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BEGIN:VEVENT
SUMMARY:Jake Fillman (Texas State University)
DTSTART;VALUE=DATE-TIME:20200417T185000Z
DTEND;VALUE=DATE-TIME:20200417T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/1
DESCRIPTION:Title: Spectra of Fibonacci Hamiltonians\nby Jake Fillman (Tex
as State University) as part of TAMU: Mathematical Physics and Harmonic An
alysis Seminar\n\n\nAbstract\nThe Fibonacci sequence is a prominent model
of a 1D quasicrystal. We will talk about some properties of continuum Schr
\\"odinger operators with potentials that are determined by the Fibonacci
sequence. We show that the spectrum is an (unbounded) Cantor set of zero L
ebesgue measure and that the local Hausdorff dimension of the spectrum ten
ds to one in the regimes of high energy and small coupling. We also show t
hat multidimensional Schr\\"odinger operators patterned on the Fibonacci s
equence can exhibit the coexistence of two phenomena: (1) Cantor structure
near the bottom of the spectrum and (2) an absence of gaps in the spectru
m at high energies. To prove (2)\, we develop an "abstract" Bethe--Sommerf
eld criterion for sums of extended Cantor sets\, which may be of independe
nt interest. [Based on joint projects with David Damanik\, Anton Gorodetsk
i\, and May Mei]\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Shipman (LSU)
DTSTART;VALUE=DATE-TIME:20200424T185000Z
DTEND;VALUE=DATE-TIME:20200424T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/2
DESCRIPTION:Title: Reducible and irreducible Fermi surfaces for periodic o
perators\nby Stephen Shipman (LSU) as part of TAMU: Mathematical Physics a
nd Harmonic Analysis Seminar\n\n\nAbstract\nI will discuss new theorems co
ncerning reducibility of the Fermi surface for periodic Schrödinger opera
tors. (1) Irreducibility for a class of planar discrete graph operators\;
(2) Reducibility of multilayer graphs due to compatible asymmetries of th
e connecting edges\; (3) Reducibility of multilayer graphs due to separabi
lity or bipartiteness of the layers. Parts of this work are in collaborat
ion with Wei Li\, Lee Fisher\, Karl-Michael Schmidt\, Ian Wood\, and Malco
lm Brown.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milivoje Lukic (Rice University)
DTSTART;VALUE=DATE-TIME:20200501T185000Z
DTEND;VALUE=DATE-TIME:20200501T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/3
DESCRIPTION:Title: Stahl--Totik regularity for continuum Schr\\"odinger op
erators\nby Milivoje Lukic (Rice University) as part of TAMU: Mathematical
Physics and Harmonic Analysis Seminar\n\n\nAbstract\nThis talk describes
joint work with Benjamin Eichinger: a\ntheory of regularity for one-dimens
ional continuum Schr\\"odinger\noperators\, based on the Martin compactifi
cation of the complement of\nthe essential spectrum. For a half-line Schr\
\"odinger operator\n$-\\partial_x^2+V$ with a bounded potential $V$\, it w
as previously\nknown that the spectrum can have zero Lebesgue measure and
even zero\nHausdorff dimension\; however\, we obtain universal thickness s
tatements\nin the language of potential theory.\nNamely\, we prove that th
e essential spectrum is not polar\, it obeys\nthe Akhiezer--Levin conditio
n\, and moreover\, the Martin function at\n$\\infty$ obeys the two-term as
ymptotic expansion $\\sqrt{-z} +\n\\frac{a}{2\\sqrt{-z}} + o(\\frac 1{\\sq
rt{-z}})$ as $z \\to -\\infty$. The\nconstant $a$ in its asymptotic expans
ion plays the role of a\nrenormalized Robin constant suited for Schr\\"odi
nger operators and\nenters a universal inequality $a \\le \\liminf_{x\\to\
\infty} \\frac 1x\n\\int_0^x V(t) dt$. This leads to a notion of regularit
y\, with\nconnections to the exponential growth rate of Dirichlet solution
s and\nthe zero counting measures for finite restrictions of the operator.
