Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 15 al 22 maggio 2017
Lunedì 15 maggio 2017
Ore 10:30, aula 009, Università di Roma Tre,
largo san L. Murialdo 1
minicorso di Geometria
David Jensen (University of Kentucky)
Tropical linear series, I
In this series of talks, we will discuss the basic combinatorial
theory of divisors on graphs and its relationship to the theory of
divisors on algebraic curves. We will cover several concrete examples
and applications to problems in algebraic geometry.
Lunedì 15 maggio 2017
Ore 14:30, aula di Consiglio
seminario di Equazioni Differenziali
Aldo Pratelli (Universitat Erlangen-Nurnberg)
Stime quantitative su insiemi con primo autovalore quasi minimale
Negli ultimi anni molto lavoro è stato fatto per dimostrare disuguaglianze
quantitative riguardo agli autovalori del Laplaciano. In particolare, la disuguaglianza
di Faber-Krahn assicura che, tra gli insiemi in RN di volume unitario,
la palla minimizza il primo autovalore con condizioni di Dirichlet al bordo; la versione
quantitativa dice che, se un insieme è un minimo a parte un piccolo errore, allora
questo insieme differisce dalla palla ottimale, nel senso del volume della differenza
simmetrica, per una potenza di questo piccolo errore. Il problema al quale siamo interessati
è il seguente: preso un insieme con il primo autovalore quasi minimale, è
possibile dire, in modo quantitativo, che anche gli altri suoi autovalori sono molto vicini
a quelli corrispondenti della palla? La risposta, positiva, è in un lavoro in
collaborazione con D. Mazzoleni.
Lunedì 15 maggio 2017
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
Junior Colloquium
Thomas Willwacher (ETH, Zurich)
Rational Homotopy Theory of the little disks operads
The little n-disks operads are classical objects in topology, introduced by Boardman-Vogt
and May in the 1970's in their study of iterated loop spaces.
They have since seen a wealth of applications in algebra and topology, and received much
attention recently due to their appearance in the manifold calculus of Goodwillie and Weiss,
and relatedly in the factorization (or topological chiral) homology by Lurie, Francis,
Beilinson-Drinfeld and others.
I report on joint work with Victor Turchin and Benoit Fresse, in which we (mostly) settle the
rational homotopy theory of the little n-disks operads, by showing that they are intrinsically
formal for n≥3, and by computing the rational homotopy type of the function spaces between
these objects.
As an application we obtain complete rational invariants of long knots in codimension≥3.
Non-specialicists are particularly welcome to attend this seminar talk: I will invest some
time to explain the relevant algebraic and topological notions, and to provide mathematical
and historical context.
Lunedì 15 maggio 2017
Ore 14:30, aula F, Università di Roma Tre,
largo san L. Murialdo 1
colloquium di Matematica
Frank Pacard (Ecole Polytechnique)
Blowing bubbles in Riemannian manifolds
Constant mean curvature surfaces are critical points of the area functional under a volume
constraint. They constitute a fairly accurate model for soap bubble and are relevant in the
study of interfaces appearing in phase separation phenomena. In this talk, I will give an
overview of known construction of constant mean curvature surfaces in Riemannian manifolds
that are endowed with generic metrics.
Lunedì 15 maggio 2017
Ore 15:00, aula Picone
seminario
Guido Pezzini (Sapienza Università di Roma)
Varietà simmetriche per gruppi di Kac-Mood
Le varietà simmetriche sono varietà di notevole importanza nella teoria dei
gruppi algebrici, hanno legami ed applicazioni fondamentali in vari campi quali geometria
Riemanniana, analisi armonica e teoria delle rappresentazioni. Nel seminario ricorderemo
alcune proprietà di queste varietà nell'ottica della teoria delle varietà
sferiche. Inoltre discuteremo di una possibile generalizzazione infinito-dimensionale, per
gruppi di Kac-Moody. Il seminario si basa su una collaborazione con Bart Van Steirteghem.
