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BEGIN:VEVENT
SUMMARY:Mikhail Karpukhin (Caltech)
DTSTART:20210220T163000Z
DTEND:20210220T171000Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/1/">Stability of the Hersch inequality for the first eige
 nvalue on the 2-sphere and generalizations</a>\nby Mikhail Karpukhin (Calt
 ech) as part of 38th Annual Western States Mathematical Physics Meeting\n\
 n\nAbstract\nStability questions for sharp inequalities are important prob
 lems in analysis. Recently\, these questions have been investigated for th
 e first eigenvalue of the Laplacian on Euclidean domains. Optimal stabilit
 y estimates for Faber-Krahn and Szego-Weinberger inequalities were obtaine
 d by Brasco-De Philippis-Velichkov and Nadirashvili\, Brasco-Pratelli resp
 ectively. In the present talk we briefly survey their results and then foc
 us on the stability of another fundamental inequality in spectral geometry
 : Hersch inequality for the first eigenvalue on the 2-dimensional sphere. 
 Furthermore\, we discuss generalizations to other surfaces and the connect
 ion to harmonic maps and minimal surfaces. Based on the joint work with M.
  Nahon\, I. Polterovich and D. Stern.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoqi Huang (Johns Hopkins University)
DTSTART:20210220T171500Z
DTEND:20210220T175500Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/2/">Weyl formulae for Schrödinger operators with critica
 lly singular potentials</a>\nby Xiaoqi Huang (Johns Hopkins University) as
  part of 38th Annual Western States Mathematical Physics Meeting\n\n\nAbst
 ract\nIn this talk we shall discuss generalizations of classical versions 
 of the Weyl formula involving Schrödinger operators $H_V= -\\Delta_g +V(x
 )$ on compact boundaryless Riemannian manifolds with critically singular p
 otentials $V$. In particular\, we extend the classical results of Avakumov
 ić\, Levitan and Hörmander by obtaining $O(\\lambda^{n-1})$ bounds for t
 he error term in the Weyl formula in the universal case when we merely ass
 ume that V belongs to the Kato class\, $\\mathcal{K}(M)$\, which is the mi
 nimal assumption to ensure that $H_V$ is essentially self-adjoint and boun
 ded from below or has favorable heat kernel bounds. We shall discuss both 
 local point-wise and integral versions of Weyl formulae\, and also improve
 ments over the error term under certain geometric conditions. This is base
 d on joint work with Christopher Sogge and Cheng Zhang.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Brennecke (Harvard University)
DTSTART:20210220T181500Z
DTEND:20210220T185500Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/3/">Bose-Einstein Condensation beyond the Gross-Pitaevski
 i Regime</a>\nby Christian Brennecke (Harvard University) as part of 38th 
 Annual Western States Mathematical Physics Meeting\n\n\nAbstract\nIn this 
 talk\, I will consider Bose gases in a box of volume one that interact thr
 ough a two-body potential with scattering length of the order $N^{-1+\\kap
 pa}$\, for $\\kappa >0$. For small enough $\\kappa \\in (0\;1/43)$\, sligh
 tly beyond the Gross-Pitaevskii regime ($\\kappa=0$)\, I will explain a pr
 oof of Bose-Einstein condensation for low-energy states that provides boun
 ds on the expectation and on higher moments of the number of excitations. 
 The talk is based on joint work with A. Adhikari and B. Schlein.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Fraas (UC Davis)
DTSTART:20210220T190000Z
DTEND:20210220T194000Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/4/">Quantum trajectories and the appearance of particle t
 racks in detectors</a>\nby Martin Fraas (UC Davis) as part of 38th Annual 
 Western States Mathematical Physics Meeting\n\n\nAbstract\nI will introduc
 e the setting of quantum trajectories and review the key general results. 
