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UID:pretalx-juliacon-2026-SMBUHF@pretalx.com
DTSTART;TZID=CET:20260812T123000
DTEND;TZID=CET:20260812T130000
DESCRIPTION:Parametric polynomial systems can be represented as dominant ma
 ps between irreducible algebraic varieties of the same dimension\, where s
 ymmetries correspond to automorphisms of these maps. Galois\, or monodromy
 \, groups provide a numerical tool for detecting the existence of such sym
 metries in solution sets. A central computational challenge\, however\, is
  to recover explicit formulas for these automorphisms in order to better u
 nderstand and more efficiently solve the systems. We combine numerical hom
 otopy continuation with multivariate rational function interpolation to co
 mpute candidate symmetries\, implemented in the Julia package [Decomposing
 PolynomialSystems.jl](https://github.com/MultivariatePolynomialSystems/Dec
 omposingPolynomialSystems.jl).\n\nFor structured systems with many variabl
 es\, such as minimal problems in computer vision\, the resulting Vandermon
 de-like interpolation matrices become prohibitively large\, leading to exp
 ensive nullspace computations and numerical instability. We address this b
 y exploiting equivariance of minimal problems with respect to matrix Lie g
 roup actions. The interpolation space of bounded-degree polynomials decomp
 oses into isotypic components as a representation of the Lie symmetry grou
 p\, allowing a substantial reduction of the problem size. This representat
 ion-theoretic decomposition is implemented in the Julia package [Decomposi
 ngGroupRepresentations.jl](https://github.com/MultivariatePolynomialSystem
 s/DecomposingGroupRepresentations.jl). Together\, these tools provide a sc
 alable Julia-based framework that integrates monodromy and computational r
 epresentation theory to recover closed-form symmetries of polynomial syste
 ms.
DTSTAMP:20260502T093456Z
LOCATION:Room 6
SUMMARY:Using monodromy and representation theory to recover symmetries of 
 polynomial systems - Viktor Korotynskiy
URL:https://pretalx.com/juliacon-2026/talk/SMBUHF/
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