP;VALUE=DATE-TIME:20201029T110532Z
UID:GASC/6
DESCRIPTION:Title: Cox rings\, linear blow-ups and the generalized Nagata
action\nby Lei Yang (Northeastern University) as part of Geometry\, Algebr
a\, Singularities\, and Combinatorics\n\n\nAbstract\nNagata gave the first
counterexample to Hilbert's 14th problem on the finite generation of inva
riant rings by actions of linear algebraic groups. His idea was to relate
the ring of invariants to a Cox ring of a projective variety. Counterexamp
les of Nagata's type 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 the Nagata action is finitely generated. It is still an o
pen problem whether counterexamples exist for $m=2$.\n\nIn this talk we co
nsider a generalized version of Nagata's action by H. Naito. Mukai envisio
ned that the ring of invariants in this case can still be related to a cox
ring of certain linear 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 gene
rated\, and we can describe their generators. This answers the question by
Mukai.\n
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BEGIN:VEVENT
SUMMARY:Jurij Volčič (Texas A&M)
DTSTART;VALUE=DATE-TIME:20201116T171500Z
DTEND;VALUE=DATE-TIME:20201116T181500Z
DTSTAMP;VALUE=DATE-TIME:20201029T110532Z
UID:GASC/7
DESCRIPTION:by Jurij Volčič (Texas A&M) as part of Geometry\, Algebra\,
Singularities\, and Combinatorics\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Dufresne (York)
DTSTART;VALUE=DATE-TIME:20201207T171500Z
DTEND;VALUE=DATE-TIME:20201207T181500Z
DTSTAMP;VALUE=DATE-TIME:20201029T110532Z
UID:GASC/8
DESCRIPTION:by Emily Dufresne (York) as part of Geometry\, Algebra\, Singu
larities\, and Combinatorics\n\nAbstract: TBA\n
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