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BEGIN:VEVENT
SUMMARY:Sasha Sodin (Queen Mary)
DTSTART;VALUE=DATE-TIME:20201112T203000Z
DTEND;VALUE=DATE-TIME:20201112T213000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/1
DESCRIPTION:Title: The Umpteen Operator\nby Sasha Sodin (Queen Mary) as part of UCI Math
ematical Physics\n\n\nAbstract\nIt was found in the 1990s that special lin
ear maps playing a role in the representation theory of the symmetric grou
p share common features with random matrices. We construct a representatio
n-theoretic operator which shares some properties with the Anderson model
(or\, perhaps\, with magnetic random Schroedinger operators)\, and show th
at indeed it boasts Lifshitz tails. The proof relies on a close connection
between the operator and the infinite board version of the fifteen puzzle
.\nNo background in the representation theory of the symmetric group will
be assumed. Based on joint work with Ohad Feldheim.\n
LOCATION:https://researchseminars.org/talk/Thouless/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mira Shamis (Queen Mary)
DTSTART;VALUE=DATE-TIME:20210114T200000Z
DTEND;VALUE=DATE-TIME:20210114T210000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/2
DESCRIPTION:Title: On the abominable properties of the Almost Mathieu operator with Liouvill
e frequencies\nby Mira Shamis (Queen Mary) as part of UCI Mathematical
Physics\n\n\nAbstract\nWe show that\, for sufficiently well approximable
frequencies\, several spectral characteristics of the Almost Mathieu opera
tor can be as poor as at all possible in the class of all discrete Schroed
inger operators. For example\, the modulus of continuity of the integrated
density of states may be no better than logarithmic. Other characteristic
s to be discussed are homogeneity\, the Parreau-Widom property\, and (for
the critical AMO) the Hausdorff content of the spectrum. Based on joint wo
rk with A. Avila\, Y. Last\, and Q. Zhou\n
LOCATION:https://researchseminars.org/talk/Thouless/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingrui Ge (UCI)
DTSTART;VALUE=DATE-TIME:20210121T180000Z
DTEND;VALUE=DATE-TIME:20210121T190000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/3
DESCRIPTION:Title: Smooth quasiperiodic SL(2\,\\R)-cocycles (I)-Global rigidity results for
rotations reducibility and Last's intersection spectrum conjecture.\nb
y Lingrui Ge (UCI) as part of UCI Mathematical Physics\n\n\nAbstract\nFor
quasiperiodic Schr\\"odinger operators with one-frequency analytic potenti
als\, from dynamical systems side\, it has been proved that the correspond
ing quasiperiodic Schr\\"odinger cocycle is either rotations reducible or
has positive Lyapunov exponent for all irrational frequency and almost eve
ry energy by Avila-Fayad-Krikorian. From spectral theory side\, the ``Schr
\\"odinger conjecture" has been verified by Avila-Fayad-Krikorian and the
``Last's intersection spectrum conjecture" has been proved by Jitomirskay
a-Marx. The proofs of above results crucially depend on the analyticity of
the potentials. Is analyticity essential for those problems? Some open p
roblems in this aspect were raised by Fayad-Krikorian and Jitomirskaya-Ma
rx. In this paper\, we prove the above mentioned results for ultra-differe
ntiable potentials.\n
LOCATION:https://researchseminars.org/talk/Thouless/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingrui Ge (UCI)
DTSTART;VALUE=DATE-TIME:20210128T180000Z
DTEND;VALUE=DATE-TIME:20210128T190000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/4
DESCRIPTION:Title: Smooth quasiperiodic SL(2\,\\R)-cocycles (II)-Sharp transition space for
the continuity of the Lyapunov exponent.\nby Lingrui Ge (UCI) as part
of UCI Mathematical Physics\n\n\nAbstract\nWe construct points of disconti
nuity of the Lyapunov exponent of quasiperiodic Shr\\"odinger cocycles in
Gevrey space $G^{s}$ with $s>2$. In contrast\, the Lyapunov exponent has b
een proved to be continuous in $G^{s}$ with $s<2$ by Klein and Cheng-Ge-Yo
u-Zhou. This shows that $G^2$ is the transition space for the continuity o
f the Lyapunov exponent.\n
LOCATION:https://researchseminars.org/talk/Thouless/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingrui Ge (UCI)
DTSTART;VALUE=DATE-TIME:20210204T180000Z
DTEND;VALUE=DATE-TIME:20210204T190000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/5
DESCRIPTION:by Lingrui Ge (UCI) as part of UCI Mathematical Physics\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/Thouless/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wencai Liu (Texas A&M)
DTSTART;VALUE=DATE-TIME:20210211T180000Z
DTEND;VALUE=DATE-TIME:20210211T190000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/6
DESCRIPTION:Title: Irreducibility of the Fermi variety for discrete periodic Schr\\"odinger
