BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Degree growth of some lattice equations defined on  a 3x3 stencil
DTSTART;VALUE=DATE-TIME:20230622T100000Z
DTEND;VALUE=DATE-TIME:20230622T103000Z
DTSTAMP;VALUE=DATE-TIME:20260625T064521Z
UID:indico-contribution-2-60@cern.ch
DESCRIPTION:Speakers: Prof. HIETARINTA\, Jarmo (University of Turku)\nWe s
 tudy the growth of complexity\, or degree growth\, of one-component\nlatti
 ce equations defined on a 3x3 stencil. The 2x2 case was discussed\nin a pr
 evious talk by T. Mase.  The equations studied here include two\n7-point e
 quations in Hirota bilinear form as well as 9-point\nBoussinesq equations 
 of regular\, modified and Schwarzian type. \nThe initial values are given 
 on a staircase or on a corner configuration and\ndepend linearly or ration
 ally on a special variable x\, and we count\nthe degree in x of the iterat
 es. Known integrable cases have linear\ngrowth if only one initial values 
 contains x\, and quadratic growth if\nall initial values contain x. Even a
  small deformation of an\nintegrable equation changes the degree growth to
  become exponential\,\nbecause the deformation will change factorization p
 roperties and\nthereby prevent cancellations. The simplest case in which o
 nly one initial\nvalue contains x is sufficient to differentiate between i
 ntegrable\nand non-integrable equations.\n\nhttp://indico.fuw.edu.pl/contr
 ibutionDisplay.py?contribId=60&sessionId=2&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=60&sessionId
 =2&confId=67
END:VEVENT
BEGIN:VEVENT
SUMMARY:Computing degree growth of birational maps from local indices of p
 olynomials
DTSTART;VALUE=DATE-TIME:20230622T103000Z
DTEND;VALUE=DATE-TIME:20230622T110000Z
DTSTAMP;VALUE=DATE-TIME:20260625T064521Z
UID:indico-contribution-2-26@cern.ch
DESCRIPTION:Speakers: Mr. WEI\, Kangning (TU Berlin)\nOne of the most impo
 rtant dynamical invariant associated to a birational map f is given by its
  dynamical degree\, or equivalently\, its algebraic entropy\, which is def
 ined via the rate of growth of the sequence deg(f^n). More concretely\, th
 e degrees deg(f^n)\, although not birationally invariant by themselves\, a
 re also of great interests in understanding the dynamics of the birational
  map. \nWe propose a general method for computing the degrees deg(f^n). Mo
 re precisely\, given a homogeneous polynomial P\, we compute the iterated 
 pullbacks of the polynomial by the map f. To do this\, we perform a sequen
 ce of blowing ups and to each blowing up we associate a local index \\mu(P
 ) to a polynomial P. Together with the degrees deg(f^n)\, these local indi
 ces satisfy a recurrence relation which can be solved to obtain the degree
 s deg(f^n).\nIn two dimensional cases\, we show that these indices are clo
 sely related to the intersection numbers. In principle\, however\, this me
 thod is applicable to birational maps in any dimension.\n\nhttp://indico.f
 uw.edu.pl/contributionDisplay.py?contribId=26&sessionId=2&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=26&sessionId
 =2&confId=67
END:VEVENT
BEGIN:VEVENT
SUMMARY:Degree growth calculations for lattice equations
DTSTART;VALUE=DATE-TIME:20230622T093000Z
DTEND;VALUE=DATE-TIME:20230622T100000Z
DTSTAMP;VALUE=DATE-TIME:20260625T064521Z
UID:indico-contribution-2-21@cern.ch
DESCRIPTION:Speakers: Dr. MASE\, Takafumi (the University of Tokyo)\nInteg
 rability criteria that have been enormously successful for second order ma
 ppings\, such as singularity confinement or zero algebraic entropy\, are o
 ften applied to lattice equations as though the latter were mere mappings.
 \nIn this talk we will show that such a naïve approach can (and does) lea
 d to all sorts of contradictions and that considerable care is needed when
  using such methods to investigate the integrability of a given lattice eq
 uation.\n\nMore precisely:\nIn this talk we show that the results of degre
 e growth calculations for lattice equations strongly depend on the initial
  value problem that one chooses\, either because of problems that arise in
  the past light-cone\, or because of interferences in the future light-con
 e.\nAmong the examples we treat are initial value problems for dKdV\, disc
 rete Liouville and dToda\, for which the degree growth becomes exponential
 \, in contrast to the common belief that discrete integrable equations mus
 t have polynomial growth and that linearizable equations necessarily have 
 linear degree growth\, regardless of the initial value problem one imposes
 .\nFinally\, as a possible remedy for one of the observed anomalies\, we a
 lso propose basing integrability tests that use growth criteria on the deg
 ree growth of a single initial value instead of all the initial values.\n\
 nReference:\nJ. Hietarinta\, T. Mase & R. Willox: J. Phys. A: Math. Theor.
  52 49LT01 (2019).\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?cont
 ribId=21&sessionId=2&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=21&sessionId
 =2&confId=67
END:VEVENT
END:VCALENDAR