Thomas Spencer
(IAS (USA))
6/9/15, 9:30 AM
In this review talk I will explain how Falco's work on the Coulomb gas is
related to the 2D XY model at T_c. In 3D I will present some open problems
at low temperature
Roland Bauerschmidt
(Harvard Univ. (USA))
6/9/15, 11:00 AM
In a recent paper http://arxiv.org/abs/1311.2237, Pierluigi Falco
derived the detailed asymptotics of the correlation function of the
critical Coulomb system in two dimensions at low density, as predicted
by Berezinskii, Kosterlitz and Thouless. In this first of a two part
lecture
we will review this result and explain some key ideas in this remarkable
achievement.
David Brydges
(British Columbia Univ. (Canada))
6/9/15, 12:00 PM
In a recent paper http://arxiv.org/abs/1311.2237, Pierluigi Falco
derived the detailed asymptotics of the correlation function of the
critical Coulomb system in two dimensions at low density, as predicted
by Berezinskii, Kosterlitz and Thouless. In this second of a two part
lecture
we will review this result and explain some of key ideas in this remarkable
achievement.
Giovanni Gallavotti
(INFN - Roma 1/ Rutgers University)
6/9/15, 2:30 PM
A manifestation of the Kondo effect is the non divergence at zero
temperature
of the susceptibility of an impurity magnetization to the action of a
field. It is a quantum phenomenon not accessible to perturbation theory
because it is essential that the interaction with the host lattice
electrons is antiferromagnetic, no matter how small. Its theory in one
dimension, due to Wilson, is...
Giuseppe Benfatto
(Tor Vergata Univ.)
6/9/15, 3:30 PM
In the last twenty years, many people in Rome have studied various
types of Fermion models, by applying rigorous RG techniques. One of
these people was Pierluigi Falco and the paper I will speak about,
written in collaboration with Vieri Mastropietro and myself, was
his last one.
The line of research on rigorous RG was open at the end of the 80's
by Giovanni Gallavotti, who published...
Prof.
Vieri Mastropietro
(Universita' di Roma Tor Vergata)
6/9/15, 4:30 PM
Around 2007 Pierluigi Falco sent me a two line mail writing
something like "then we can prove the kadanoff relation $x_- x_+=1$". This
was the end of a two year discussion between we two (which I will be
recall in my seminar)
on the renormalization/non renormalization of the anomalies in quantum
field theory and its implications for universality in statistical
mechanics; the complete...
Prof.
Juerg Froehlich
(ETH Zurich)
6/10/15, 9:30 AM
I present an outline of the theory of information acquisition in quantum mechanics. I discuss some relevant mathematical techniques from functional analysis and probability theory needed to develop this theory. In order to keep the presentation down to earth, I focus on the discussion of concrete examples of indirect and non-demolition measurements.
Marcello Porta
(Zurich Univ.)
6/10/15, 11:00 AM
Graphene is a recently discovered material, which can be
considered as the first realization of a two-dimensional crystal. Its
unique physical properties elicited great interest in the condensed matter
physics community, both from a theoretical and an experimental point of
view.
Remarkably, some interesting features of graphene can be understood from a
mathematically rigorous viewpoint....
Prof.
Alessandro Giuliani
(Univ. Roma Tre)
6/10/15, 12:00 PM
Perfect matchings of Z^2 (also known as non-interacting dimers on the
square lattice) are an exactly solvable 2D statistical mechanics model. It
is known that the associated height function behaves at large distances
like a massless gaussian field, with the variance of height gradients
growing logarithmically with the distance. As soon as dimers mutually
interact, via e.g. a local energy...
Pronob K. Mitter
(Montpellier Univ. (France))
6/10/15, 2:30 PM
There is considerable interest at present in Singular
Stochastic PDEs especially
in connection with Rough Path Theory in different guises. The mathematical
work started with results by Gianni Jona-Lasinio
and myself a long time ago. I will review what was was accomplished at
the time and the progress that
has been made since then. One reason for presenting this to this audience
is...
Gianni Jona-Lasinio
(INFN - Roma 1)
6/10/15, 3:30 PM
We consider SPDE's whose solutions are distribution-valued fields. An
example is provided by the stochastic quantization of a scalar field in
d=2,3 where infinite counter-terms are necessary. We review large
deviation estimates for probabilistic weak solutions in d=2, derived long ago
with P. K. Mitter, which show that the rate functional does not depend on the
renormalization counter...
Benedetto Scoppola
(Univ. Tor Vergata Roma)
6/10/15, 4:30 PM
We will discuss the connection between the cluster expansion
and the probabilistic method, used in order
to give a-priori bounds for discrete combinatorics problems.
Accurate estimates of the radius of convergence of the cluster
expansion, as the Fernandez-Procacci construction, allow better
estimates in the related combinatorics
problems. We provide concrete examples of applications of...
Christoph Kopper
(Ecole Polytechnique Palaiseau)
6/11/15, 9:30 AM
We prove that the cancellation of the chiral anomaly
in four-dimensional axial QED, as a consequence of a
sum rule on the fermion charges, is valid to all
orders in perturbation theory. The proof is based on
analysing separately the fermionic and bosonic
renormalization group flows.
Abdelmalek Abdesselam
(Virginia Univ. (USA))
6/11/15, 11:00 AM
Hierarchical models a.k.a. the approximate recursion played a
fundamental role in the discovery
of the epsilon-expansion for critical exponents by Wilson and Fisher. In
a not so well known 1972 article,
Wilson showed, at the heuristic level, that at a nontrivial hierarchical
model fixed point, the elementary field
has no anomalous scaling whereas the composite square field does...
Alvaro Ferraz
(Rio Grande do Norte Univ. (Brazil))
6/11/15, 12:00 PM
We present an overview of the field-theoretical renormalzation group
approach for interacting electrons in the normal phase of the optimally
doped cuprates. Earlier calculations predicted the existence of d-wave
charge density instabilities(d-CDW) which were later verifed in several
experiments in non-Lanthanum materials. However the onset of the so-called
pseudogap state remains an open...
Dr
Michele Correggi
(Roma Tre University)
6/11/15, 2:30 PM
We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $ S \geq \frac{1}{2} $. We report on a rigorous proof of the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution
to the free energy at low temperatures. Our proof comes with explicit,
constructive upper and lower bounds on the error...
Federico Bonetto
(Georgia Tech - Atlanta)
6/11/15, 3:30 PM
We rigorously analyze the quantum phase transition between a
metallic and an
insulating phase in (non solvable) interacting spin chains or one
dimensional
fermionic systems. In particular, we prove the persistence of Luttinger
liquid behavior in the presence of an interaction even arbitrarily close to
the critical point, where the Fermi velocity vanishes and the two Fermi
points...
