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SUMMARY:Rob Silversmith (Northeastern)
DTSTART;VALUE=DATE-TIME:20200515T190000Z
DTEND;VALUE=DATE-TIME:20200515T200000Z
DTSTAMP;VALUE=DATE-TIME:20220128T014310Z
UID:agstanford/8
DESCRIPTION:Title: Studying subschemes of affine/projective space via matroids\nby Rob
Silversmith (Northeastern) as part of Stanford algebraic geometry seminar
\n\n\nAbstract\nGiven a homogeneous ideal $I$ in a polynomial ring\, one m
ay apply the following combinatorial operation: for each degree $d$\, make
a list of all subsets $S$ of the set of degree-$d$ monomials such that $S
$ is the set of nonzero coefficients of an element of $I$. For each $d$\,
this set of subsets is a combinatorial object called a matroid. As $d$ var
ies\, the resulting sequence of matroids is called the tropicalization of
$I$.\n\nI will discuss some of the many questions one can ask about tropic
alizations of ideals\, and how they are related to some classical question
s in combinatorial algebraic geometry\, such as the classification of toru
s orbits on Hilbert schemes of points in $\\mathbb{C}^2$. Some unexpected
combinatorial objects appear: e.g. when studying tropicalizations of subsc
hemes of $\\mathbb{P}^1$\, one is led to Schur polynomials and binary neck
laces.\n
LOCATION:https://researchseminars.org/talk/agstanford/8/
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