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SUMMARY:Wencai Liu (Texas A&M)
DTSTART:20210211T180000Z
DTEND:20210211T190000Z
DTSTAMP:20260423T053138Z
UID:Thouless/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Thouless/6/"
 >Irreducibility of the Fermi variety for discrete periodic Schr\\"odinger 
 operators</a>\nby Wencai Liu (Texas A&M) as part of UCI Mathematical Physi
 cs\n\n\nAbstract\nLet $H_0$ be a discrete periodic  Schr\\"odinger operato
 r on $\\Z^d$:\n\n$$H_0=-\\Delta+V\,$$ where $\\Delta$ is the discrete Lapl
 acian and $V:\\Z^d\\to \\R$ is periodic.    We prove that  for any $d\\geq
 3$\,    the Fermi variety at every energy level  is irreducible  (modulo p
 eriodicity).  For $d=2$\,    we prove that the Fermi variety at every ener
 gy level except for the average of  the potential    is irreducible  (modu
 lo periodicity) and  the Fermi variety at the average of  the potential ha
 s at most two irreducible components  (modulo periodicity). \n\nThis is sh
 arp since for  $d=2$ and a constant potential  $V$\,   \n\nthe Fermi varie
 ty at  $V$-level  has exactly  two irreducible components (modulo periodic
 ity).  \n\nIn particular\,  we show that  the Bloch variety  is irreducibl
 e \n\n(modulo periodicity)  for any $d\\geq 2$.\n
LOCATION:https://researchseminars.org/talk/Thouless/6/
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