67
Conferences
false
[["minutes", "Minutes"], ["notes", "Notes"], ["paper", "Paper"], ["poster", "Poster"], ["slides", "Slides"], ["summary", "Summary"]]
University of Warsaw
krolb@fuw.edu.pl
307
SIDE14@fuw.edu.pl,maciejun@fuw.edu.pl,aszer@fuw.edu.pl
SIDE 14.2
SIDE 14.2 is the fourteenth in a series of biennial conferences dedicated to Symmetries and
Integrability of Difference Equations, and in particular to: ordinary and partial difference equations,
analytic difference equations, orthogonal polynomials and special functions, symmetries and
reductions, discrete differential geometry, integrable discrete systems on graphs, integrable
dynamical mappings, (discrete) PainlevĂ© equations, integrability criteria, Yang-Baxter type
equations, cluster algebras, difference Galois theory, quantum mappings, quantum field theory on
space-time lattices, representation theory, combinatorics, numerical models of differential
equations, discrete stochastic models and other related topics.
False
Faculty of Physics, University of Warsaw
Pasteura 5, Warsaw
Lecture hall: 0.06
2023-06-19T08:00:00
2023-06-23T18:10:00
2022-10-24T15:25:45
2023-06-19T02:50:33
Europe/Warsaw
Faculty of Physics, University of Warsaw
maciejun@fuw.edu.pl
University of Warsaw
aszer@fuw.edu.pl
68
false
[["minutes", "Minutes"], ["notes", "Notes"], ["paper", "Paper"], ["poster", "Poster"], ["slides", "Slides"], ["summary", "Summary"]]
Entwinning Yang-Baxter maps and their extensions over Grassmann algebras
Dr.
University of Essex
g.papamikos@essex.ac.uk
Dr.
University of Essex
g.papamikos@essex.ac.uk
Faculty of Physics, University of Warsaw
Pasteura 5, Warsaw
Lecture hall: 0.06
2023-06-19T12:00:00
2023-06-19T12:30:00
00:30
I will present certain birational maps that are solutions of the parametric entwining
Yang-Baxter equation. These maps are obtained via the refactorisation problem of
certain Darboux transformations associated with the Lax operators of certain soliton
PDEs. I will also present various dynamical properties of the derived maps, such
as existence of invariants and associated symplectic or Poisson structures, and I will
prove their complete integrability in the Liouville sense, where possible. Then I will
describe the generalisation of such maps over Grassmann algebras using refactorisation
of products of supermatrices, i.e. Darboux transformations with bosonic and fermionic
entries. I will use the analogue of the characteristic polynomial, which in this non-
commutative setting is the characteristic function, to define an analogue of a spectral
curve. The latter can be used to obtain invariants of these maps involving Grassmann
variables. New higher dimensional commutative maps can be obtained fixing the or-
der of the Grassmann algebra Î“(n) and I will discuss integrability properties of these
derived commutative maps.