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SUMMARY:Entwinning Yang-Baxter maps and their extensions over Grassmann al
 gebras
DTSTART;VALUE=DATE-TIME:20230619T100000Z
DTEND;VALUE=DATE-TIME:20230619T103000Z
DTSTAMP;VALUE=DATE-TIME:20260914T051756Z
UID:indico-contribution-68@cern.ch
DESCRIPTION:Speakers: Dr. PAPAMIKOS\, Georgios (University of Essex)\nI wi
 ll present certain birational maps that are solutions of the parametric en
 twining\nYang-Baxter equation. These maps are obtained via the refactorisa
 tion problem of\ncertain Darboux transformations associated with the Lax o
 perators of certain soliton\nPDEs. I will also present various dynamical p
 roperties of the derived maps\, such\nas existence of invariants and assoc
 iated symplectic or Poisson structures\, and I will\nprove their complete 
 integrability in the Liouville sense\, where possible. Then I will\ndescri
 be the generalisation of such maps over Grassmann algebras using refactori
 sation\nof products of supermatrices\, i.e. Darboux transformations with b
 osonic and fermionic\nentries. I will use the analogue of the characterist
 ic polynomial\, which in this non-\ncommutative setting is the characteris
 tic function\, to define an analogue of a spectral\ncurve. The latter can 
 be used to obtain invariants of these maps involving Grassmann\nvariables.
  New higher dimensional commutative maps can be obtained fixing the or-\nd
 er of the Grassmann algebra Γ(n) and I will discuss integrability propert
 ies of these\nderived commutative maps.\n\nhttp://indico.fuw.edu.pl/contri
 butionDisplay.py?contribId=68&sessionId=4&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=68&sessionId
 =4&confId=67
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