Lunedì 15 maggio 2017
Ore 16:00, aula di Consiglio
seminario di Probabilità e Statistica
T.G. Kurtz (University of Wisconsin-Madison)
Stochastic equations for processes built from bounded generators
The generator for a pure jump process with bounded jump rate is a bounded operator on the
space of measurable functions. For any such process, it is simple to write a stochastic
equation driven by a Poisson random measure. Uniqueness for both the stochastic equation
and the corresponding martingale problem is immediate, and consequently, the martingale
problem and the stochastic equation are equivalent in the sense that they uniquely
characterize the same process. A variety of Markov processes, including many interacting
particle models, have generators which are at least formally given by infinite sums of
bounded generators. In considerable generality, we can write stochastic equations that
are equivalent to these generators in the sense that every solution of the stochastic
equation is a solution of the martingale problem and every solution of the martingale
problem determines a weak solution of the stochastic equation. It follows that uniqueness
for one approach is equivalent to uniqueness for the other.
Lunedì 15 maggio 2017
Ore 16:30, aula Picone
seminario
Giovanni Cerulli Irelli (Sapienza Università di Roma)
The cluster multiplication formula
In 2005, Caldero and Chapoton introduced a formula that provide an intrinsic description
of the cluster variables of cluster algebras associated with Dynkin quivers. The key to
prove the formula was a cluster multiplication formula. This formula was extended to
acyclic quivers by Caldero and Keller in 2006 and further generalized by Hubery and
independently by Fan Xu in 2010. In a more general context the multiplication formula
was proved to hold by Yann Palu in his PhD thesis in 2009. In this talk I will revise
the history of this formula and provide a new proof which seems much more simple than
the previous ones. This is part of a joint project with F. Esposito, H. Franzen and M. Reineke.
Martedì 16 maggio 2017
Ore 14:00, aula 311, Università di Roma Tre,
largo san L. Murialdo 1
esame finale di Dottorato
Giovanni Antinucci
Interacting Fermions on the half-line: Boundary counterterms and Boundary corrections
Martedì 16 maggio 2017
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
seminario di Equazioni Differenziali
Matteo Novaga (Università di Pisa)
A nonlocal perimeter of Minkowski type
I consider a nonlocal perimeter functional inspired by the
Minkowski content, whose main feature is that it interpolates between the
classical perimeter and the volume functional. I will discuss in
particular existence and properties of minimizers.
Martedì 16 maggio 2017
Ore 15:00, aula 21, Università UNINT, via C. Colombo 200
Differential Geometry Afternoon
Massimiliano Pontecorvo (Università di Roma Tre)
On bi-Hermitian surfaces
We present an overview of results giving a satisfactory classification of compact
bi-Hermitian surfaces (S,J±). That is to say compact complex surfaces
(S,J+) admitting a Hermitian metric g and a different complex structure
J- which is also g-Hermitian.
Herman Gluck (University of Pennsylvania)
Germs of fibrations of spheres by great circles always extend to the whole sphere
We will prove that every germ of a smooth fibration of an odd-dimensional round sphere
by great circles extends to such a fibration of the entire sphere, a result previously known
only in dimension three.
In doing so, we will see a connection between this result and one of the most desirable
unsolved problems in the subject, namely to prove that the space of all smooth great circle
fibrations of an odd-dimensional sphere deformation retracts to its subspace of Hopf fibrations,
again known only in dimension three. We will prove an infinitesimal version of this unsolved
problem, and then see how it leads to the germ extension result.
We will also say a few words about how the study of fibrations of round spheres by great
subspheres is related to the (only partially solved) Blaschke Problem in differential geometry
in the large, which seeks to characterize the simplest spaces by the global behavior of their
geodesics. This is joint work with Patricia Cahn and Haggai Nuchi.
Mercoledì 17 maggio 2017
Ore 13:00, aula D'Antoni, Università di Roma Tor Vergata
seminario
Simona Settepanella (Hokkaido University)
Intersection lattice of Discriminantal arrangement and hypersurfaces in Grassmannian
In 1989 Manin and Schechtman considered a family of arrangements of hyperplanes generalizing
classical braid arrangements which they called the Discriminantal arrangements. Such an arrangement
consists of parallel translates of collection of n hyperplanes in general position in Ck which fail
to form a generic arrangement in Ck. In 1994 Falk showed that the combinatorial type of
Discriminantal arrangement depends on the collection of n hyperplanes in general position in Ck.