We\nalso present applications to decaying and ergodic potentials.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Li (LSU)
DTSTART;VALUE=DATE-TIME:20200508T185000Z
DTEND;VALUE=DATE-TIME:20200508T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/4
DESCRIPTION:Title: Embedded eigenvalues of the Neumann Poincaré operator\
nby Wei Li (LSU) as part of TAMU: Mathematical Physics and Harmonic Analys
is Seminar\n\n\nAbstract\nThe Neumann-Poincaré (NP) operator arises in bo
undary value problems\, and plays an important role in material design\, s
ignal amplification\, particle detection\, etc. The spectrum of the NP ope
rator on domains with corners was studied by Carleman before tools for rig
orous discussion were created\, and received a lot of attention in the pas
t ten years. In this talk\, I will present our discovery and verification
of eigenvalues embedded in the continuous spectrum of this operator. The m
ain ideas are decoupling of spaces by symmetry and construction of approxi
mate eigenvalues. This is based on two works with Stephen Shipman and Karl
-Mikael Perfekt.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Jauslin (Princeton University)
DTSTART;VALUE=DATE-TIME:20200515T185000Z
DTEND;VALUE=DATE-TIME:20200515T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/5
DESCRIPTION:Title: A simple equation to study interacting Bose gasses\nby
Ian Jauslin (Princeton University) as part of TAMU: Mathematical Physics a
nd Harmonic Analysis Seminar\n\n\nAbstract\nIn this talk\, I will discuss
a partial differential equation introduced by\n Lieb in 1963 in the conte
xt of studying interacting Bose gasses. I will first\n discuss how this e
quation can be used to accurately compute physically\n relevant quantitie
s related to the Bose gas\, such as the ground state energy\n and condens
ate fraction. I will then present a construction of the solutions\n to th
e equation\, and discuss some of their properties.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Kachkovskiy (MSU)
DTSTART;VALUE=DATE-TIME:20200522T185000Z
DTEND;VALUE=DATE-TIME:20200522T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/6
DESCRIPTION:Title: On spectral band edges of discrete periodic Schrodinger
operators\nby Ilya Kachkovskiy (MSU) as part of TAMU: Mathematical Physic
s and Harmonic Analysis Seminar\n\n\nAbstract\nWe consider discrete Schrod
inger operators on $\\ell^2(\\mathbb Z^d)$\, periodic with respect to some
lattice $\\Gamma$ in $\\mathbb Z^d$ of full rank. Our main goal is to stu
dy dimensions of level sets of spectral band functions at the energies cor
responding to their extremal values (the edges of the bands).Suppose that
$d\\ge 3$ and the dual lattice $\\Gamma’$ does not contain the vector $(
1/2\,…\,1/2)$. Then the above mentioned level sets have dimension at mos
t $d-2$.\n\nSuppose that $d=2$ and the dual lattice does not contain vecto
rs of the form $(1/p\,1/p)$ and $(1/p\,-1/p)$ for all $p\\ge 2$. Then the
same statement holds (in other words\, the corresponding level sets are fi
nite modulo $\\mathbb Z^d$).For all lattices that do not satisfy the above
assumptions\, there are known counterexamples of level sets of dimensions
$d-1$.\n\nPart of the argument also implies a discrete Bethe-Sommerfeld p
roperty: if $d\\ge 2$ and the dual lattice does not contain the vector $(1
/2\,…\,1/2)$\, then\, for sufficiently small potentials (depending on th
e lattice)\, the spectrum of the periodic Schrodinger operator is an inter
val. Previously\, this property was studied by Kruger\, Embree-Fillman\, J
itomirskaya-Han\, and Fillman-Han. Our proof is different and implies some
new cases.\n\nThe talk is based on joint work with in progress with N. Fi
lonov.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Fischbacher (UC Irvine)
DTSTART;VALUE=DATE-TIME:20200529T185000Z
DTEND;VALUE=DATE-TIME:20200529T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/7
DESCRIPTION:Title: Logarithmic lower bounds for the entanglement entropy o
f droplet states for the XXZ model on the ring\nby Christoph Fischbacher
(UC Irvine) as part of TAMU: Mathematical Physics and Harmonic Analysis S
eminar\n\n\nAbstract\nWe study the free XXZ quantum spin model defined on
a ring of size L and \nshow that the bipartite entanglement entropy of eig
enstates belonging to \nthe first energy band above the vacuum ground stat