operators\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/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Kachkovskiy (MSU)
DTSTART;VALUE=DATE-TIME:20210218T180000Z
DTEND;VALUE=DATE-TIME:20210218T190000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/7
DESCRIPTION:Title: Perturbative diagonalisation for Maryland-type quasiperiodic operators wi
th flat pieces\nby Ilya Kachkovskiy (MSU) as part of UCI Mathematical
Physics\n\n\nAbstract\nWe consider quasiperiodic operators on $\\Z^d$ with
unbounded monotone sampling functions ("Maryland-type")\, which are not r
equired to be strictly monotone and are allowed to have flat segments. Und
er several geometric conditions on the frequencies\, lengths of the segmen
ts\, and their positions\, we show that these operators enjoy Anderson loc
alization at large disorder.\n\nThe talk is based on the joint work with S
. Krymskii\, L. Parnovskii\, and R. Shterenberg.\n
LOCATION:https://researchseminars.org/talk/Thouless/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oluwadara Ogunkoya (University of Alabama at Birmingham)
DTSTART;VALUE=DATE-TIME:20210225T180000Z
DTEND;VALUE=DATE-TIME:20210225T190000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/8
DESCRIPTION:Title: Entanglement Entropy Bounds in the Higher Spin XXZ Chain\nby Oluwadar
a Ogunkoya (University of Alabama at Birmingham) as part of UCI Mathematic
al Physics\n\n\nAbstract\nWe consider the Heisenberg XXZ spin-$J$ chain ($
J\\in\\mathbb{N}/2$) with anisotropy parameter $\\Delta$. Assuming that $\
\Delta>2J$\, and introducing threshold energies $E_{K}:=K\\left(1-\\frac{2
J}{\\Delta}\\right)$\, we show that the bipartite entanglement entropy (EE
) of states belonging to any spectral subspace with energy less than $E_{K
+1}$ satisfy a logarithmically corrected area law with prefactor $(2\\lflo
or K/J\\rfloor-2)$.\n\nThis generalizes previous results by Beaud and Warz
el as well as Abdul-Rahman\, Stolz and one of the authors (C. Fischbacher)
\, who covered the spin-$1/2$ case.\n
LOCATION:https://researchseminars.org/talk/Thouless/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Fischbacher (University of Alabama at Birmingham)
DTSTART;VALUE=DATE-TIME:20210304T180000Z
DTEND;VALUE=DATE-TIME:20210304T190000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/9
DESCRIPTION:Title: Entanglement Entropy Bounds in the Higher Spin XXZ Chain\nby Christop
h Fischbacher (University of Alabama at Birmingham) as part of UCI Mathema
tical Physics\n\n\nAbstract\nWe consider the Heisenberg XXZ spin-$J$ chain
($J\\in\\mathbb{N}/2$) with anisotropy parameter $\\Delta$. Assuming that
$\\Delta>2J$\, and introducing threshold energies $E_{K}:=K\\left(1-\\fra
c{2J}{\\Delta}\\right)$\, we show that the bipartite entanglement entropy
(EE) of states belonging to any spectral subspace with energy less than $E
_{K+1}$ satisfy a logarithmically corrected area law with prefactor $(2\\l
floor K/J\\rfloor-2)$.\n\nThis generalizes previous results by Beaud and W
arzel as well as Abdul-Rahman\, Stolz and C. Fischbacher\, who covered the
spin-$1/2$ case.\n
LOCATION:https://researchseminars.org/talk/Thouless/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiwen Zhang (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20210415T170000Z
DTEND;VALUE=DATE-TIME:20210415T180000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/11
DESCRIPTION:Title: Approximating the Ground State Eigenvalue via the Landscape Potential\nby Shiwen Zhang (University of Minnesota) as part of UCI Mathematical P
hysics\n\n\nAbstract\nIn this talk\, we study the ground state energy of a
Schroedinger operator and its relation to the landscape potential. For th
e 1-d Bernoulli Anderson model\, we show that the ratio of the ground stat
e energy and the minimum of the landscape potential approaches $\\pi^2/8$
as the domain size approaches infinity. We then discuss some numerical sti
mulations and conjectures for excited states and for other random potentia
ls. The talk is based on joint work with I. Chenn and W. Wang.\n
LOCATION:https://researchseminars.org/talk/Thouless/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milivoje Lukic (Rice)
DTSTART;VALUE=DATE-TIME:20210422T170000Z
DTEND;VALUE=DATE-TIME:20210422T180000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/13
DESCRIPTION:Title: Reflectionless canonical systems: almost periodicity and character-autom
orphic Fourier transforms\nby Milivoje Lukic (Rice) as part of UCI Mat
hematical Physics\n\n\nAbstract\nThis talk describes joint work with Roman
Bessonov and Peter\nYuditskii. In the spectral theory of self-adjoint and
unitary\noperators in one dimension (such as Schrodinger\, Dirac\, and Ja
cobi\noperators)\, a half-line operator is encoded by a Weyl function\; fo
r\nwhole-line operators\, the reflectionless property is a\npseudocontinua
tion relation between the two half-line Weyl functions.\nWe develop the th
