BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mikhail Karpukhin (Caltech)
DTSTART:20210220T163000Z
DTEND:20210220T171000Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/1/">Stability of the Hersch inequality for the fir
 st eigenvalue on the 2-sphere and generalizations</a>\nby Mikhail Karpukhi
 n (Caltech) as part of 38th Annual Western States Mathematical Physics Mee
 ting\n\n\nAbstract\nStability questions for sharp inequalities are importa
 nt problems in analysis. Recently\, these questions have been investigated
  for the first eigenvalue of the Laplacian on Euclidean domains. Optimal s
 tability estimates for Faber-Krahn and Szego-Weinberger inequalities were 
 obtained by Brasco-De Philippis-Velichkov and Nadirashvili\, Brasco-Pratel
 li respectively. In the present talk we briefly survey their results and t
 hen focus on the stability of another fundamental inequality in spectral g
 eometry: Hersch inequality for the first eigenvalue on the 2-dimensional s
 phere. Furthermore\, we discuss generalizations to other surfaces and the 
 connection to harmonic maps and minimal surfaces. Based on the joint work 
 with M. Nahon\, I. Polterovich and D. Stern.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoqi Huang (Johns Hopkins University)
DTSTART:20210220T171500Z
DTEND:20210220T175500Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/2/">Weyl formulae for Schrödinger operators with 
 critically singular potentials</a>\nby Xiaoqi Huang (Johns Hopkins Univers
 ity) as part of 38th Annual Western States Mathematical Physics Meeting\n\
 n\nAbstract\nIn this talk we shall discuss generalizations of classical ve
 rsions of the Weyl formula involving Schrödinger operators $H_V= -\\Delta
 _g +V(x)$ on compact boundaryless Riemannian manifolds with critically sin
 gular potentials $V$. In particular\, we extend the classical results of A
 vakumović\, Levitan and Hörmander by obtaining $O(\\lambda^{n-1})$ bound
 s for the error term in the Weyl formula in the universal case when we mer
 ely assume that V belongs to the Kato class\, $\\mathcal{K}(M)$\, which is
  the minimal assumption to ensure that $H_V$ is essentially self-adjoint a
 nd bounded from below or has favorable heat kernel bounds. We shall discus
 s both local point-wise and integral versions of Weyl formulae\, and also 
 improvements over the error term under certain geometric conditions. This 
 is based on joint work with Christopher Sogge and Cheng Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Brennecke (Harvard University)
DTSTART:20210220T181500Z
DTEND:20210220T185500Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/3/">Bose-Einstein Condensation beyond the Gross-Pi
 taevskii Regime</a>\nby Christian Brennecke (Harvard University) as part o
 f 38th Annual Western States Mathematical Physics Meeting\n\n\nAbstract\nI
 n this talk\, I will consider Bose gases in a box of volume one that inter
 act through a two-body potential with scattering length of the order $N^{-
 1+\\kappa}$\, for $\\kappa >0$. For small enough $\\kappa \\in (0\;1/43)$\
 , slightly beyond the Gross-Pitaevskii regime ($\\kappa=0$)\, I will expla
 in a proof of Bose-Einstein condensation for low-energy states that provid
 es bounds on the expectation and on higher moments of the number of excita
 tions. The talk is based on joint work with A. Adhikari and B. Schlein.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Fraas (UC Davis)
DTSTART:20210220T190000Z
DTEND:20210220T194000Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/4/">Quantum trajectories and the appearance of par
 ticle tracks in detectors</a>\nby Martin Fraas (UC Davis) as part of 38th 
 Annual Western States Mathematical Physics Meeting\n\n\nAbstract\nI will i
 ntroduce the setting of quantum trajectories and review the key general re
 sults. Then I will focus on a particular model describing the phenomenon t
 hat a quantum particle propagating in a detector\, such as a Wilson cloud 
 chamber\, leaves a track close to a classical trajectory. For this model I
  will present a mathematically rigorous analysis of the appearance of part
 icle tracks\, assuming that the Hamiltonian of the particle is quadratic i