 Then I will focus on a particular model describing the phenomenon that a q
 uantum particle propagating in a detector\, such as a Wilson cloud chamber
 \, leaves a track close to a classical trajectory. For this model I will p
 resent a mathematically rigorous analysis of the appearance of particle tr
 acks\, assuming that the Hamiltonian of the particle is quadratic in the p
 osition-and momentum operators\, as for a freely moving particle or a harm
 onic oscillator.\n\nThe talk is based on a joint work with M. Ballesteros\
 , T. Benoist and J. Frohlich.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wencai Liu (Texas A&M University)
DTSTART:20210220T210000Z
DTEND:20210220T214000Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/5/">Irreducibility of the Fermi variety for discrete peri
 odic Schrödinger operators and  its applications</a>\nby Wencai Liu (Texa
 s A&M University) as part of 38th Annual Western States Mathematical Physi
 cs Meeting\n\n\nAbstract\nLet $H_0$ be a discrete periodic  Schrödinger o
 perator on $\\mathbb{Z}^d$:\n$$H_0=-\\Delta+V\,$$\nwhere $\\Delta$ is the 
 discrete Laplacian and $V\\colon\\mathbb{Z}^d\\to \\mathbb{R}$ is periodic
 .    We prove that  for any $d\\geq3$\,    the Fermi variety at every ener
 gy level  is irreducible  (modulo periodicity).  For $d=2$\,    we prove t
 hat the Fermi variety at every energy level except for the average of  the
  potential    is irreducible  (modulo periodicity) and  the Fermi variety 
 at the average of  the potential has at most two irreducible components  (
 modulo periodicity). \nThis is sharp since for  $d=2$ and a constant poten
 tial  $V$\,    the Fermi variety at  $V$-level  has exactly  two irreducib
 le components (modulo periodicity).  \nIn particular\,  we show that  the 
 Bloch variety  is irreducible \n(modulo periodicity)  for any $d\\geq 2$. 
 \n\nAs  applications\, we prove that\nthe level set of any  extrema of any
   spectral band functions\,  spectral band edges  in particular\,  \nhas d
 imension at most $d-2$  for any $d\\geq 3$\,  and  finite  cardinality\nfo
 r $d=2$. \nWe also  show  that $H=-\\Delta +V+v$ does not have any embedde
 d eigenvalues provided that $v$ decays super-exponentially.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaowen Zhu (UC Irvine)
DTSTART:20210220T214500Z
DTEND:20210220T222500Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/6/">Dynamical localization for the 2-d\, 3-d Anderson mod
 el with singular potentials</a>\nby Xiaowen Zhu (UC Irvine) as part of 38t
 h Annual Western States Mathematical Physics Meeting\n\n\nAbstract\nFor th
 e $n$-d ($n>1$) Anderson model with singular potentials\, the bootstrap Mu
 ltiscale Analysis (MSA) could only provide a weaker probability estimates 
 comparing to the model with Hölder continuous potentials\, which makes th
 e derivation of Anderson localization\, dynamical localization and strong 
 dynamical localization harder to achieve. In this talk\, we'll introduce a
  variant of the first and second spectral reduction methods introduced by 
 Germinet and Klein which could derive the localization results for models 
 with such weaker MSA results. In particular\, we showed the dynamical loca
 lization and strong dynamical localization for the 2-d and 3-d Anderson mo
 del with singular potential.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Harrop-Griffiths (UCLA)
DTSTART:20210220T224500Z
DTEND:20210220T232500Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/7/">Sharp well-posedness for the cubic NLS and mKdV on th
 e line</a>\nby Benjamin Harrop-Griffiths (UCLA) as part of 38th Annual Wes
 tern States Mathematical Physics Meeting\n\n\nAbstract\nThe 1d cubic nonli
 near Schrödinger equation (NLS) and the modified Korteweg-de Vries equati
 on (mKdV) are two of the most intensively studied nonlinear dispersive equ
 ations. Not only are they important physical models\, arising\, for exampl
 e\, from the study of fluid dynamics and nonlinear optics\, but they also 
 have a rich mathematical structure: they are both members of the ZS-AKNS h
 ierarchy of integrable equations. In this talk\, we discuss an optimal wel
 l-posedness result for the cubic NLS and mKdV on the line. An essential in
 gredient in our arguments is the demonstration of a local smoothing effect
  for both equations\, which in turn rests on the discovery of a one-parame
 ter family of microscopic conservation laws. This is joint work with Rowan
  Killip and Monica Vişan.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannis Angelopoulos (Caltech)
DTSTART:20210220T233000Z
DTEND:20210221T001000Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/8/">Late-time tails for linear waves on black hole spacet
 imes and applications</a>\nby Yannis Angelopoulos (Caltech) as part of 38t
 h Annual Western States Mathematical Physics Meeting\n\n\nAbstract\nI will
  present some recent and past work (that has been done jointly with Stefan
 os Aretakis and Dejan Gajic) on the precise asymptotics of linear waves on
  the exterior (up to and including the event horizon) of subextremal and e
 xtremal black holes. Particular examples of such spacetimes are the full f
 amily of Reissner-Nordstrom black hole spacetimes\, and the full subextrem
 al family of Kerr black hole spacetimes. I will also discuss the special c
 ase of linear waves localized in angular frequency\, and I will present as
  well some applications on scattering and nonlinear problems.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Becker (University of Cambridge)
DTSTART:20210221T163000Z
DTEND:20210221T171000Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/9/">Mathematics of magic angles for bilayer graphene</a>\
 nby Simon Becker (University of Cambridge) as part of 38th Annual Western 
 States Mathematical Physics Meeting\n\n\nAbstract\nMagic angles are a hot 
 topic in condensed matter physics: when two sheets of graphene are twisted
  by those angles the resulting material is superconducting. Please do not 
 be scared by the physics though: I will present a very simple operator who
 se spectral properties are thought to determine which angles are magical. 
