Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo
Sapienza Università di Roma
Settimana dall'8 al 14 ottobre 2018
Lunedì 8 ottobre 2018
Ore 12:00, aula di Consiglio
seminario di Dipartimento
Alessandro Teta (Sapienza Università di Roma)
Alcuni problemi matematici in Meccanica Quantistica
Si discutono alcuni risultati che riguardano comportamenti effettivi
di sistemi quantistici a bassa energia, caratterizzati da un singolo
parametro fisico noto come lunghezza di scattering. Si fara' inoltre
cenno al problema, di natura anche concettuale, di descrivere l'emergere
di comportamenti classici in sistemi quantistici.
Lunedì 8 ottobre 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Francesca De Marchis (Sapienza Università di Roma)
Uniqueness via Morse index of positive solutions of the Lane-Emden problem
We present a Morse index computation for positive solution of the classical
Lane-Emden problem in planar domains, obtained via an accurate asymptotic analysis
of the solutions as the exponent tends to infinity. When the domain in convex this
result allows to prove uniqueness of positive solutions (for large values of the
exponent), giving a first positive general answer to a conjecture raised by Dancer
[JDE, 1979]. The results are obtained in collaboration with M. Grossi, I. Ianni and F. Pacella.
Lunedì 8 ottobre 2018
Ore 16:00, aula B
seminario/corso di Fisica Matematica
Soeren Fournais (Aarhus Universitet)
On upper bounds to the energy of the dilute Bose gas
In this course we will review recent work on the different
upper bounds for the ground state energy of a gas of interacting bosons
in the thermodynamic limit. We start by considering quasi-free states to
realize that these reproduce the leading order asymptotics of the energy
but not the expected first correction term. This part is based on work
by Erdos-Schlein-Yau and Napiorkowski-Reuvers-Solovej. Then we pass to
the more involved trial states by Yau-Yin and prove that such a state
can indeed give the expected correction term.
The course will essentially be elementary. Only a basic knowledge of
mathematical quantum mechanics will be needed.
Mercoledì 10 ottobre 2018
Ore 14:00, aula di Consiglio
seminario di Algebra e Geometria
Catriona Maclean (Université Grenoble Alpes)
Classifying approximable algebras
Approximable algebras, introduced by Huayi Chen, are those
for which a Fujita-type theorem holds.
Any full dimensional sub-algebra of the section algebra of a big line
bundle is approximable : we will see that the converse is false, but
becomes true if the notion of big line bundle is somewhat generalised.
Mercoledì 10 ottobre 2018
Ore 16:00, aula di Consiglio
seminario/corso di Fisica Matematica
Soeren Fournais (Aarhus Universitet)
On upper bounds to the energy of the dilute Bose gas
In this course we will review recent work on the different
upper bounds for the ground state energy of a gas of interacting bosons
in the thermodynamic limit. We start by considering quasi-free states to
realize that these reproduce the leading order asymptotics of the energy
but not the expected first correction term. This part is based on work
by Erdos-Schlein-Yau and Napiorkowski-Reuvers-Solovej. Then we pass to
the more involved trial states by Yau-Yin and prove that such a state
can indeed give the expected correction term.
The course will essentially be elementary. Only a basic knowledge of
mathematical quantum mechanics will be needed.
Mercoledì 10 ottobre 2018
Ore 16:00, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario di Algebre di Operatori
Alexander Stottmeister
Operator algebras, lattice gauge theory, and renormalization
We will discuss an operator-algebraic approach to lattice gauge theory
and its relation to a recent construction by Jones of representations of
the Thompson group. Furthermore, we will outline a framework of rigorous
renormalization group theory and scaling/continuum limits in this
context.
Giovedì 11 ottobre 2018
Ore 14:30, aula 211, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Geometria
Eduardo Esteves (IMPA, Rio de Janeiro)
Limit linear series: an approach for all stable curves
I will present an approach to extend Eisenbud's and Harris' notion
of limit linear series to all stable curves. I will describe the objects,
how they vary in families and how a fine moduli space for them can be constructed.
The talk is based on ongoing work with Omid Amini (ENS Paris).
Venerdì 12 ottobre 2018
Ore 14:00, aula B
seminario/corso di Fisica Matematica
Soeren Fournais (Aarhus Universitet)
On upper bounds to the energy of the dilute Bose gas
In this course we will review recent work on the different
upper bounds for the ground state energy of a gas of interacting bosons
in the thermodynamic limit. We start by considering quasi-free states to
realize that these reproduce the leading order asymptotics of the energy
but not the expected first correction term. This part is based on work
by Erdos-Schlein-Yau and Napiorkowski-Reuvers-Solovej. Then we pass to
the more involved trial states by Yau-Yin and prove that such a state
can indeed give the expected correction term.
The course will essentially be elementary. Only a basic knowledge of
mathematical quantum mechanics will be needed.
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