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SUMMARY:Cristhian Garay López (CIMAT (Guanajuato))
DTSTART:20230602T140000Z
DTEND:20230602T150000Z
DTSTAMP:20260423T052334Z
UID:LAGARTOS/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGARTOS/60/
 ">Infinite matroids in tropical differential algebra</a>\nby Cristhian Gar
 ay López (CIMAT (Guanajuato)) as part of (LAGARTOS) Latin American Real a
 nd Tropical Geometry Seminar\n\n\nAbstract\nGiven a  set $\\Sigma\\subset 
 K[x_1\,\\ldots\,x_n]$ of homogeneous linear polynomials\,  a classical res
 ult in tropical algebraic geometry states that the tropicalization (with r
 espect to the trivial valuation) of the corresponding variety $V(\\Sigma)\
 \subset K^n$  is a fan $B(V(\\Sigma))\\subset(\\mathbb{R}\\cup\\{-\\infty\
 \})^n$ that depends only on the matroid over the set of labels $E=[n]$ ass
 ociated to the ideal $(\\Sigma)$. Moreover\, this set is tropically convex
  in the sense that it is  closed  under  tropical  linear  combinations. \
 n\n\nWe discuss an analogue of this result in the context of tropical diff
 erential algebraic geometry\, namely\,  if $\\Sigma\\subset K[\\![t_1\,\\l
 dots\,t_m]\\!][x_{1\,J}\,\\ldots\,x_{n\,J}\\::\\:J\\in\\mathbb{N}^m]$ is c
 ertain type of set of homogeneous linear differential polynomials with coe
 fficients in $K[\\![t_1\,\\ldots\,t_m]\\!]$\, then the tropicalization (wi
 th respect to the trivial valuation) of the set of formal solutions $Sol(\
 \Sigma)\\subset K[\\![t_1\,\\ldots\,t_m]\\!]^n$  is  a  matroid $B(Sol(\\S
 igma))$ over the set of labels $E=\\mathbb{N}^{mn}$\, where  $m\,n$ are po
 sitive integers. Moreover\, this set is tropically convex in the sense tha
 t it is  closed  under  boolean  linear  combinations\, i.e.\, it is a com
 mutative and idempotent monoid.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/60/
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