Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 12 al 18 marzo 2018
Lunedì 12 marzo 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Jens Wirth (Universitat Stuttgart)
Global calculus of differential operators on groups and homogeneous spaces
The talk will provide a short overview on the global calculus of operators on Lie groups
and their homogeneous spaces with particular focus on the (simpler) compact case.
Results include global characterisations of hypo-elliptic operators, spectral calculus
results within global classes of pseudo-differential operators and calculus-based proofs
of mapping properties for such operators.
Lunedì 12 marzo 2018
Ore 16:00, aula di Consiglio
seminario di Probabilità
Federico Camia (New York - Dubai University)
Limit Theorems and Random Fractal Curves in Statistical Mechanics
Rigorous statistical mechanics deals with stochastic systems that have a large number
of components and for which geometry often plays an important role. The main goal is to
understand their average behavior and deviations from that. Statistical mechanics has
many applications to physics and other fields, but in this talk I will only focus on some
aspects of its mathematical theory which combine discrete probability, stochastic processes
and complex analysis. For concreteness, I will discuss two specific (two-dimensional) models,
percolation and the Ising model, both with a long history. After introducing the two models,
I will present an approach to the study of two-dimensional systems that leads to a special
family of random fractal curves and that has produced, in the last twenty years, deep results
and major breakthroughs.
Martedì 13 marzo 2018
Ore 14:30, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario di Equazioni Differenziali
Tobias Weth (Goethe-University Frankfurt)
Serrin's overdetermined problem on the sphere
In this talk, I will discuss Serrin's overdetermined boundary value problem
u=0, ∂ηu=c on ∂Ω
Martedì 13 marzo 2018
Ore 14:30, aula 311, pal. C, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Fisica Matematica
G. Marcelli (Sapienza Università di Roma)
Spin conductance and spin conductivity in topological insulators: analysis of Kubo-like terms
We investigate spin transport in 2-dimensional insulators, with the long-term goal of establishing
whether any of the transport coefficients corresponds to the Fu-Kane-Mele index which characterizes
2d time-reversal-symmetric topological insulators.
Inspired by the Kubo theory of charge transport, and by using a proper definition of the spin current
operator [Phys. Rev. Lett. 96, 076604 (2006)], we define the Kubo-like spin conductance GK
and spin conductivity σK. We prove that for any gapped, periodic, near-sighted
discrete Hamiltonian, the above quantities are mathematically well-defined and the
equality GK=σK holds true.
Moreover, we argue that the physically relevant condition to obtain the equality above is
the vanishing of the mesoscopic average of the spin-torque response, which holds true under our hypotheses
on the Hamiltonian operator. This vanishing condition might be relevant in view of further extensions
of the result, e.g. to ergodic random discrete Hamiltonians or to Schrodinger operators on the continuum.
A central role in the proof is played by the trace per unit volume and by two generalizations of the trace,
the principal value trace and its directional version.
This seminar is based on joint work with Gianluca Panati (La Sapienza, Roma) and Clement Tauber (ETH, Zurich).
Martedì 13 marzo 2018
Ore 15:00, aula di Consiglio
seminario di Modellistica Differenziale Numerica
Silvia Falletta (Politecnico di Torino)
Metodi FEM-BEM di tipo spazio-tempo per la risoluzione di problemi di
propagazione di onde in domini illimitati
In questo seminario presenterò problemi di propagazione di onde in domini
illimitati bi e tridimensionali. Per la risoluzione di tali problemi mediante metodi FEM,
considererò una condizione non riflettente basata su un'equazione integrale di tipo
spazio-tempo, discretizzata in tempo mediante formule di quadratura di convoluzione di
Lubich e in spazio mediante un metodo di Galerkin o di collocazione. Oltre a risultare
numericamente stabile e a mostrare un'ottimale accuratezza, la condizione NRBC ha la
proprietà di poter essere applicata a contorni artificiali di forma generica; inoltre,
dal punto di vista numerico, risulta competitiva con ben note (ma meno accurate) condizioni
NRBC di tipo locale. L'approccio proposto è stato applicato a diversi problemi di propagazione
di onde: onde acustiche generate da sorgenti localizzate lontano dall'ostacolo, scatterate
da uno o più ostacoli fissi o in movimento, onde sismiche che si propagano in mezzi
isotropi. I risultati numerici ottenuti dimostrano l'efficienza e l'accuratezza del metodo proposto.
Martedì 13 marzo 2018
Ore 15:30, aula 311, pal. C, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Probabilità
Federico Camia (New York University, Abu Dhabi)
Scaling Limits for the Planar Ising Model
behavior of lattice models of statistical mechanics. In the scaling limit, the lattice spacing is sent
to zero while focus is kept on some macroscopic object or collection of objects within the model.
