BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jürg Fröhlich (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20200709T150000Z
DTEND;VALUE=DATE-TIME:20200709T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/1
DESCRIPTION:Title: Res
ults on interacting Bose Gases\nby Jürg Fröhlich (ETH Zürich) as pa
rt of Analysis\, Quantum Fields\, and Probability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AQFP/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thierry Bodineau (Ecole Polytechnique)
DTSTART;VALUE=DATE-TIME:20200917T150000Z
DTEND;VALUE=DATE-TIME:20200917T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/2
DESCRIPTION:Title: Log
-Sobolev inequality for the continuum sine-Gordon model\nby Thierry Bo
dineau (Ecole Polytechnique) as part of Analysis\, Quantum Fields\, and Pr
obability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AQFP/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Aizenman (Princeton)
DTSTART;VALUE=DATE-TIME:20201210T160000Z
DTEND;VALUE=DATE-TIME:20201210T173000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/3
DESCRIPTION:Title: Mar
ginal triviality of the scaling limits of 4D critical Ising and $\\Phi^4$
models\nby Michael Aizenman (Princeton) as part of Analysis\, Quantum
Fields\, and Probability\n\n\nAbstract\nThe talk will present the recent p
roof that in four\ndimensions the spin fluctuations of Ising-type models a
t their critical\npoints are Gaussian in their scaling limits (infinite vo
lume\, vanishing\nlattice spacing). Similar statement is proven for the s
caling limits of\nmore general $\\Phi^4$ fields constructed through a latt
ice cutoff. The\nproofs are facilitated by the systems’ random current r
epresentation\, in\nwhich the deviation from Wick's law are expressed in t
erms of\nintersection probabilities of random currents with prescribed sou
rces.\nThis approach previously yielded such statements for D>4. Their rec
ent\nextension to the marginal dimension was enabled by a multiscale analy
sis\nof the critical clusters’ intersections. (Joint work with Hugo\nD
uminil-Copin.)\n
LOCATION:https://researchseminars.org/talk/AQFP/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Vargas (Ecole Normale Supérieure)
DTSTART;VALUE=DATE-TIME:20201112T160000Z
DTEND;VALUE=DATE-TIME:20201112T173000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/4
DESCRIPTION:Title: Lio
uville conformal field theory: equivalence between the path integral and t
he bootstrap construction\nby Vincent Vargas (Ecole Normale Supérieur
e) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nL
iouville conformal field theory (LCFT) is a family of Conformal field theo
ries which arise in a wide variety of contexts in the physics and the prob
abilistic literature: SUSY Yang-Mills\, the scaling limit of large planar
maps\, etc... There are two main and seemingly unrelated approaches to LCF
T in the physics literature: one in the Feynman path integral formulation
and one in the conformal bootstrap approach. Recently\, we constructed rig
orously LCFT in the Feynman path integral formulation via probability theo
ry (and more specifically the Gaussian Free Field). In this talk\, I will
present recent work which shows that both approaches (probabilistic constr
uction of the Feynman path integral and conformal bootstrap) are in fact i
dentical. A key ingredient in our work is the analysis of an infinite dime
nsional semigroup\, the so-called Liouville semigroup. Based on a series o
f joint works with C. Guillarmou\, F. David\, A. Kupiainen and R. Rhodes.\
n
LOCATION:https://researchseminars.org/talk/AQFP/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slava Rychkov (IHES)
DTSTART;VALUE=DATE-TIME:20201008T150000Z
DTEND;VALUE=DATE-TIME:20201008T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/5
DESCRIPTION:Title: CFT
Osterwalder-Schrader Theorem\nby Slava Rychkov (IHES) as part of Anal
ysis\, Quantum Fields\, and Probability\n\n\nAbstract\nMost QFT axioms are
only good to prove theorems but not to compute anything measurable. One e
xception are the Euclidean Conformal Field Theory (CFT) axioms in d>=3 dim
ensions\, which do lead to surprisingly strong “bootstrap" constraints o
n scaling dimensions of various conjecturally existing Euclidean CFTs (suc
