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BEGIN:VEVENT
SUMMARY:Sasha Sodin (Queen Mary)
DTSTART:20201112T203000Z
DTEND:20201112T213000Z
DTSTAMP:20260404T111100Z
UID:Thouless/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/1/">The Umpteen Operator</a>\nby Sasha Sodin (Queen Mary) as part of U
 CI Mathematical Physics\n\n\nAbstract\nIt was found in the 1990s that spec
 ial linear maps playing a role in the representation theory of the symmetr
 ic group share common features with random matrices. We construct a repres
 entation-theoretic operator which shares some properties with the Anderson
  model (or\, perhaps\, with magnetic random Schroedinger operators)\, and 
 show that indeed it boasts Lifshitz tails. The proof relies on a close con
 nection between the operator and the infinite board version of the fifteen
  puzzle.\nNo background in the representation theory of the symmetric grou
 p will be assumed. Based on joint work with Ohad Feldheim.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mira Shamis (Queen Mary)
DTSTART:20210114T200000Z
DTEND:20210114T210000Z
DTSTAMP:20260404T111100Z
UID:Thouless/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/2/">On the abominable properties of the Almost Mathieu operator with L
 iouville frequencies</a>\nby Mira Shamis (Queen Mary) as part of UCI Mathe
 matical Physics\n\n\nAbstract\nWe show that\, for sufficiently well approx
 imable frequencies\, several spectral characteristics of the Almost Mathie
 u operator can be as poor as at all possible in the class of all discrete 
 Schroedinger operators. For example\, the modulus of continuity of the int
 egrated density of states may be no better than logarithmic. Other charact
 eristics to be discussed are homogeneity\, the Parreau-Widom property\, an
 d (for the critical AMO) the Hausdorff content of the spectrum. Based on j
 oint work with A. Avila\, Y. Last\, and Q. Zhou\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingrui Ge (UCI)
DTSTART:20210121T180000Z
DTEND:20210121T190000Z
DTSTAMP:20260404T111100Z
UID:Thouless/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/3/">Smooth quasiperiodic SL(2\,\\R)-cocycles (I)-Global rigidity resul
 ts for rotations reducibility and Last's intersection spectrum conjecture.
 </a>\nby Lingrui Ge (UCI) as part of UCI Mathematical Physics\n\n\nAbstrac
 t\nFor quasiperiodic Schr\\"odinger operators with one-frequency analytic 
 potentials\, from dynamical systems side\, it has been proved that the cor
 responding quasiperiodic Schr\\"odinger cocycle is either rotations reduci
 ble or has positive Lyapunov exponent for all irrational frequency and alm
 ost every 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 Jito
 mirskaya-Marx. The proofs of above results crucially depend on the analyti
 city of the potentials. Is analyticity  essential for those problems? Some
  open problems in this aspect were raised by  Fayad-Krikorian and Jitomirs
 kaya-Marx. In this paper\, we prove the above mentioned results for ultra-
 differentiable potentials.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingrui Ge (UCI)
DTSTART:20210128T180000Z
DTEND:20210128T190000Z
DTSTAMP:20260404T111100Z
UID:Thouless/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/4/">Smooth quasiperiodic SL(2\,\\R)-cocycles (II)-Sharp transition spa
 ce for the continuity of the Lyapunov exponent.</a>\nby Lingrui Ge (UCI) a
 s part of UCI Mathematical Physics\n\n\nAbstract\nWe construct points of d
 iscontinuity of the Lyapunov exponent of quasiperiodic Shr\\"odinger cocyc
 les in Gevrey space $G^{s}$ with $s>2$. In contrast\, the Lyapunov exponen
 t has been proved to be continuous in $G^{s}$ with $s<2$ by Klein and Chen
 g-Ge-You-Zhou. This shows that $G^2$ is the transition space for the conti
 nuity of the Lyapunov exponent.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingrui Ge (UCI)
DTSTART:20210204T180000Z
DTEND:20210204T190000Z
DTSTAMP:20260404T111100Z
UID:Thouless/5
DESCRIPTION:by Lingrui Ge (UCI) as part of UCI Mathematical Physics\n\nAbs
 tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wencai Liu (Texas A&M)
DTSTART:20210211T180000Z
DTEND:20210211T190000Z
DTSTAMP:20260404T111100Z
UID:Thouless/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/6/">Irreducibility of the Fermi variety for discrete periodic Schr\\"o
 dinger operators</a>\nby Wencai Liu (Texas A&M) as part of UCI Mathematica
