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BEGIN:VEVENT
SUMMARY:Eric Seré
DTSTART:20210614T133000Z
DTEND:20210614T143000Z
DTSTAMP:20260422T212830Z
UID:MCQM21/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MCQM21/1/">D
 irac-Coulomb operators with general charge distribution: results and open 
 problems</a>\nby Eric Seré as part of Mathematical Challenges in Quantum 
 Mechanics 2021 Workshop\n\n\nAbstract\nThis talk is based on joint works w
 ith M.J. Esteban and M. Lewin. Consider an electron moving in the attracti
 ve Coulomb potential generated by a non-negative finite measure representi
 ng an external charge density. If the total charge is fixed\, it is well k
 nown that the lowest eigenvalue of the corresponding Schrodinger operator 
 is minimized when the measure is a delta. We investigate the conjecture th
 at the same holds for the relativistic Dirac-Coulomb operator. First we gi
 ve conditions ensuring that this operator has a natural self-adjoint reali
 sation and that its eigenvalues are given by min-max formulas. Then we def
 ine a critical charge such that\, if the total charge is fixed below it\, 
 then there exists a measure minimising the first eigenvalue of the Dirac-C
 oulomb operator. Moreover this optimal measure concentrates on a compact s
 et of Lebesgue measure zero. The last property is proved using a new uniqu
 e continuation principle for Dirac operators.\n
LOCATION:https://researchseminars.org/talk/MCQM21/1/
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BEGIN:VEVENT
SUMMARY:Michael Weinstein
DTSTART:20210614T150000Z
DTEND:20210614T160000Z
DTSTAMP:20260422T212830Z
UID:MCQM21/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MCQM21/2/">T
 ight binding approximation of continuum 2D quantum materials</a>\nby Micha
 el Weinstein as part of Mathematical Challenges in Quantum Mechanics 2021 
 Workshop\n\n\nAbstract\nWe consider 2D quantum materials\, modeled by a co
 ntinuum Schroedinger operator whose potential\nis composed of an array of 
 identical potential wells centered on the vertices of a discrete subset\, 
 \\Omega\, of the plane. \nWe study the low-lying spectrum in the regime of
  very deep potential wells.\n\nWe present results on scaled resolvent norm
  convergence to a discrete (tight-binding) operator and\, \nin the transla
 tion invariant case\, corresponding results on the scaled convergence of l
 ow-lying dispersion surfaces.\nExamples include the single electron model 
 for bulk graphene ($\\Omega$=honeycomb lattice)\, and \na sharply terminat
 ed graphene half-space\, interfaced with the vacuum along an arbitrary lin
 e-cut. \nWe also apply our methods to the case of strong constant perpendi
 cular magnetic fields. \nThis is joint work with CL Fefferman and J Shapir
 o.\n\nA detailed analysis of the spectrum of the limiting tight binding mo
 del on a honeycomb lattice\, which is terminated along an arbitrary ration
 al line-cut (joint work with CL Fefferman and S Fliss)\, will be presented
  in the upcoming lecture of CL Fefferman.\n
LOCATION:https://researchseminars.org/talk/MCQM21/2/
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BEGIN:VEVENT
SUMMARY:Ari Laptev
DTSTART:20210615T133000Z
DTEND:20210615T143000Z
DTSTAMP:20260422T212830Z
UID:MCQM21/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MCQM21/3/">S
 ymmetry Results in Two-Dimensional Inequalities for Aharonov–Bohm Magnet
 ic Fields</a>\nby Ari Laptev as part of Mathematical Challenges in Quantum
  Mechanics 2021 Workshop\n\n\nAbstract\nWe study functional and spectral p
 roperties of perturbations of a magnetic second order differential operato
 r on a circle.\n\nThis operator appears when considering the restriction t
 o the unit circle of a two dimensional Schrödinger operator with the Bohm
 -Aharonov vector potential.\n\nWe prove some Hardy-type inequalities and s
 harp Keller-Lieb-Thirring inequalities.\n
LOCATION:https://researchseminars.org/talk/MCQM21/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Fefferman
DTSTART:20210615T150000Z
DTEND:20210615T160000Z
DTSTAMP:20260422T212830Z
UID:MCQM21/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MCQM21/4/">G
 raphene edge states in a tight binding model</a>\nby Charles Fefferman as 
 part of Mathematical Challenges in Quantum Mechanics 2021 Workshop\n\n\nAb
 stract\nWe study a standard tight binding model of graphene\, sharply\nter
 minated along an edge. It is well known that zero energy (“flat band”)
 \n edge states arise for a "zigzag" edge\, while an "armchair" edge\ngives
  rise to no edge states.\n\nWe present joint work with S. Fliss and M. Wei
 nstein that determines\nwhich rational edges give rise to flat band edge s
 tates\, and exhibits\nformulas for such edge states when they exist. The j
 oint work includes\nalso preliminary results on non-flat-band edge states.
 \n\nThanks to results presented in Michael Weinstein's lecture\, flat band
 s\nfor a tight binding model give rise to almost flat band edge states\nfo
 r a continuum model.\n
LOCATION:https://researchseminars.org/talk/MCQM21/4/
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