h as the critical point of the 3d Ising and O(2) models). In this talk I w
ill not discuss the bootstrap as such\, but I will explain the Euclidean C
FT axioms and will relate them to the Osterwalder-Schrader and Wightman ax
ioms. The OS linear growth condition does not obviously follow from the Eu
clidean CFT axioms\, but fortunately there is a route to Wightman axioms w
hich does not rely on the Glaser-Osterwalder-Schrader construction. Based
on work in progress with Petr Kravchuk and Jiaxin Qiao.\n
LOCATION:https://researchseminars.org/talk/AQFP/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcello Porta (SISSA)
DTSTART;VALUE=DATE-TIME:20210114T160000Z
DTEND;VALUE=DATE-TIME:20210114T173000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/6
DESCRIPTION:Title: Ano
maly non-renormalization in interacting Weyl semimetals\nby Marcello P
orta (SISSA) as part of Analysis\, Quantum Fields\, and Probability\n\n\nA
bstract\nWeyl semimetals are three-dimensional condensed matter systems ch
aracterized by a degenerate Fermi surface\, consisting of a pair of `Weyl
nodes'. Correspondingly\, in the infrared limit\, these systems behave eff
ectively as Weyl fermions in 3+1 dimensions. As predicted by Nielsen and N
inomiya in 1983\, when exposed to electromagnetic fields these materials a
re expected to simulate the axial anomaly of QED\, by giving rise to a net
quasi-particle flow between Weyl nodes.\n \n\nWe consider a class of inte
racting lattice models for Weyl semimetals and prove that the quadratic re
sponse of the quasi-particle flow is universal\, and equal to the chiral t
riangle graph of QED. Universality is the counterpart of the Adler-Bardeen
non-renormalization property of the axial anomaly for QED\, in a condense
d matter setting. Our proof relies on the rigorous Wick rotation for real-
time transport coefficients\, on constructive bounds for Euclidean ground
state correlations\, and on lattice Ward Identities. Joint work with A. Gi
uliani and V. Mastropietro.\n
LOCATION:https://researchseminars.org/talk/AQFP/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laszlo Erdös (IST Austria)
DTSTART;VALUE=DATE-TIME:20210211T160000Z
DTEND;VALUE=DATE-TIME:20210211T173000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/7
DESCRIPTION:Title: Eig
enstate thermalisation hypothesis and functional CLT for Wigner matrices\nby Laszlo Erdös (IST Austria) as part of Analysis\, Quantum Fields\,
and Probability\n\n\nAbstract\nWe prove that any deterministic matrix is
approximately the identity in the eigenbasis of a large random Wigner matr
ix W with an optimal error inversely proportional to the square root of th
e dimension. This verifies a strong form of Quantum Unique Ergodicity wit
h an optimal convergence rate and we also prove Gaussian fluctuations arou
nd this convergence after a small spectral averaging. This requires to ext
end the classical CLT for linear eigenvalue statistics\, Tr f(W)\, to incl
ude a deterministic matrix A and we identify three different modes of fl
uctuation for Tr f(W)A in the entire mesoscpic regime. The key technical t
ool is a new multi-resolvent local law for Wigner ensemble.\n
LOCATION:https://researchseminars.org/talk/AQFP/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Longo (Roma "Tor Vergata")
DTSTART;VALUE=DATE-TIME:20210311T160000Z
DTEND;VALUE=DATE-TIME:20210311T173000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/8
DESCRIPTION:Title: The
massive modular Hamiltonian\nby Roberto Longo (Roma "Tor Vergata") as
part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nA solu
tion of the Klein-Gordon equation can be viewed as a signal carried by a c
lassical wave packet\, or as the wave function of a quantum particle\, or
as a coherent state in Quantum Field Theory. Our recent work concerns the
definition\, computation and interpretation of the local entropy of this o
bject and its relation to quantum energy inequalities. The Operator Algebr
aic approach\, in particular the Tomita-Takesaki modular theory\, provides
a natural framework and powerful methods for our analysis. In this talk\,
I will discuss part of the general ground for our analysis and some key r
esults\, in particular the solution of an old problem in QFT: the descript
