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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:20240414T171416Z
UID:indico-contribution-4-68@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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SUMMARY:Tetrahedron maps and symmetries of 3D integrable discrete equation
s.
DTSTART;VALUE=DATE-TIME:20230619T093000Z
DTEND;VALUE=DATE-TIME:20230619T100000Z
DTSTAMP;VALUE=DATE-TIME:20240414T171416Z
UID:indico-contribution-4-70@cern.ch
DESCRIPTION:Speakers: Dr. TONGAS\, Anastasios (Department of Mathematics\,
University of Patras GR)\nI will discuss a connection between the tetrahe
dron equation for maps\nand the consistency property of integrable discret
e equations on\n$\\mathbb{Z}^3$. The connection is based on the invariants
of symmetry\ngroups of the lattice equations\, generalizing a method deve
loped in the\ncontext of Yang-Baxter maps. The method will be demonstrated
to certain\noctahedron type lattice equations\, leading to some new examp
les of\ntetrahedron maps and integrable coupled lattice equations.\n\nThe
talk is based on a joint work with Pavlos Kassotakis\, Maciej\nNieszporski
and Vassilis Papageorgiou.\n\nhttp://indico.fuw.edu.pl/contributionDispla
y.py?contribId=70&sessionId=4&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=70&sessionId
=4&confId=67
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SUMMARY:Towards a factorised solution of the Yang-Baxter equation with Uq(
sln) symmetry
DTSTART;VALUE=DATE-TIME:20230619T103000Z
DTEND;VALUE=DATE-TIME:20230619T110000Z
DTSTAMP;VALUE=DATE-TIME:20240414T171416Z
UID:indico-contribution-4-34@cern.ch
DESCRIPTION:Speakers: Mr. MORRIS\, Benjamin (University of Leeds)\nThe tal
k will discuss the emergence of factorised solutions of the Yang-Baxter eq
uation in terms of transposition operators acting in q-difference (differe
ntial) representations of the algebra Uq(sln) (U(sln))\, respectively. I w
ill focus on the q-deformed case\, where all but one of the transposition
operators are constructed explicitly and the proof of a crucial symmetric
group relation introduces a surprising terminating q-series identity relat
ing q-Lauricella series of differing rank. The inability to obtain an appr
opriate q-analogue of a known factorisation result for the U(sl_n) Lax ope
rator for n>3\, is discussed as an obstruction to finding the missing tran
sposition operator.\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?con
tribId=34&sessionId=4&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=34&sessionId
=4&confId=67
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