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SUMMARY:Rank-stability of polynomial equations - Tomer Bauer (Bar-Ilan Uni
 versity)
DTSTART:20251128T114500Z
DTEND:20251128T124500Z
UID:TALK240640@talks.cam.ac.uk
DESCRIPTION:Ulam's stability problem asks if every "almost" solution of an
  equation (i.e. an approximate solution with respect to some metric) is "c
 lose" to an exact solution. Extending the thoroughly studied theory of gro
 up stability\, we study Ulam stability type problems for associative and L
 ie algebras. Namely\, we investigate obstacles to rank-approximation of ma
 trix "almost" solutions by exact solutions for systems of non-commutative 
 polynomial equations.\nThis leads to a rich theory of stable associative a
 nd Lie algebras\, with connections to linear soficity\, amenability\, grow
 th\, and group stability. We develop rank-stability and instability criter
 ia\, examine the effect of algebraic constructions on rank-stability\, and
  prove that while finite-dimensional associative algebras are rank-stable\
 , "most" finite-dimensional Lie algebras are not.\nJoint work with Guy Bla
 char and Be'eri Greenfeld.
LOCATION:Seminar Room 1\, Newton Institute
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