 l Physics\n\n\nAbstract\nLet $H_0$ be a discrete periodic  Schr\\"odinger 
 operator on $\\Z^d$:\n\n$$H_0=-\\Delta+V\,$$ where $\\Delta$ is the discre
 te Laplacian and $V:\\Z^d\\to \\R$ is periodic.    We prove that  for any 
 $d\\geq3$\,    the Fermi variety at every energy level  is irreducible  (m
 odulo periodicity).  For $d=2$\,    we prove that the Fermi variety at eve
 ry energy level except for the average of  the potential    is irreducible
   (modulo periodicity) and  the Fermi variety at the average of  the poten
 tial has at most two irreducible components  (modulo periodicity). \n\nThi
 s is sharp since for  $d=2$ and a constant potential  $V$\,   \n\nthe Ferm
 i variety at  $V$-level  has exactly  two irreducible components (modulo p
 eriodicity).  \n\nIn particular\,  we show that  the Bloch variety  is irr
 educible \n\n(modulo periodicity)  for any $d\\geq 2$.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Kachkovskiy (MSU)
DTSTART:20210218T180000Z
DTEND:20210218T190000Z
DTSTAMP:20260404T111100Z
UID:Thouless/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/7/">Perturbative diagonalisation for Maryland-type quasiperiodic opera
 tors with flat pieces</a>\nby Ilya Kachkovskiy (MSU) as part of UCI Mathem
 atical Physics\n\n\nAbstract\nWe consider quasiperiodic operators on $\\Z^
 d$ with unbounded monotone sampling functions ("Maryland-type")\, which ar
 e not required to be strictly monotone and are allowed to have flat segmen
 ts. Under several geometric conditions on the frequencies\, lengths of the
  segments\, and their positions\, we show that these operators enjoy Ander
 son localization at large disorder.\n\nThe talk is based on the joint work
  with S. Krymskii\, L. Parnovskii\, and R. Shterenberg.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oluwadara Ogunkoya (University of Alabama at Birmingham)
DTSTART:20210225T180000Z
DTEND:20210225T190000Z
DTSTAMP:20260404T111100Z
UID:Thouless/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/8/">Entanglement Entropy Bounds in the Higher Spin XXZ Chain</a>\nby O
 luwadara Ogunkoya (University of Alabama at Birmingham) as part of UCI Mat
 hematical Physics\n\n\nAbstract\nWe consider the Heisenberg XXZ spin-$J$ c
 hain ($J\\in\\mathbb{N}/2$) with anisotropy parameter $\\Delta$. Assuming 
 that $\\Delta>2J$\, and introducing threshold energies $E_{K}:=K\\left(1-\
 \frac{2J}{\\Delta}\\right)$\, we show that the bipartite entanglement entr
 opy (EE) of states belonging to any spectral subspace with energy less tha
 n $E_{K+1}$ satisfy a logarithmically corrected area law with prefactor $(
 2\\lfloor K/J\\rfloor-2)$.\n\nThis generalizes previous results by Beaud a
 nd Warzel as well as Abdul-Rahman\, Stolz and one of the authors (C. Fisch
 bacher)\, who covered the spin-$1/2$ case.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Fischbacher (University of Alabama at Birmingham)
DTSTART:20210304T180000Z
DTEND:20210304T190000Z
DTSTAMP:20260404T111100Z
UID:Thouless/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/9/">Entanglement Entropy Bounds in the Higher Spin XXZ Chain</a>\nby C
 hristoph Fischbacher (University of Alabama at Birmingham) as part of UCI 
 Mathematical Physics\n\n\nAbstract\nWe consider the Heisenberg XXZ spin-$J
 $ chain ($J\\in\\mathbb{N}/2$) with anisotropy parameter $\\Delta$. Assumi
 ng that $\\Delta>2J$\, and introducing threshold energies $E_{K}:=K\\left(
 1-\\frac{2J}{\\Delta}\\right)$\, we show that the bipartite entanglement e
 ntropy (EE) of states belonging to any spectral subspace with energy less 
 than $E_{K+1}$ satisfy a logarithmically corrected area law with prefactor
  $(2\\lfloor K/J\\rfloor-2)$.\n\nThis generalizes previous results by Beau
 d and Warzel as well as Abdul-Rahman\, Stolz and C. Fischbacher\, who cove
 red the spin-$1/2$ case.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiwen Zhang (University of Minnesota)
DTSTART:20210415T170000Z
DTEND:20210415T180000Z
DTSTAMP:20260404T111100Z
UID:Thouless/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/11/">Approximating the Ground State Eigenvalue via the Landscape Poten
 tial</a>\nby Shiwen Zhang (University of Minnesota) as part of UCI Mathema
 tical Physics\n\n\nAbstract\nIn this talk\, we study the ground state ener
 gy of a Schroedinger operator and its relation to the landscape potential.