e satisfy a \nlogarithmically corrected area law. This is joint work with
Ruth Schulte \n(LMU).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Kuchment (TAMU)
DTSTART;VALUE=DATE-TIME:20200731T185000Z
DTEND;VALUE=DATE-TIME:20200731T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/8
DESCRIPTION:Title: Spectral properties of periodically perforated spaces\n
by Peter Kuchment (TAMU) as part of TAMU: Mathematical Physics and Harmoni
c Analysis Seminar\n\n\nAbstract\nWe study spectra of Schr\\"odinger opera
tors with periodic \npotentials in R^n with periodic perforations. We prov
e analytic \ndependence on the shape of the perforation and absolute conti
nuity of \nthe spectrum.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Casey Rodriguez (MIT)
DTSTART;VALUE=DATE-TIME:20200807T203000Z
DTEND;VALUE=DATE-TIME:20200807T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/9
DESCRIPTION:Title: The Radiative Uniqueness Conjecture for Bubbling Wave M
aps\nby Casey Rodriguez (MIT) as part of TAMU: Mathematical Physics and Ha
rmonic Analysis Seminar\n\n\nAbstract\nWe will discuss the finite time bre
akdown of solutions to a canonical example of a geometric wave equation: e
nergy critical wave maps. Breakthrough works of Krieger-Schlag–Tataru\,
Rodnianski-Sterbenz and Raphael–Rodnianski produced examples of wave map
s that develop singularities in finite time. These solutions break down by
concentrating energy at a point in space (via bubbling a harmonic map) bu
t have a regular limit\, away from the singular point\, as time approaches
the final time of existence. The regular limit is referred to as the radi
ation. This mechanism of breakdown occurs in many other PDE including ener
gy critical wave equations\, Schrodinger maps and Yang-Mills equations. A
basic question is the following:\n\nCan we give a precise description of a
ll bubbling singularities for wave maps with the goal of finding the natur
al unique continuation of such solutions past the singularity?\n\nIn this
talk\, we will discuss recent work (joint with J. Jendrej and A. Lawrie) w
hich is the first to directly and explicitly connect the radiative compone
nt to the bubbling dynamics by constructing and classifying bubbling solut
ions with a simple form of prescribed radiation. Our results serve as an i
mportant first step in formulating and proving the following Radiative Uni
queness Conjecture for a large class of wave maps: every bubbling solution
is uniquely characterized by its radiation\, and thus\, every bubbling so
lution can be uniquely continued past blow-up time while conserving energy
.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Avy Soffer (Rutgers)
DTSTART;VALUE=DATE-TIME:20200814T185000Z
DTEND;VALUE=DATE-TIME:20200814T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/10
DESCRIPTION:Title: Evolution of NLS with Bounded Data\nby Avy Soffer (Rutg
ers) as part of TAMU: Mathematical Physics and Harmonic Analysis Seminar\n
\n\nAbstract\nWe study the nonlinear Schrodinger equation (NLS) with bound
ed initial data which does not vanish at infinity. Examples include period
ic\, quasi-periodic and random initial data. On the lattice we prove that
solutions are polynomially bounded in time for any bounded data. In the co
ntinuum\, local existence is proved for real analytic data by a Newton ite
ration scheme. Global existence for NLS with a regularized nonlinearity fo
llows by analyzing a local energy norm (arXiv:2003.08849 [math.AP]\, J.Sta
t.Phys\, 2020).\nThis is a joint work with Ben Dodson and Tom Spencer.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Tovbis (University of Central Florida)
DTSTART;VALUE=DATE-TIME:20200821T185000Z
DTEND;VALUE=DATE-TIME:20200821T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/11
DESCRIPTION:Title: Soliton and breather gases for the focusing Nonlinear S
chrödinger equation (fNLS): spectral theory and possible applications\nby
Alexander Tovbis (University of Central Florida) as part of TAMU: Mathema
tical Physics and Harmonic Analysis Seminar\n\n\nAbstract\nIn the talk we
introduce the idea of an "integrable gas" as a collection of large random
ensembles of special localized solutions (solitons\, breathers) of a given
integrable system. These special solutions can be treated as "particles".
