BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Chris Soteros (Mathematics U Saskatchewan - Canada)
DTSTART:20240315T160000Z
DTEND:20240315T170000Z
DTSTAMP:20260423T022925Z
UID:GEOTOP-A/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/64/
 ">Establishing that Knots and Links are Localized for Ring polymers in nan
 ochannels</a>\nby Chris Soteros (Mathematics U Saskatchewan - Canada) as p
 art of GEOTOP-A seminar\n\n\nAbstract\nLattice models have proved useful f
 or studying the entanglement complexity of polymers. In 1988 Sumners and W
 hittington used a lattice model to prove that knotting is inevitable for s
 ufficiently long ring polymers and that knot complexity increases with pol
 ymer length. In the lattice model\, a ring polymer is represented by a pol
 ygon on the simple cubic lattice. Subsequently\, Monte Carlo simulations o
 f lattice polygons led to a 1996 conjecture consistent with the idea that 
 knots occur in a localized way in fixed knot-type polygons. That is\, the 
 "knotted part" is expected to be small relative to the length of the polyg
 on. Recently a first proof of this conjecture has been established for the
  special case of polygons confined to an infinity x 2 x 1 lattice tube. Th
 e proof relies on a combination of novel knot theory and lattice combinato
 rics\, and the results also extend to non-split links. Monte Carlo simulat
 ions support that the conjecture also holds for larger lattice tubes. Thus
  one expects that knots and links will also be localized for DNA in nano c
 hannel experiments. A lattice tube model has also been used to study the e
 ntanglement complexity of two polygons which both span the tube\, a scenar
 io for which it is known that linking is inevitable. In this case\, eviden
 ce suggest that knots are still localized but the linked part is not. I wi
 ll review some of the proofs and Monte Carlo results for these lattice tub
 e models and highlight some of the remaining open questions.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/64/
END:VEVENT
END:VCALENDAR