In the last twenty years there has been tremendous progress in the study of the continuum scaling limits
of some classical models, such as two-dimensional percolation and the planar Ising model, which are of
interest because they undergo a phase transition. At or near the phase transition point the scaling limit
is supposed to give rise to a Euclidean field theory. In this talk I will briefly introduce the planar
Ising model and then describe some recent results concerning the scaling limit of the Ising magnetization
and the truncated two-point function. The talk is based on joint work with Christoph Garban and Chuck Newman,
Rene Conijn and Demeter Kiss, and Jianping Jiang and Chuck Newman.
Mercoledì 14 marzo 2018
Ore 16:00, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario
Stefano Viaggiu (Università di Roma Tor Vergata)
A statistical description of black hole entropy, its corrections and the origin of the
cosmological constant
We present a new approach to describe the Black hole entropy in terms of trapped gravitons inside
the event horizon. The discrete spectrum of the so trapped gravitons is obtained together with the
thermodynamical quantities. Moreover, we obtain the log corrections to the black hole entropy by
means of a (Planckian) mechanism converting radiation into a gamma linear equation of state.
Finally, it is shown how with the help of this mechanism, a statistical description of the dark
energy is indeed possible.
Giovedì 15 marzo 2018
Ore 14:30, aula di Consiglio
seminario P(n)/N(p)
Riccardo Molle (Università di Roma Tor Vergata)
Infinitely many solutions for some Schroedinger equations
The talk deals with a classical model Schroedinger equation (P), with subcritical nonlinearity.
Problem (P) has been widely investigated since the '50s but only in recent years the question
of the existence of infinitely many positive nonradial solutions has been addressed.
Actually, the problem has been solved with some additional assumptions on the shape of the
potential (f.i. symmetry or smallness) or on the dimension of the space. Here we present some
results concerning the existence of infinitely many positive solutions without those assumptions.
We find solutions with finite and with infinite energy (joint works with D. Passaseo).
Finally also a result on the existence of infinitely many nodal solutions is presented (joint
work with G. Cerami and D. Passaseo). The methods used in the proofs are completely variational.
Giovedì 15 marzo 2018
Ore 14:30, aula 211, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Geometria
Pietro De Poi (Università di Udine)
Fano Congruences
We study congruences of lines of Pn (i.e. subvarieties of the Grassmannian of
(co)dimension n-1) X defined by 3-forms, a class of congruences that are irreducible components of
some reducible linear congruences, and their residual Y.
We prove that X, and its fundamental locus F if n is odd, are Fano varieties of index 3 and that X
is smooth; F is smooth as well if n<10.
We study the Hilbert scheme of these congruences X, proving that the choice of the 3-form bijectively
corresponds to X, except when n=5. Y is analysed in terms of the quadrics containing the linear span
of X and we determine the singularities and the irreducible components of its fundamental locus.
Joint work with Emilia Mezzetti, Daniele Faenzi and Kristian Ranestad.
Venerdì 16 marzo 2018
Ore 14:00, aula D'Antoni, dipartimento di Matematica,
Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario
Kirill Zainoulline (University of Ottawa)
Equivariant oriented cohomology and generalized Schubert calculus
This lecture can be viewed as an introduction to algebraic oriented cohomology theories (cohomology/Chow
groups, K-theory, (local) elliptic cohomology, algebraic cobordism, etc.) and their (mostly T-)equivariant
analogues. Our basic motivating example is the algebraic cobordism Omega which was constructed by
Levine-Morel around 05's.
This theory serves as an algebraic analogue of the usual complex cobordism from algebraic topology of 60's
(similarly, the Chow group serves as an algebraic version of the usual singular cohomology).
We explain a general procedure which allows to compute such theories for generalized flag varieties G/P.
The talk is based on my joint results with Calmes, Petrov, Zhong and others.
Venerdì 2 marzo 2018
Ore 15:30, aula D'Antoni, dipartimento di Matematica,
Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario
Kirill Zainoulline (University of Ottawa)
Equivariant motives and Sheaves on moment graphs
Goresky, Kottwitz and MacPherson showed that the equivariant cohomology of varieties equipped with an
action of a torus T can be described using the so called moment graph, hence, translating computations
in equivariant cohomology into a combinatorial problem. Braden and MacPherson proved that the information
contained in this moment graph is sufficient to compute the equivariant intersection cohomology of the
variety. In order to do this, they introduced the notion of a sheaf on moment graph whose space of
sections (stalks) describes the (local) intersection cohomology. These results motivated a series of
paper by Fiebig, where he developed and axiomatized sheaves of moment graphs theory and exploited
Braden-MacPherson's construction to attack representation theoretical problems.
In the talk we explain how to extend this theory of sheaves on moment graphs to an arbitrary algebraic
oriented equivariant cohomology h in the sense of Levine-Morel (e.g. to K-theory or algebraic cobordism).
Moreover, we show that in the case of a total flag variety X the space of global sections of the
respective h-sheaf also describes an endomorphism ring of the equivariant h-motive of X.
This is a very recent joint work with Rostislav Devyatov and Martina Lanini.
Venerdì 16 marzo 2018
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Carlotta Maffei (Sapienza Università di Roma) e altri
La vita e la matematica del mondo miscoscopico - parte II
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