Known laws of pairwise elastic collisions allow one to write the heuristi
c "equation of state" for the gas of such particles.\n\nIn this talk we co
nsider soliton and breather gases for the fNLS as special thermodynamic li
mits of finite gap (nonlinear multi phase wave) fNLS solutions. In this li
mit the rate of growth of the number of bands is linked with the rate of (
simultaneous) shrinkage of the size of individual bands. This approach lea
ds to the derivation of the equation of state for the gas and its certain
limiting regimes (condensate\, ideal gas limits)\, as well as construction
of various interesting examples. We also discuss the recent progress and
perspectives of future work\, as well as some possible applications.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seonghyeon Jeong (MSU)
DTSTART;VALUE=DATE-TIME:20200911T185000Z
DTEND;VALUE=DATE-TIME:20200911T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/12
DESCRIPTION:Title: Strong MTW type condition to local Holder regularity in
generated Jacobian equations\nby Seonghyeon Jeong (MSU) as part of TAMU:
Mathematical Physics and Harmonic Analysis Seminar\n\n\nAbstract\nn this
talk\, we present a proof of local Holder regularity of solutions to gener
ated Jacobian equations as a generalization of optimal transport case\, wh
ich is proved by George Loeper. We compare structures of generated Jacobia
n equations with optimal transport\, and point out differences with diffic
ulties which the differences can cause. For local Holder regularity theory
\, we use (G3s) condition and solution in Alexandrov sense. (G3s) is a str
ict positiveness type condition on MTW tensor associated to the generating
function G\, and Alexandrov solution is a solution that satisfies pullbac
k measure condition. (G3s) is used to show a quantitative version of (glp)
\, which gives some room for G-subdifferentials of solutions. Then the ine
quality for Holder regularity is shown by comparing volumes of G-subdiffer
entials using the fact that our solutions is in Alexandrov sense.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Breuer (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20201001T150000Z
DTEND;VALUE=DATE-TIME:20201001T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/13
DESCRIPTION:Title: Periodic Jacobi Matrices on Trees\nby Jonathan Breuer (
Hebrew University of Jerusalem) as part of TAMU: Mathematical Physics and
Harmonic Analysis Seminar\n\n\nAbstract\nThe theory of periodic Jacobi mat
rices on the line is extremely rich and very well studied. Viewing the lin
e as a regular tree of degree 2 leads to a natural generalization to perio
dic Jacobi matrices on general trees. This family of operators\, which is
at least as rich (by definition)\, but considerably less well understood\,
is at the center of this talk. We review some of the few known results\,
present some examples\, and discuss open problems and directions for futur
e research. The talk is based on joint work with Nir Avni and Barry Simon.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Delio Mugnolo (University of Hagen)
DTSTART;VALUE=DATE-TIME:20201008T150000Z
DTEND;VALUE=DATE-TIME:20201008T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/14
DESCRIPTION:Title: Bi-Laplacians on graphs: self-adjoint extensions and pa
rabolic theory\nby Delio Mugnolo (University of Hagen) as part of TAMU: Ma
thematical Physics and Harmonic Analysis Seminar\n\n\nAbstract\nElastic be
ams have been studied by means of hyperbolic equations driven by bi-Laplac
ian operators since the early 18th century: several properties of the corr
esponding parabolic equation on the whole Euclidean space have been discov
ered since the 1960s by Krylov\, Hochberg\, and Davies\, among others. On
a bounded domain or a metric graph\, the bi-Laplacian is generally not any
more acting as a squared operator\, though: this strongly affects the feat
ures of associated PDEs.\n\nI am going to present a full characterization
of self-adjoint extensions of the bi-Laplacian\, focusing on a class of re
alizations that encode dynamic boundary conditions. Maximum principles of
parabolic equations will also be discussed: after a transient time\, I am
going to show that solutions often display Markovian features.\n\nThis is
joint work with Federica Gregorio.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaqi Yang (GeorgiaTech)
DTSTART;VALUE=DATE-TIME:20200925T185000Z
DTEND;VALUE=DATE-TIME:20200925T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/15
DESCRIPTION:Title: Persistence of Invariant Objects in Functional Differen
tial Equations close to ODEs\nby Jiaqi Yang (GeorgiaTech) as part of TAMU:
Mathematical Physics and Harmonic Analysis Seminar\n\n\nAbstract\nWe cons
ider functional differential equations which are perturbations of ODEs in
$\\mathbb{R}^n$. This is a singular perturbation problem even for small pe
rturbations. We prove that for small enough perturbations\, some invariant
objects of the unperturbed ODEs persist and depend on the parameters with
high regularity. We formulate a-posteriori type of results in the case wh
en the unperturbed equations admit periodic orbits. The results apply to s
tate-dependent delay equations and equations which arise in the study of e