 n the position-and momentum operators\, as for a freely moving particle or
  a harmonic oscillator.\n\nThe talk is based on a joint work with M. Balle
 steros\, T. Benoist and J. Frohlich.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wencai Liu (Texas A&M University)
DTSTART:20210220T210000Z
DTEND:20210220T214000Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/5/">Irreducibility of the Fermi variety for discre
 te periodic Schrödinger operators and  its applications</a>\nby Wencai Li
 u (Texas A&M University) as part of 38th Annual Western States Mathematica
 l Physics Meeting\n\n\nAbstract\nLet $H_0$ be a discrete periodic  Schröd
 inger operator 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 p
 eriodic.    We prove that  for any $d\\geq3$\,    the Fermi variety at eve
 ry energy level  is irreducible  (modulo periodicity).  For $d=2$\,    we 
 prove that the Fermi variety at every energy level except for the average 
 of  the potential    is irreducible  (modulo periodicity) and  the Fermi v
 ariety at the average of  the potential has at most two irreducible compon
 ents  (modulo periodicity). \nThis is sharp since for  $d=2$ and a constan
 t potential  $V$\,    the Fermi variety at  $V$-level  has exactly  two ir
 reducible components (modulo periodicity).  \nIn particular\,  we show tha
 t  the Bloch variety  is irreducible \n(modulo periodicity)  for any $d\\g
 eq 2$. \n\nAs  applications\, we prove that\nthe level set of any  extrema
  of any  spectral band functions\,  spectral band edges  in particular\,  
 \nhas dimension at most $d-2$  for any $d\\geq 3$\,  and  finite  cardinal
 ity\nfor $d=2$. \nWe also  show  that $H=-\\Delta +V+v$ does not have any 
 embedded eigenvalues provided that $v$ decays super-exponentially.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaowen Zhu (UC Irvine)
DTSTART:20210220T214500Z
DTEND:20210220T222500Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/6/">Dynamical localization for the 2-d\, 3-d Ander
 son model with singular potentials</a>\nby Xiaowen Zhu (UC Irvine) as part
  of 38th Annual Western States Mathematical Physics Meeting\n\n\nAbstract\
 nFor the $n$-d ($n>1$) Anderson model with singular potentials\, the boots
 trap Multiscale Analysis (MSA) could only provide a weaker probability est
 imates comparing to the model with Hölder continuous potentials\, which m
 akes the derivation of Anderson localization\, dynamical localization and 
 strong dynamical localization harder to achieve. In this talk\, we'll intr
 oduce a variant of the first and second spectral reduction methods introdu
 ced by Germinet and Klein which could derive the localization results for 
 models with such weaker MSA results. In particular\, we showed the dynamic
 al localization and strong dynamical localization for the 2-d and 3-d Ande
 rson model with singular potential.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Harrop-Griffiths (UCLA)
DTSTART:20210220T224500Z
DTEND:20210220T232500Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/7/">Sharp well-posedness for the cubic NLS and mKd
 V on the line</a>\nby Benjamin Harrop-Griffiths (UCLA) as part of 38th Ann
 ual Western States Mathematical Physics Meeting\n\n\nAbstract\nThe 1d cubi
 c nonlinear Schrödinger equation (NLS) and the modified Korteweg-de Vries
  equation (mKdV) are two of the most intensively studied nonlinear dispers
 ive equations. Not only are they important physical models\, arising\, for
  example\, from the study of fluid dynamics and nonlinear optics\, but the
 y also have a rich mathematical structure: they are both members of the ZS
 -AKNS hierarchy of integrable equations. In this talk\, we discuss an opti
 mal well-posedness result for the cubic NLS and mKdV on the line. An essen
 tial ingredient in our arguments is the demonstration of a local smoothing
  effect for both equations\, which in turn rests on the discovery of a one
 -parameter family of microscopic conservation laws. This is joint work wit
 h Rowan Killip and Monica Vişan.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannis Angelopoulos (Caltech)
DTSTART:20210220T233000Z
DTEND:20210221T001000Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/8/">Late-time tails for linear waves on black hole