ion of the modular Hamiltonian associated with a space ball B in the free
scalar massive QFT\; this sets up the formula for the entropy density of a
real wave packet.\n
LOCATION:https://researchseminars.org/talk/AQFP/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Weber (Bath)
DTSTART;VALUE=DATE-TIME:20210610T150000Z
DTEND;VALUE=DATE-TIME:20210610T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/9
DESCRIPTION:Title: Gib
bs measures in infinite dimensions - Some new results on a classical topic
\nby Hendrik Weber (Bath) as part of Analysis\, Quantum Fields\, and P
robability\n\n\nAbstract\nGibbs measures on spaces of functions or distrib
utions play an important role in \nvarious contexts in mathematical physic
s. They can\, for example\, be viewed as continuous \ncounterparts of cla
ssical spin models such as the Ising model\, they are an important steppin
g \nstone in the rigorous construction of Quantum Field Theories\, and the
y are invariant under the \nflow of certain dispersive PDEs\, permitting t
o develop a solution theory with random initial data\, \nwell below the de
terministic regularity threshold. \n\nThese measures have been constructed
and studied\, at least since the 60s\, but over the last few \nyears ther
e has been renewed interest\, partially due to new methods in stochastic a
nalysis\, including\nHairer’s theory of regularity structures and Gubine
lli-Imkeller-Perkowski’s theory of \nparacontrolled distributions. \n\nI
n this talk I will present two independent but complementary results that
can be obtained with \nthese new techniques. I will first show how to obta
in estimates on samples from of the Euclidean \n$\\phi^4_3$ measure\, base
d on SPDE methods. I will then discuss a new method to show the \nemergenc
e of phase transitions in the phi^4_3 theory. \n\nThis is based on joint w
orks with \nA. Chandra\, A. Moinat https://arxiv.org/abs/1910.13854\n\n
and \n\nA. Chandra\, T. Gunaratnam https://arxiv.org/abs/2006.15933\n
LOCATION:https://researchseminars.org/talk/AQFP/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Faulkner
DTSTART;VALUE=DATE-TIME:20210408T150000Z
DTEND;VALUE=DATE-TIME:20210408T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/10
DESCRIPTION:Title: Al
gebraic approach to quantum error correction and the AdS/CFT correspondenc
e\nby Thomas Faulkner as part of Analysis\, Quantum Fields\, and Proba
bility\n\n\nAbstract\nI will discuss the quantum error correction (QEC) ap
proach to the AdS/CFT correspondence from an algebraic point of view. I w
ill study exact QEC codes as models of AdS/CFT and connect these models to
Longo-Rehren subnets. I do this by proving the existence of a consistent
assignment of conditional expectations acting on the boundary theory algeb
ras. I will also discuss shortcomings of these exact codes that will hopef
ully be fixed by introducing small errors.\n
LOCATION:https://researchseminars.org/talk/AQFP/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andras Vasy (Stanford)
DTSTART;VALUE=DATE-TIME:20210701T150000Z
DTEND;VALUE=DATE-TIME:20210701T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/11
DESCRIPTION:Title: Th
e Feynman propagator and its positivity properties\nby Andras Vasy (St
anford) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstra
ct\nOne usually considers wave equations as evolution equations\, i.e. imp
oses initial data and solves them. Equivalently\, one can consider the for
ward and backward solution operators for the wave equation\; these solve a
n equation $Lu=f$\, for say $f$ compactly supported\, by demanding that $u
$ is supported at points which are reachable by forward\, respectively bac
kward\, time-like or light-like curves. This property corresponds to causa
lity. But it has been known for a long time that in certain settings\, suc
h as Minkowski space\, there are other ways of solving wave equations\, na
mely the Feynman and anti-Feynman solution operators (propagators). I will
explain a general setup in which all of these propagators are inverses of
the wave operator on appropriate function spaces\, and also mention posit
ivity properties\, and the connection to spectral and scattering theory in
Riemannian settings\, self-adjointness\, as well as to the classical para