In 1997 Bayer and Brandt divided generic arrangements in Ck in 'very generic' and 'non very generic'
depending of the intersection lattice of associated Discriminatal arrangement.
In 1999 Athanasiadis provided a full description of intersection lattice for Discriminantal
arrangement in the very generic case. More recently, in 2016, Libgober and Settepanella gave a
description of rank 2 intersection lattice of Discriminantal arrangement in non very generic case,
providing a sufficient geometric condition for a generic arrangement in Ck to be non very generic.
In this talk we will recall their result and we will show that non very generic arrangements in C3
satisfying their condition correspond to points in a degree 2 hypersurface in the complex
Grassmannian Gr(3,n). This is a joint work with S. Sawada and S. Yamagata.
Mercoledì 17 maggio 2017
Ore 14:30, aula E
seminario di Storia della Facoltà
Miriam Focaccia (Centro Studi e Ricerche Enrico Fermi)
Uno scienziato galantuomo a via Panisperna Pietro Blaserna e la nascita dell'Istituto
fisico di Roma
Nel seminario l'autrice presenterà il suo recente libro in cui, partendo da un'accurata
ricostruzione storica del contesto scientifico, sociale e politico, ricostruisce un'immagine
più definita del fisico Pietro Blaserna, personaggio dalla personalità decisamente
multiforme, soprattutto dal punto di vista della sua attività di organizzatore e leader
della politica della ricerca a cavallo tra Otto e Novecento, nonché del suo ruolo nella
formazione di un nuovo status istituzionale della disciplina fisica in Italia attraverso la sua
intensa attività.
Mercoledì 17 maggio 2017
Ore 15:00, aula di Consiglio
seminario di Algebra e Geometria
Edoardo Sernesi (Università di Roma Tre)
Syzygy schemes of a canonical curve
It is possible to associate certain 'Syzygy schemes' to the minimal resolution of a projective
curve. Not much is known about them. I will give an overview of known results in the case of
canonical curves and report on recent results obtained in collaboration with M. Aprodu and
A. Bruno.
Mercoledì 17 maggio 2017
Ore 17:00, aula III
seminario Scienza Matematica e Società
Angelo Vulpiani (Sapienza Università di Roma)
Caos deterministico: origini e relazioni con la probabilità
Il caos deterministico nasce dal lavoro di Poincaré sul problema dei tre corpi e venne
riscoperto negli anni 60 del 20-mo secolo. Ora è ben chiaro che non siamo di fronte ad
una patologia matematica bensì ad un comportamento generico presente in molti ambiti
(astronomia, chimica, ottica, geofisica etc).
L'essenza del caos deterministico può essere riassunta nella sua sensibile dipendenza
dalle condizioni iniziali, passata al grande pubblico come 'effetto farfalla'.
Il fatto che due traiettorie molto vicine si allontanino velocemente (in modo esponenziale)
ha interessanti conseguenze sia pratiche che concettuali. In particolare verrà discusso la
rilevanza del caos nel problema delle previsioni; e la possibilità dell'utilizzo di un
approccio probabilistico anche in sistemi deterministici caotici.
Giovedì 18 maggio 2017
Ore 14:30, aula di Consiglio
seminario PDN P(n)
Daniele Bartolucci (Università di Roma Tor Vergata)
Global bifurcation analysis of mean field equations and the Onsager microcanonical
description of two-dimensional turbulence
We discuss the solution of two long standing open problems closely related to the mean field
Liouville-type equation (Pλ).
On one side, we find the global behaviour of the entropy for the mean field Microcanonical
Variational Principle ((MVP) for short), as it arise in the Onsager description of two-dimensional
turbulence on strictly starshaped domains of second kind.
Among other things we find a region of strict convexity of the entropy.
On the other side, to achieve that goal, we have to catch the global bifurcation diagram of
solutions of the mean field equation (Pλ), emanating from λ=0 and
crossing λ=8π.
