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SUMMARY:Integrable boundary conditions for quad-graph systems: classificat
 ion and applications
DTSTART;VALUE=DATE-TIME:20230620T100000Z
DTEND;VALUE=DATE-TIME:20230620T103000Z
DTSTAMP;VALUE=DATE-TIME:20260517T100046Z
UID:indico-contribution-17-10@cern.ch
DESCRIPTION:Speakers: Dr. ZHANG\, Cheng (Shanghai University)\nThe notion 
 of boundary conditions for quad-graph systems will first be introduced. Th
 e boundary conditions are naturally defined on triangles that arise as dua
 lization of given quad-graphs with boundary. For three-dimensionally consi
 stent quad-graph systems\, the so-called integrable boundary conditions wi
 ll be characterized as boundary conditions satisfying the boundary consist
 ency condition that is a consistency condition defined on a half of a rhom
 bic-dodecahedron. Based on these notions\, three main results will then be
  presented: a classification of integrable boundary conditions for quad-eq
 uations of the ABS classification\; Lax formulations of integrable boundar
 y conditions\; and the so-called open boundary reduction technique as syst
 ematic a means to construct integrable mappings from integrable initial-bo
 undary value problems for quad-graph systems. This talk is based on [Caudr
 elier\, Crampe\, CZ\, Sigma\, 10(014)\, 2014]\, [Caudrelier\, van der Kamp
 \, CZ\, IMRN\, rnac207\, 2021] and [Sun\, CZ\, IMRN\, rnab188\, 2022].\n\n
 http://indico.fuw.edu.pl/contributionDisplay.py?contribId=10&sessionId=17&
 confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=10&sessionId
 =17&confId=67
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BEGIN:VEVENT
SUMMARY:Deformations of the van Diejen model
DTSTART;VALUE=DATE-TIME:20230620T093000Z
DTEND;VALUE=DATE-TIME:20230620T100000Z
DTSTAMP;VALUE=DATE-TIME:20260517T100046Z
UID:indico-contribution-17-22@cern.ch
DESCRIPTION:Speakers: ATAI\, Farrokh (University of Leeds)\nThe (quantum) 
 van Diejen model is an integrable many-body system defined by a family of 
 mutually commuting analytic difference operators that is known to have hyp
 eroctahedral symmetry in its variables and $E_8$ Weyl group symmetry in it
 s parameters (under certain constraint). \nIn this talk\, new generalizati
 ons of the van Diejen Hamiltonian - and some exact eigenfunctions - are pr
 esented. In particular\, I present a Chalykh-Feigin-Sergeev-Veselov type d
 eformation of the van Diejen Hamiltonian\, which is given by an analytic d
 ifference operator with two shift parameters\, along with the correspondin
 g weight function and kernel function identities.\nIf time permits\, I wil
 l also present how some (formal) eigenfunctions of this deformed van Dieje
 n model are related to elliptic hypergeometric integrals of Selberg type.\
 n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?contribId=22&sessionId=
 17&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=22&sessionId
 =17&confId=67
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BEGIN:VEVENT
SUMMARY:Integrable maps\; from algebraic construction to geometric underst
 anding
DTSTART;VALUE=DATE-TIME:20230620T103000Z
DTEND;VALUE=DATE-TIME:20230620T110000Z
DTSTAMP;VALUE=DATE-TIME:20260517T100046Z
UID:indico-contribution-17-76@cern.ch
DESCRIPTION:Speakers: Dr. VAN DER KAMP\, Peter (La Trobe University)\nInte
 grable maps can be obtained as periodic or open reductions from lattice eq
 uations which satisfy consistency conditions.\nAn open reduction (this wil
 l be explained in the talk by Cheng Zhang) from Q1_0 was decomposed as a c
 omposition of Manin involutions on each curve of the invariant pencil.\nHo
 wever\, one of the involution points appeared to be curve-dependent....\n\
 nhttp://indico.fuw.edu.pl/contributionDisplay.py?contribId=76&sessionId=17
 &confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=76&sessionId
 =17&confId=67
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