eory of reflectionless canonical systems with an\narbitrary Dirichlet-regu
lar Widom spectrum with the Direct Cauchy\nTheorem property. This generali
zes\, to an infinite gap setting\, the\nconstructions of finite gap quasip
eriodic (algebro-geometric)\nsolutions of stationary integrable hierarchie
s. Instead of theta\nfunctions on a compact Riemann surface\, the construc
tion is based on\nreproducing kernels of character-automorphic Hardy space
s in Widom\ndomains with respect to Martin measure. We also construct unit
ary\ncharacter-automorphic Fourier transforms which generalize the\nPaley-
Wiener theorem. Finally\, we find the correct notion of almost\nperiodicit
y which holds in general for canonical system parameters in\nArov gauge\,
and we prove generically optimal results for almost\nperiodicity for Potap
ov-de Branges gauge\, and Dirac operators.\n
LOCATION:https://researchseminars.org/talk/Thouless/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Larson (Caltech)
DTSTART;VALUE=DATE-TIME:20210506T170000Z
DTEND;VALUE=DATE-TIME:20210506T180000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/14
DESCRIPTION:Title: On the spectrum of the Kronig-Penney model in a constant electric field<
/a>\nby Simon Larson (Caltech) as part of UCI Mathematical Physics\n\n\nAb
stract\nWe are interested in the nature of the spectrum of the one-dimensi
onal Schr\\"odinger operator\n$$\n - \\frac{d^2}{dx^2}-Fx + \\sum_{n \\in
\\mathbb{Z}}g_n \\delta(x-n)\n$$\nwith $F>0$ and two different choices of
the coupling constants $\\{g_n\\}_{n\\in \\mathbb{Z}}$. In the first mode
l $g_n \\equiv \\lambda$ and we prove that if $F\\in \\pi^2 \\mathbb{Q}$ t
hen the spectrum is $\\mathbb{R}$ and is furthermore absolutely continuous
away from an explicit discrete set of points. In the second model $g_n$ a
re independent random variables with mean zero and variance $\\lambda^2$.
Under certain assumptions on the distribution of these random variables we
prove that almost surely the spectrum is dense pure point if $F < \\lambd
a^2/2$ and purely singular continuous if $F> \\lambda^2/2$. Based on joint
work with Rupert Frank.\n
LOCATION:https://researchseminars.org/talk/Thouless/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenghe Zhang (UCR)
DTSTART;VALUE=DATE-TIME:20210429T170000Z
DTEND;VALUE=DATE-TIME:20210429T180000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/15
DESCRIPTION:Title: Positivity of the Lyapunov exponent for potentials generated by hyperbol
ic transformations\nby Zhenghe Zhang (UCR) as part of UCI Mathematical
Physics\n\n\nAbstract\nIn this talk\, I will introduce a recent work in s
howing positivity of the Lyapunov exponent for Schr\\"odinger operators wi
th potentials generated by hyperbolic dynamics. Specifically\, we showed t
hat if the base dynamics is a subshift of finite type with an ergodic meas
ure admitting a local product structure and if it has a fixed point\, then
for all nonconstant H\\"older continuous potentials\, the set of energies
with zero Lyapunov exponent is a discrete set. If the potentials are loca
lly constant or globally fiber bunched\, then the set of zero Lyapunov exp
onent is finite. We also showed that for generic such potentials\, we have
full positivity in the general case and uniform postivity in the special
cases. Such hyperbolic dynamics include expanding maps such as the doublin
g map on the unit circle\, or Anosov diffeomorphism such as the Arnold's
Cat map on 2-dimensional torus. It also can be applied to Markov chains w
hose special cases include the i.i.d. random variable. This is a joint wit
h A. Avila and D. Damanik.\n
LOCATION:https://researchseminars.org/talk/Thouless/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Fillman (Texas State University)
DTSTART;VALUE=DATE-TIME:20210527T170000Z
DTEND;VALUE=DATE-TIME:20210527T180000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/18
DESCRIPTION:Title: Spectral and dynamical properties of aperiodic quantum walks\nby Jak
e Fillman (Texas State University) as part of UCI Mathematical Physics\n\n
\nAbstract\nQuantum walks are quantum mechanical analogues of classical ra
ndom walks. We will discuss the case of one-dimensional walks in which the
quantum coins are modulated by an aperiodic sequence\, with an emphasis o
n almost-periodic models. [Talk based on joint works with Christopher Cedz
ich\, David Damanik\, Darren Ong\, and Zhenghe Zhang]\n
LOCATION:https://researchseminars.org/talk/Thouless/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Han (LSU)
DTSTART;VALUE=DATE-TIME:20210624T170000Z
DTEND;VALUE=DATE-TIME:20210624T180000Z
DTSTAMP;VALUE=DATE-TIME:20240329T015903Z
UID:Thouless/20
DESCRIPTION:by Rui Han (LSU) as part of UCI Mathematical Physics\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/Thouless/20/
END:VEVENT
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