  spacetimes and applications</a>\nby Yannis Angelopoulos (Caltech) as part
  of 38th Annual Western States Mathematical Physics Meeting\n\n\nAbstract\
 nI will present some recent and past work (that has been done jointly with
  Stefanos Aretakis and Dejan Gajic) on the precise asymptotics of linear w
 aves on the exterior (up to and including the event horizon) of subextrema
 l and extremal black holes. Particular examples of such spacetimes are the
  full family of Reissner-Nordstrom black hole spacetimes\, and the full su
 bextremal family of Kerr black hole spacetimes. I will also discuss the sp
 ecial case of linear waves localized in angular frequency\, and I will pre
 sent as well some applications on scattering and nonlinear problems.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Becker (University of Cambridge)
DTSTART:20210221T163000Z
DTEND:20210221T171000Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/9/">Mathematics of magic angles for bilayer graphe
 ne</a>\nby Simon Becker (University of Cambridge) as part of 38th Annual W
 estern 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 opera
 tor whose spectral properties are thought to determine which angles are ma
 gical. It comes from a recent PR Letter by Tarnopolsky–Kruchkov–Vishwa
 nath. The mathematics behind this is an elementary blend of representation
  theory (of the Heisenberg group in characteristic three)\, Jacobi theta f
 unctions and spectral instability of non-self-adjoint operators (involving
  Hoermander’s bracket condition in a very simple setting). The results w
 ill be illustrated by colourful numerics which suggest some open problems.
  This is joint work with M. Embree\, J. Wittsten\, and M. Zworski.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Drouot (University of Washington)
DTSTART:20210221T171500Z
DTEND:20210221T175500Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/10/">Mathematical aspects of topological insulator
 s</a>\nby Alexis Drouot (University of Washington) as part of 38th Annual 
 Western States Mathematical Physics Meeting\n\n\nAbstract\nTopological ins
 ulators are intriguing materials that block conduction in their interior (
 the bulk) but support robust asymmetric currents along their edges. \nI wi
 ll discuss their analytic\, geometric and topological aspects using an adi
 abatic framework favorable to quantitative predictions.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingrui Ge (UC Irvine)
DTSTART:20210221T181500Z
DTEND:20210221T185500Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/11/">Transition space for the continuity of the Ly
 apunov exponent of quasiperiodic Schrödinger cocycles</a>\nby Lingrui Ge 
 (UC Irvine) as part of 38th Annual Western States Mathematical Physics Mee
 ting\n\n\nAbstract\nWe construct discontinuous point of the Lyapunov expon
 ent of quasiperiodic Schrödinger cocycles in the Gevrey space $G^{s}$ wit
 h $s>2$. In contrast\, the Lyapunov exponent has been proved to be continu
 ous  in the Gevrey space $G^{s}$ with $s<2$. This shows that  $G^2$ is the
  transition space for the continuity of the Lyapunov exponent.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Zhao (UC Irvine)
DTSTART:20210221T190000Z
DTEND:20210221T194000Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/12/">Localization and delocalization for the $\\ta
 n^2\\pi(\\theta)$ model</a>\nby Xin Zhao (UC Irvine) as part of 38th Annua
 l Western States Mathematical Physics Meeting\n\n\nAbstract\nThe $\\tan^2\
 \pi(\\theta)$ model is the following one frequency \nquasiperiodic Schröd
 inger operator 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 mo
 del appeared in physics literature and is the prototypical case \nof an un
 bounded non-monotone potential.\n\nDefine\n$$\\beta(\\alpha)=\\limsup\\lim
 its_{n\\rightarrow\\infty}-\\frac{\\ln\\|k\\alpha\\|}{|k|}.$$\n$$\n\\delta
 (\\alpha\,\\theta)=\\limsup\\limits_{n\\rightarrow\\infty}-\\frac{\\ln\\|2
 \\theta+n\\alpha\\|_{\\R/\\Z}}{|n|}\,\n$$\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 localiz
 ation in the positive \nLyapunov exponent regime.\n\n$\\quad$  2. If $\\be
 ta(\\alpha)=0$ 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://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART:20210221T210000Z