metrix construction of Duistermaat and Hormander.\n
LOCATION:https://researchseminars.org/talk/AQFP/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abdelmalek Abdesselam (U Virginia)
DTSTART;VALUE=DATE-TIME:20211014T150000Z
DTEND;VALUE=DATE-TIME:20211014T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/12
DESCRIPTION:Title: Ex
ploring conformal invariance with hierarchical models\nby Abdelmalek A
bdesselam (U Virginia) as part of Analysis\, Quantum Fields\, and Probabil
ity\n\n\nAbstract\nIn the context of the AdS/CFT correspondence\, in Eucli
dean signature\, an important basic fact is the bijection between conforma
l transformations of the boundary and hyperbolic isometries of the bulk. A
n infinite regular tree with the graph distance can be seen as a quintesse
ntial bare-bones version of a hyperbolic space. It turns out there is a na
tural way to define analogues of conformal maps on the boundary of such a
tree and\, quite miraculously\, these are in bijection with tree isometrie
s. Moreover\, a Euclidean QFT on this boundary is the same as a hierarchic
al model as considered by Dyson in his study of the long-range Ising model
and by Wilson when he introduced the approximate renormalization group re
cursion. I will try to give a pedagogical introduction to this circle of i
deas\, and I will discuss a particular model where there is hope to be abl
e to prove conformal invariance from first principles via a rigorous nonpe
rturbative renormalization group approach.\n
LOCATION:https://researchseminars.org/talk/AQFP/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Chatterjee (Stanford)
DTSTART;VALUE=DATE-TIME:20211111T160000Z
DTEND;VALUE=DATE-TIME:20211111T173000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/13
DESCRIPTION:Title: So
me progress on 3D Yang-Mills\nby Sourav Chatterjee (Stanford) as part
of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nI will talk
about some recent progress on the problem of constructing 3D Euclidean Yan
g-Mills theories. This is based on joint work with Sky Cao.\n
LOCATION:https://researchseminars.org/talk/AQFP/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiko Ogata (Tokyo)
DTSTART;VALUE=DATE-TIME:20220113T120000Z
DTEND;VALUE=DATE-TIME:20220113T133000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/14
DESCRIPTION:Title: An
invariant of symmetry protected topological phases with on-site finite gr
oup symmetry for two-dimensional Fermion systems\nby Yoshiko Ogata (To
kyo) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\
nWe consider SPT-phases with on-site finite group G symmetry for two-dimen
sional Fermion systems.We derive an invariant of the classification.\n
LOCATION:https://researchseminars.org/talk/AQFP/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Kennedy (Arizona)
DTSTART;VALUE=DATE-TIME:20211209T160000Z
DTEND;VALUE=DATE-TIME:20211209T173000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075520Z
UID:AQFP/15
DESCRIPTION:Title: Re
normalization group maps for Ising models and tensor networks\nby Tom
Kennedy (Arizona) as part of Analysis\, Quantum Fields\, and Probability\n
\n\nAbstract\nWe will briefly review Wilson-Kadanoff type renormalization
group (RG) maps for Ising spin systems and the lack of progress in provin
g that there is a non-trivial fixed point for these maps. (These maps are
also known as real-space RG transformations.) The Ising model can be writt
en as a tensor network\, and RG maps can be defined in the tensor network
formalism. Numerical studies of such RG maps have been quite successful at
reproducing the known critical behavior in two dimensions. In joint work
with Slava Rychkov we proved that in two dimensions for a particular tenso
r network RG map the high temperature fixed point is locally stable\, i.e.
\, there is a neighborhood of the high temperature fixed point such that f
or an initial tensor in this neighborhood\, the iterations of the RG map c
onverge to the high temperature fixed point. We hope that this is a modest
first step towards proving the existence of a non-trivial fixed point for
a tensor network RG map which would correspond to the critical point of t
he Ising model.\n
LOCATION:https://researchseminars.org/talk/AQFP/15/
END:VEVENT
END:VCALENDAR