 It comes from a recent PR Letter by Tarnopolsky–Kruchkov–Vishwanath. T
 he mathematics behind this is an elementary blend of representation theory
  (of the Heisenberg group in characteristic three)\, Jacobi theta function
 s and spectral instability of non-self-adjoint operators (involving Hoerma
 nder’s bracket condition in a very simple setting). The results will be 
 illustrated by colourful numerics which suggest some open problems. This i
 s joint work with M. Embree\, J. Wittsten\, and M. Zworski.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Drouot (University of Washington)
DTSTART:20210221T171500Z
DTEND:20210221T175500Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/10/">Mathematical aspects of topological insulators</a>\n
 by Alexis Drouot (University of Washington) as part of 38th Annual Western
  States Mathematical Physics Meeting\n\n\nAbstract\nTopological insulators
  are intriguing materials that block conduction in their interior (the bul
 k) but support robust asymmetric currents along their edges. \nI will disc
 uss their analytic\, geometric and topological aspects using an adiabatic 
 framework favorable to quantitative predictions.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/10
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingrui Ge (UC Irvine)
DTSTART:20210221T181500Z
DTEND:20210221T185500Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/11/">Transition space for the continuity of the Lyapunov 
 exponent of quasiperiodic Schrödinger cocycles</a>\nby Lingrui Ge (UC Irv
 ine) as part of 38th Annual Western States Mathematical Physics Meeting\n\
 n\nAbstract\nWe construct discontinuous point of the Lyapunov exponent of 
 quasiperiodic Schrödinger cocycles in the Gevrey space $G^{s}$ with $s>2$
 . In contrast\, the Lyapunov exponent has been proved to be continuous  in
  the Gevrey space $G^{s}$ with $s<2$. This shows that  $G^2$ is the transi
 tion space for the continuity of the Lyapunov exponent.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/11
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Zhao (UC Irvine)
DTSTART:20210221T190000Z
DTEND:20210221T194000Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/12/">Localization and delocalization for the $\\tan^2\\pi
 (\\theta)$ model</a>\nby Xin Zhao (UC Irvine) as part of 38th Annual Weste
 rn States Mathematical Physics Meeting\n\n\nAbstract\nThe $\\tan^2\\pi(\\t
 heta)$ model is the following one frequency \nquasiperiodic Schrödinger o
 perator on $\\ell^2(\\Z)$\,\n$$\n(H_{\\lambda\,\\alpha\,\\theta}u)_n=u_{n+
 1}+u_{n-1}+\\lambda\\tan^2\\pi(\\theta+n\\alpha)u_{n}.\n$$\nThis model app
 eared in physics literature and is the prototypical case \nof an unbounded
  non-monotone potential.\n\nDefine\n$$\\beta(\\alpha)=\\limsup\\limits_{n\
 \rightarrow\\infty}-\\frac{\\ln\\|k\\alpha\\|}{|k|}.$$\n$$\n\\delta(\\alph
 a\,\\theta)=\\limsup\\limits_{n\\rightarrow\\infty}-\\frac{\\ln\\|2\\theta
 +n\\alpha\\|_{\\R/\\Z}}{|n|}\,\n$$\nwhere $\\|x\\|_{\\R/\\Z}=dist(x\,\\Z)$
 .\n\nWe prove\n\n$\\quad$  1. If $\\beta(\\alpha)=\\delta(\\alpha\,\\theta
 )=0$\, then \n$H_{\\lambda\,\\alpha\,\\theta}$ has Anderson localization i
 n the positive \nLyapunov exponent regime.\n\n$\\quad$  2. If $\\beta(\\al
 pha)=0$ and $\\delta(\\alpha\,\\theta)>0$\, then \n$H_{\\lambda\,\\alpha\,
 \\theta}$ has purely singular continuous spectrum on \nthe set $\\{E:0 < L
 (E) < \\delta(\\alpha\,\\theta)\\}$.\n\nPart (2) is a sharp result.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/12
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART:20210221T210000Z
DTEND:20210221T214000Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/13/">Invariant Gibbs measures for the three-dimensional w
 ave equation with a Hartree nonlinearity</a>\nby Bjoern Bringmann (UCLA) a
 s part of 38th Annual Western States Mathematical Physics Meeting\n\n\nAbs
 tract\nIn this talk\, we discuss the construction and invariance of the Gi
 bbs measure for a three-dimensional wave equation with a Hartree-nonlinear
 ity.\nIn the first part of the talk\, we construct the Gibbs measure and e
