Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 21 al 27 settembre 2015
Martedì 22 settembre 2015
Ore 14:30, aula 311, Università degli Studi Roma Tre
(largo san L. Murialdo 1)
Seminario di Fisica Matematica
Niels Benedikter (University of Copenaghen)
Mean-Field Theory for Fermionic Mixed States
The dynamics of fermionic systems at high density can be described by
Hartree-Fock theory. At positive temperature, typical initial data are
quasifree mixed states (e.g. Gibbs state). I will explain how the Araki-Wyss
representation can be used to treat the positive temperature setting by
methods first developed for zero temperature, and use it to give a rigorous
derivation of the Hartree-Fock equations for mixed initial data.
Mercoledì 23 settembre 2015
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
Agata Smoktunowicz (Edinburgh)
On the Jacobson radical of noncommutative rings
The Jacobson radical of a ring was introduced in 1945 by Jacobson, and
has been studied ener since; consequently its structure is well understood.
Around 2007, Rump showed some surprising connections between Jacobson
radical rings and solutions to the Young-Baxter equation. In particular
he showed that Jacobson radical rings are in one-to-one correspondence
with two-sided braces. Recently, Gateva-Ivanova found that there is a
one-to-one correspondence between braces and symmetric groups in the sense
of Takeuchi, that is braided groups with the involutive Young-Baxter operator.
Hence Jacobson radical rings can be used to construct examples of braided groups
and braces. Moreover, every Jacobson radical ring yields a solution to the
Young-Baxter equation. In this talk we will look at some old and new methods
of constructing Jacobson radical rings and nil rings (recall that a nil ring
is a ring in which every element to some power is zero, and that every nil
ring is Jacobson radical). We then answer a question of Amberg and Sysak from
1997 by constructing a nil ring whose adjoint group is not an Engel group.
We also mention some other examples of Jacobson radical rings related to
differential polynomial rings.
Mercoledì 23 settembre 2015
Ore 16:00, aula di Consiglio
Seminario di Fisica Matematica
Andrea Di Stefano (Sapienza Università di Roma)
Kinetic description of random walks in Markov environments
We consider the random walk (RW) of a tagged particle moving in
Rd, d≥1, according to a jump process
and interacting with an evolving random environment (RE). The latter is
formed by infinitely many particles which evolve according to some
non-equilibrium Markov dynamics in Rd (e.g.
Birth-and-death dynamics, dynamics of jumping particles, etc.).
We describe different techniques to study the statistical evolution
in the course of the microscopic stochastic dynamics of RWRE.
In particular, we construct the evolution of correlation functions
satisfying a Ruelle-type bound and perform a mesoscopic (mean-field)
scaling limit to derive a system of two kinetic equations for the
densities of RE and of the tagged particle, respectively.
This system turns out to describe a non-autonomous RW where one takes
into account just a mean effect that particles of RE have on the motion
of the jumping particle.
Mercoledì 23 settembre 2015
Ore 16:00, aula Dal Passo, Università di Roma Tor Vergata
Yasuyuki Kawahigashi (University of Tokyo)
A remark on gapped domain walls between topological phases
Giovedì 24 settembre 2015
Ore 14:00, aula Dal Passo, Università di Roma Tor Vergata
Dynamical Systems Working Seminars
Micheal Jackobson (University of Maryland)
Ergodic properties of some attractors with countable Markov partitions
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