DTEND:20210221T214000Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/13/">Invariant Gibbs measures for the three-dimens
 ional wave equation with a Hartree nonlinearity</a>\nby Bjoern Bringmann (
 UCLA) as part of 38th Annual Western States Mathematical Physics Meeting\n
 \n\nAbstract\nIn this talk\, we discuss the construction and invariance of
  the Gibbs measure for a three-dimensional wave equation with a Hartree-no
 nlinearity.\nIn the first part of the talk\, we construct the Gibbs measur
 e and examine its properties. We discuss the mutual singularity of the Gib
 bs measure and the so-called Gaussian free field. In contrast\, the Gibbs 
 measure for one or two-dimensional wave equations is absolutely continuous
  with respect to the Gaussian free field.\n\nIn the second part of the tal
 k\, we discuss the probabilistic well-posedness of the corresponding nonli
 near wave equation\, which is needed in the proof of invariance. At the mo
 ment\, this is the only theorem proving the invariance of any singular Gib
 bs measure under a dispersive equation.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Larson (Caltech)
DTSTART:20210221T214500Z
DTEND:20210221T222500Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/14/">On the spectrum of the Kronig-Penney model in
  a constant electric field</a>\nby Simon Larson (Caltech) as part of 38th 
 Annual Western States Mathematical Physics Meeting\n\n\nAbstract\nWe are i
 nterested in the nature of the spectrum of the one-dimensional Schrödinge
 r operator\n$$\n- \\frac{d^2}{dx^2}-Fx + \\sum_{n \\in \\mathbb{Z}}g_n \\d
 elta(x-n)\n$$\nwith $F>0$ and two different choices of the coupling consta
 nts $\\{g_n\\}_{n\\in \\mathbb{Z}}$. In the first model $g_n \\equiv \\lam
 bda$ and we prove that if $F\\in \\pi^2 \\mathbb{Q}$ the spectrum is absol
 utely continuous away from a discrete set of points. In the second model $
 g_n$ are i.i.d. random variables with mean zero\, variance $\\lambda^2$\, 
 with absolutely continuous and compactly supported distribution. For this 
 model we prove that almost surely the spectrum is pure point if $F/\\lambd
 a^2 < 1/2$ and purely singular continuous if $F/\\lambda^2> 1/2$. Based on
  joint work with Rupert Frank.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Fischbacher (UC Irvine)
DTSTART:20210221T224500Z
DTEND:20210221T232500Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/15/">Entanglement entropy in the Heisenberg XXZ mo
 del</a>\nby Christoph Fischbacher (UC Irvine) as part of 38th Annual Weste
 rn States Mathematical Physics Meeting\n\n\nAbstract\nIn this talk\, I wil
 l give an overview over recent results on the entanglement entropy for the
  one-dimensional Heisenberg XXZ model. For the spin-1/2 case\, Beaud and W
 arzel showed that generic low-energy states satisfy a logarithmically corr
 ected area law. I will talk about the extension of this result to higher-e
 nergy states 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. Ogu
 nkoya).\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART:20210221T233000Z
DTEND:20210222T001000Z
DTSTAMP:20260404T094804Z
UID:WesternStatesMathPhysMeeting/16
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Weste
 rnStatesMathPhysMeeting/16/">A Nonlocal Evolution Equation Modeling Roots 
 of Polynomials under Repeated Differentiation</a>\nby Stefan Steinerberger
  (University of Washington) as part of 38th Annual Western States Mathemat
 ical Physics 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 relativ
 ely simple nonlocal evolution equation (the nonlocality is given by a Hilb
 ert transform)\; it has two nice closed-form solutions\, a shrinking semic
 ircle and a family of Marchenko-Pastur distributions. This sounds like obj
 ects that one encounters in Free Probability Theory and these things are i
 ndeed connected. Finally\, I will discuss the case of polynomials with roo
 ts in the complex plane which is also extremely rich. There are many nice 
 pictures and many open problems.\n
LOCATION:https://stable.researchseminars.org/talk/WesternStatesMathPhysMee
 ting/16/
END:VEVENT
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