The (MVP) suggests the right variable (which is the energy) to be used to obtain a global
parametrization of solutions of (Pλ). In particular a crucial spectral
simplification is obtained by using the fact that, by definition, solutions of the (MVP)
maximize the entropy at fixed energy and total vorticity.
Giovedì 18 maggio 2017
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
seminario
Marco Mazzucchelli (ENS Lyon & CNRS)
Minimal Boundaries in Tonelli Lagrangian Systems
In this talk, which is based on joint work with Luca Asselle and
Gabriele Benedetti, I will present a few recent results concerning action
minimizing periodic orbits of Tonelli Lagrangian systems on an orientable
closed surface. I will show that in every level of a suitable low energy
range there is a 'minimal boundary': a global minimizer of the Lagrangian
action on the space of smooth boundaries of open sets of the surface.
Minimal boundaries satisfy an analogue of the celebrated graph theorem of
Mather: in the tangent bundle, the union of the supports of all lifted
minimal boundaries with a given energy projects injectively to the base. I
will also present some corollaries of these statements to the existence of
simple periodic orbits with low energy on non-orientable closed surfaces,
and to the existence of infinitely many closed geodesics on certain
Finsler 2-spheres.
Giovedì 18 maggio 2017
Ore 14:30, aula 211, Università di Roma Tre,
largo san L. Murialdo 1
seminario di Geometria
David Jensen (University of Kentucky)
Linear systems on general curves of fixed gonality
The geometry of an algebraic curve is governed by its linear systems. While many curves exhibit
bizarre and pathological linear systems, the general curve does not. This is a consequence of the
Brill-Noether theorem, which says that the space of linear systems of given degree and rank on
a general curve has dimension equal to its expected dimension. In this talk, we will discuss a
generalization of this theorem to general curves of fixed gonality. To prove this result, we use
tropical and combinatorial methods. This is joint work with Dhruv Ranganathan, based on prior
work of Nathan Pflueger.
Giovedì 18 maggio 2017
Ore 16:00, aula Dal Passo, Università di Roma Tor Vergata
seminario
Wei Cheng (Nanjing University)
On the singular dynamics of weak KAM solutions
Let H be a Tonelli Hamiltonian. We consider the propagation of
singularities along generalized characteristics by an intrinsic method.
We will show that, for a prescribed solution u which has the
representation in the form of inf-convolution, the relevant precess of
sup-convolution determines the propagation of singulars and generalized
characteristics for singular initial data. This method leads to the global
result under mild Tonelli conditions. We will also discuss the application
of this methods to the associated singular dynamics in both topological
and differential sense. This is based on joint work with Piermarco
Cannarsa and Albert Fathi.
Venerdì 19 maggio 2017
Ore 09:45, aula IV, Università Niccolò Cusano, via don C. Gnocchi 3
International workshop on Nonlinear analysis
09:45 Tomas Caraballo (Universidad de Sevilla, Spain) On 2D-Navier-Stokes equations with
bounded or unbounded delay
10:45 Michel Chipot (Universitat Zurich) Minimal Solutions to some Variational
Inequalities
12:00 Giorgio Fusco (Università de L'Aquila) Heteroclinic connections between global
minimizers of the the Ginzburg-Landau functional
Venerdì 19 maggio 2017
Ore 17:00, aula III
assemblea U.M.I.
11.00 Francesco Maggi (ICTP Trieste)
Teoremi isoperimetrici, problemi aperti e nuovi risultati
12.10 Rita Pardini (Università di Pisa)
Tori complessi, varietà abeliane e varietà proiettive irregolari
14.15 Assemblea e dibattito
Tutte le informazioni relative a questo notiziario devono pervenire
esclusivamente all'indirizzo di posta elettronica
seminari@mat.uniroma1.it
entro le ore 24 del giovedì precedente la settimana interessata.
Le comunicazioni pervenute in ritardo potranno essere ignorate.
Tutti coloro che desiderano ricevere questo notiziario via e-mail sono
invitati a comunicare il proprio indirizzo di posta elettronica a
seminari@mat.uniroma1.it.
Il Direttore