  For the 1-d Bernoulli Anderson model\, we show that the ratio of the grou
 nd state energy and the minimum of the landscape potential approaches $\\p
 i^2/8$ as the domain size approaches infinity. We then discuss some numeri
 cal stimulations and conjectures for excited states and for other random p
 otentials. The talk is based on joint work with I. Chenn and W. Wang.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milivoje Lukic (Rice)
DTSTART:20210422T170000Z
DTEND:20210422T180000Z
DTSTAMP:20260404T111100Z
UID:Thouless/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/13/">Reflectionless canonical systems: almost periodicity and characte
 r-automorphic Fourier transforms</a>\nby Milivoje Lukic (Rice) as part of 
 UCI Mathematical Physics\n\n\nAbstract\nThis talk describes joint work wit
 h Roman Bessonov and Peter\nYuditskii. In the spectral theory of self-adjo
 int and unitary\noperators in one dimension (such as Schrodinger\, Dirac\,
  and Jacobi\noperators)\, a half-line operator is encoded by a Weyl functi
 on\; for\nwhole-line operators\, the reflectionless property is a\npseudoc
 ontinuation relation between the two half-line Weyl functions.\nWe develop
  the theory of reflectionless canonical systems with an\narbitrary Dirichl
 et-regular Widom spectrum with the Direct Cauchy\nTheorem property. This g
 eneralizes\, to an infinite gap setting\, the\nconstructions of finite gap
  quasiperiodic (algebro-geometric)\nsolutions of stationary integrable hie
 rarchies. Instead of theta\nfunctions on a compact Riemann surface\, the c
 onstruction is based on\nreproducing kernels of character-automorphic Hard
 y spaces in Widom\ndomains with respect to Martin measure. We also constru
 ct unitary\ncharacter-automorphic Fourier transforms which generalize the\
 nPaley-Wiener theorem. Finally\, we find the correct notion of almost\nper
 iodicity which holds in general for canonical system parameters in\nArov g
 auge\, and we prove generically optimal results for almost\nperiodicity fo
 r Potapov-de Branges gauge\, and Dirac operators.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Larson (Caltech)
DTSTART:20210506T170000Z
DTEND:20210506T180000Z
DTSTAMP:20260404T111100Z
UID:Thouless/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/14/">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\nAbstract\nWe are interested in the nature of the spectrum of the one-
 dimensional 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 cho
 ices of the coupling constants $\\{g_n\\}_{n\\in \\mathbb{Z}}$. In the fir
 st model $g_n \\equiv \\lambda$ and we prove that if $F\\in \\pi^2 \\mathb
 b{Q}$ then the spectrum is $\\mathbb{R}$ and is furthermore absolutely con
 tinuous away from an explicit discrete set of points. In the second model 
 $g_n$ are independent random variables with mean zero and variance $\\lamb
 da^2$. Under certain assumptions on the distribution of these random varia
 bles we prove that almost surely the spectrum is dense pure point if $F < 
 \\lambda^2/2$ and purely singular continuous if $F> \\lambda^2/2$. Based o
 n joint work with Rupert Frank.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenghe Zhang (UCR)
DTSTART:20210429T170000Z
DTEND:20210429T180000Z
DTSTAMP:20260404T111100Z
UID:Thouless/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/15/">Positivity of the Lyapunov exponent for potentials generated by h
 yperbolic transformations</a>\nby Zhenghe Zhang (UCR) as part of UCI Mathe
 matical Physics\n\n\nAbstract\nIn this talk\, I will introduce a recent wo
 rk in showing positivity of the Lyapunov exponent for Schr\\"odinger opera
 tors with potentials generated by hyperbolic dynamics. Specifically\, we s
 howed that if the base dynamics is a subshift of finite type with an ergod
 ic measure admitting a local product structure and if it has a fixed point
 \, then for all nonconstant H\\"older continuous potentials\, the set of e
 nergies with zero Lyapunov exponent is a discrete set. If the potentials a
 re locally constant or globally fiber bunched\, then the set of zero Lyapu
 nov exponent is finite. We also showed that for generic such potentials\, 
 we have full positivity in the general case and uniform postivity in the s
 pecial cases. Such hyperbolic dynamics include expanding maps such as the 
 doubling map on the unit circle\, or  Anosov diffeomorphism such as the Ar
 nold's Cat map on 2-dimensional torus. It also  can be applied to Markov c
 hains whose special cases include the i.i.d. random variable. This is a jo
 int with A. Avila and D. Damanik.\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Fillman (Texas State University)
DTSTART:20210527T170000Z
DTEND:20210527T180000Z
DTSTAMP:20260404T111100Z
UID:Thouless/18
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Thoul
 ess/18/">Spectral and dynamical properties of aperiodic quantum walks</a>\
 nby Jake Fillman (Texas State University) as part of UCI Mathematical Phys
 ics\n\n\nAbstract\nQuantum walks are quantum mechanical analogues of class
 ical random walks. We will discuss the case of one-dimensional walks in wh
 ich the quantum coins are modulated by an aperiodic sequence\, with an emp
 hasis on almost-periodic models. [Talk based on joint works with Christoph
 er Cedzich\, David Damanik\, Darren Ong\, and Zhenghe Zhang]\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Han (LSU)
DTSTART:20210624T170000Z
DTEND:20210624T180000Z
DTSTAMP:20260404T111100Z
UID:Thouless/20
DESCRIPTION:by Rui Han (LSU) as part of UCI Mathematical Physics\n\nAbstra
 ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Thouless/20/
END:VEVENT
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