 xamine its properties. We discuss the mutual singularity of the Gibbs meas
 ure and the so-called Gaussian free field. In contrast\, the Gibbs measure
  for one or two-dimensional wave equations is absolutely continuous with r
 espect to the Gaussian free field.\n\nIn the second part of the talk\, we 
 discuss the probabilistic well-posedness of the corresponding nonlinear wa
 ve equation\, which is needed in the proof of invariance. At the moment\, 
 this is the only theorem proving the invariance of any singular Gibbs meas
 ure under a dispersive equation.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/13
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Larson (Caltech)
DTSTART:20210221T214500Z
DTEND:20210221T222500Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/14/">On the spectrum of the Kronig-Penney model in a cons
 tant electric field</a>\nby Simon Larson (Caltech) as part of 38th Annual 
 Western States Mathematical Physics Meeting\n\n\nAbstract\nWe are interest
 ed in the nature of the spectrum of the one-dimensional Schrödinger opera
 tor\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 model $g_n \\equiv \\lambda$ an
 d we prove that if $F\\in \\pi^2 \\mathbb{Q}$ the spectrum is absolutely c
 ontinuous away from a discrete set of points. In the second model $g_n$ ar
 e i.i.d. random variables with mean zero\, variance $\\lambda^2$\, with ab
 solutely continuous and compactly supported distribution. For this model w
 e prove that almost surely the spectrum is pure point if $F/\\lambda^2 < 1
 /2$ and purely singular continuous if $F/\\lambda^2> 1/2$. Based on joint 
 work with Rupert Frank.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/14
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Fischbacher (UC Irvine)
DTSTART:20210221T224500Z
DTEND:20210221T232500Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/15/">Entanglement entropy in the Heisenberg XXZ model</a>
 \nby Christoph Fischbacher (UC Irvine) as part of 38th Annual Western Stat
 es Mathematical Physics Meeting\n\n\nAbstract\nIn this talk\, I will give 
 an overview over recent results on the entanglement entropy for the one-di
 mensional Heisenberg XXZ model. For the spin-1/2 case\, Beaud and Warzel s
 howed that generic low-energy states satisfy a logarithmically corrected a
 rea law. I will talk about the extension of this result to higher-energy s
 tates for the spin-1/2 case (joint work with H. Abdul-Rahman and G. Stolz)
  but also to the case of higher local spins (joint work with O. Ogunkoya).
 \n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/15
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART:20210221T233000Z
DTEND:20210222T001000Z
DTSTAMP:20260422T212828Z
UID:WesternStatesMathPhysMeeting/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WesternState
 sMathPhysMeeting/16/">A Nonlocal Evolution Equation Modeling Roots of Poly
 nomials under Repeated Differentiation</a>\nby Stefan Steinerberger (Unive
 rsity of Washington) as part of 38th Annual Western States Mathematical Ph
 ysics Meeting\n\n\nAbstract\nSuppose you have a polynomial $p_n$ of degree
  $n$ whose $n$ real roots are roughly distributed like a Gaussian (or some
  other nice distribution) and you differentiate $t\\times n$ times where $
 0< t <1$ What's the distribution of the $(1-t)n$ roots of that $(t\\times 
 n)$-th derivative? How does it depend on $t$? We identify a relatively sim
 ple nonlocal evolution equation (the nonlocality is given by a Hilbert tra
 nsform)\; it has two nice closed-form solutions\, a shrinking semicircle a
 nd a family of Marchenko-Pastur distributions. This sounds like objects th
 at one encounters in Free Probability Theory and these things are indeed c
 onnected. Finally\, I will discuss the case of polynomials with roots in t
 he complex plane which is also extremely rich. There are many nice picture
 s and many open problems.\n
LOCATION:https://researchseminars.org/talk/WesternStatesMathPhysMeeting/16
 /
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