lectrodynamics. The proof is constructive and leads to an algorithm. This
is a joint work with Joan Gimeno and Rafael de la Llave.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Matos (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20201002T185000Z
DTEND;VALUE=DATE-TIME:20201002T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/16
DESCRIPTION:Title: Dynamical Contrast on Highly Correlated Anderson-type m
odels\nby Rodrigo Matos (Texas A&M University) as part of TAMU: Mathematic
al Physics and Harmonic Analysis Seminar\n\n\nAbstract\nWe present example
s of random Schödinger operators obtained in a similar fashion but exhibi
ting distinct transport properties. The models are constructed by connecti
ng\, in different ways\, infinitely many copies of the one dimensional And
erson model. \nSpectral aspects of the models will also be presented. In p
articular\, we obtain a physically motivated example of a random operator
with purely absolutely continuous spectrum where the transient and recurre
nt components coexist. This can be interpreted as a sharp phase transition
within the absolutely continuous spectrum. Time allowing\, I will discuss
some tools related to harmonic analysis\, including a version of Boole's
equality which\, to the best of our knowledge\, is new. Based on joint wor
k with Rajinder Mavi and Jeffrey Schenker.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farhan Abedin (Michigan State University)
DTSTART;VALUE=DATE-TIME:20201030T185000Z
DTEND;VALUE=DATE-TIME:20201030T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/18
DESCRIPTION:Title: Hele-Shaw Flow and Parabolic Integro-Differential Equat
ions\nby Farhan Abedin (Michigan State University) as part of TAMU: Mathem
atical Physics and Harmonic Analysis Seminar\n\n\nAbstract\nI will present
a regularization result for a special case of the two-phase Hele-Shaw fre
e boundary problem (a.k.a. interfacial Darcy flow)\, which models the evol
ution of two immiscible fluids flowing in the narrow gap between two paral
lel plates and subject to an external pressure source. Assuming that the f
luid interface is given by the graph of a function\, recent work of Chang-
Lara\, Guillen\, and Schwab establishes the equivalence between the Hele-S
haw free boundary problem and a first-order parabolic integro-differential
equation. By exploiting this equivalence and using available regularity t
heory for nonlocal parabolic equations\, we show that if the gradient of t
he graph of the fluid interface has a Dini modulus of continuity for all t
imes\, then the gradient must be Holder continuous. This is joint work wit
h Russell Schwab (MSU).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Kitagawa (Michigan State University)
DTSTART;VALUE=DATE-TIME:20201023T185000Z
DTEND;VALUE=DATE-TIME:20201023T195000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/19
DESCRIPTION:Title: On free discontinuities in optimal transport\nby Jun Ki
tagawa (Michigan State University) as part of TAMU: Mathematical Physics a
nd Harmonic Analysis Seminar\n\n\nAbstract\nIt is well known that regulari
ty results for the optimal transport (Monge-Kantorovich) problem require r
igid geometric restrictions. In this talk\, we consider the structure of t
he set of ``free discontinuities'' which arise when transporting mass from
a connected domain to a disconnected one\, and show regularity of this se
t\, along with a stability result under suitable perturbations of the targ
et measure. These are based on a non-smooth implicit function theorem for
convex functions\, which is of independent interest. This talk is based on
joint work with Robert McCann (Univ. of Toronto).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Egger (Technion)
DTSTART;VALUE=DATE-TIME:20201029T150000Z
DTEND;VALUE=DATE-TIME:20201029T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050526Z
UID:MPHA/20
DESCRIPTION:Title: Well-defined spectral position for Neumann domains\nby
Sebastian Egger (Technion) as part of TAMU: Mathematical Physics and Harmo
nic Analysis Seminar\n\n\nAbstract\nA Laplacian eigenfunction on a two-dim
ensional Riemannian manifold provides a natural partition generated by spe
cific gradient flow lines of the eigenfunction. The restricted eigenfuncti
on onto the partition's components satisfies Neumann boundary conditions a
nd the components are therefore coined 'Neumann domains'. Neumann domains
represent a complementary path to the famous nodal-domain partition to stu
dy elliptic eigenfunctions where the latter is associated with the Dirichl
et Laplacian. A very basic but fundamental property of nodal domains is th
at the restricted eigenfunction onto a nodal domain always gives the groun
d-state of the Dirichlet Laplacian. That feature becomes significantly mor
e complex for Neumann domains due to the presence of possible cusps and cr
acks. In this talk\, we focus on this problem and show that the spectral p
osition for Neumann domains is well-defined. Moreover\, we provide explici
t examples of Neumann domains displaying a fundamentally different behavio
r in their spectral position than their nodal-domain counterparts.\n
END:VEVENT
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