BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Critical Points Of Discrete Periodic Operators - Frank Sottile (Te
 xas A&M University)
DTSTART:20240123T114500Z
DTEND:20240123T124500Z
UID:TALK208054@talks.cam.ac.uk
DESCRIPTION:It is believed that the dispersion relation of a Schrodinger o
 perator with a&nbsp\; periodic&nbsp\; potential has&nbsp\; non-degenerate&
 nbsp\; critical&nbsp\; points\, for&nbsp\; general values of the potential
  and&nbsp\; interaction strengths.&nbsp\; In work with Kuchment and Do\, w
 e&nbsp\; considered this for discrete operators on&nbsp\; a periodic graph
  G\, for then the dispersion relation&nbsp\; is an algebraic hypersurface.
 &nbsp\; We showed how\, for a given&nbsp\; periodic graph G\, this may be&
 nbsp\; established from a single numerical&nbsp\; verification\, if&nbsp\;
  we knew&nbsp\; the&nbsp\; number of&nbsp\; critical points&nbsp\; for gen
 eral values of the parameters.With Matthew Faust\,&nbsp\; we use ideas fro
 m combinatorial&nbsp\; algebraic geometry to give&nbsp\; an&nbsp\; upper&n
 bsp\; bound&nbsp\; for&nbsp\; the&nbsp\; number&nbsp\; of&nbsp\; critical&
 nbsp\; points&nbsp\; at&nbsp\; generic parameters\, and&nbsp\; also a&nbsp
 \; criterion for&nbsp\; when that&nbsp\; bound is&nbsp\; obtained.&nbsp\; 
 The dispersion relation has a natural&nbsp\; compactification in a toric v
 ariety\, and the criterion concerns&nbsp\; the smoothness of the dispersio
 n&nbsp\; relation at toric infinity.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR