## Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma

Settimana dal 14-01-2019 al 20-01-2019

Lunedì 14 gennaio 2019
Ore 14:15, aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
Isabelle Gallagher (ENS, Paris)
Some results on the convergence from particle to Boltzmann and fluid dynamics
In this talk we shall report on some recent progress with Thierry Bodineau, Laure Saint-Raymond and Sergio Simonella, concerning the derivation of the Boltzmann equation, and of some fluid equations, starting from particle systems as the number of particles goes to infinity, in the low density limit. We shall in particular discuss the appearance of irreversibility in the limiting procedure.

Lunedì 14 gennaio 2019
Ore 16:00, Aula D'Antoni, Dipartimento di Matematica di Tor Vergata
Projective Wonderful Models for Toric Arrangements and their Cohomology
Joint with Giovanni Gaffi. I plan to sketch an algorithmic procedure which allows to build projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T in analogy with the case of subspaces in a linear or projective space. The main step of the construction is a combinatorial algorithm that produces a projective toric variety in which the closure of each layer of the arrangement is smooth. The explicit procedure of our construction allows us to describe the integer cohomology rings of such models by generators and relations.

Martedì 15 gennaio 2019
Ore 10:00, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Giovanni Cerulli Irelli
Geometric methods in representaiton theory of finite dimensional algebras
This is an introductory course to the representation theory of finite dimensional algebras and in particular of quivers. As a geometric application we will see how to use techniques of representation theory for the study of geometric aspects of quiver Grassmannians.

Martedì 15 gennaio 2019
Ore 11:30, Aula 211 - Pal. C, Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre Largo San Leonardo Murialdo,1
Seminario di Probabilità
Luca Avena (Leiden University, NL)
Mixing time on dynamic configuration model
We are interested in understanding the mixing time (i.e. the time to reach equilibrium) for a discrete-time random walk moving on a network changing over time in a random fashion. To this aim, we consider a specific model where the underlying evolving network has n vertices, it is initially sampled from the so-called configuration model (a random graph ensemble with a prescribed vertex-degree sequence) and at each time-unit a given fraction of the edge set is randomly rewired. We characterize the mentioned mixing-time for a random walk without backtracking as a function of the fraction of rewired edges. This work extends to a dynamic setup previous works on random walks on static random graphs. In particular, we show that the mixing-time is speeded-up by the presence of the edge-rewiring dynamics and depending on whether such a dynamics is slow, moderate or fast, we show the presence of so-called cutoff , half-cutoff, or absence of cutoff, respectively. Joint work with Hakan Guldas, Remco van der Hofstad and Frank den Hollander

Martedì 15 gennaio 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Universita' degli Studi di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Pierpaolo Esposito (Universita' di Roma 3)
Log-determinants in conformal geometry
I will report on a recent result, in collaboration with A. Malchiodi, concerning a four-dimensional PDE of Liouville type arising in the theory of log-determinants in conformal geometry. The differential operator combines a linear fourth-order part with a quasi-linear second-order one. Since both have the same scaling behavior, compactness issues are very delicate and even the "linear theory" is problematic. For the log-determinant of the conformal laplacian we succeed to show existence and uniqueness of fundamental solutions, quantization property for non-compact solutions and existence results via critical point theory.

Martedì 15 gennaio 2019
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Dottorato
Lorenzo Luzzi (Roma Tor Vergata)
Convergenza di algoritmi per il riconoscimento di gesti con algebre di Clifford
I numeri di Clifford (o Algebre di Clifford) permettono un calcolo vettoriale indipendente dalle coordinate (coordinate-free). Essi si stanno rivelando sempre più utili nella scrittura di algoritmi efficienti e robusti. A tale proposito, Lorenzo Luzzi ha recentemente ottenuto risultati di convergenza riguardo alcuni algoritmi per il riconoscimento di gesti, considerando nuove applicazioni all'analisi e alla geometria differenziale. In questo seminario presenterà l'algoritmo FTL! , introdotto recentemente nel panorama dei riconoscitori di gesti in 2D, dal punto di vista matematico. Per far questo, tramite strumenti propri delle algebre di Clifford, introdurrà una "distanza tra forme" che utilizzerà per definire l'algoritmo. Una volta analizzate le sue proprietà ne illustrerà la convergenza ed una eventuale variante. Nella parte conclusiva mostrerà in breve delle sue applicazioni al riconoscimento di gesti su superfici.

Martedì 15 gennaio 2019
Ore 16:00, Aula D’Antoni, Dipartimento di Matematica, Universita' di Roma "Tor Vergata", Via della Ricerca Scientifica 1
Seminario di Analisi Complessa
Andrew Zimmer (Louisiana State University)
Two boundary rigidity results for holomorphic maps
In this talk we discuss two boundary versions of the Schwarz lemma. The first is for general holomorphic self maps of bounded convex domains with $$C^2$$ boundary. The second is for biholomorphisms of domains who have an invariant Kahler metric with bounded sectional curvature. The proof of the first relies on some new results about the boundary values of complex geodesics. The proof of the second uses many techniques from Riemannian Geometry: the dynamical behavior of the geodesic flow, deforming metrics using the Ricci flow, injectivity radius estimates, etc.

Mercoledì 16 gennaio 2019
Ore 14:00, aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Paolo Antonini (SISSA)
La congettura di Baum-Connes localizzata nell’elemento unità di un gruppo discreto
In collaborazione con S. Azzali e G. Skandalis abbiamo costruito per un gruppo discreto $$\Gamma$$, una versione della mappa di assembly di Baum-Connes "localizzata nell’elemento identità di $$\Gamma$$". Ne risulta una versione più debole della congettura di Baum-Connes che ancora implica la congettura di Novikov (forte) sull’invarianza omotopica delle segnature superiori delle varietà. Nella prima parte del seminario verranno introdotte la congettura di Novikov e la congettura di Baum Connes; nella seconda parte verrà illustrata la costruzione della mappa localizzata. In particolare il collegamento con la congettura di Novikov è mostrato calcolando il dominio della nuova mappa tramite un confronto preciso, in termini di $$K$$-teoria a coefficienti reali, tra lo spazio classificante per azioni proprie di $$\Gamma$$ con quello che classifica le azioni libere e proprie.

Mercoledì 16 gennaio 2019
Ore 15:00, Aula D’Antoni, Dipartimento di Matematica, Universita' di Roma "Tor Vergata", Via della Ricerca Scientifica 1
Corso di Dottorato
Prof. Han Peters (University of Amsterdam)
Holomorphic dynamics: Wandering Fatou Components
The iteration of rational functions, acting on the Riemann sphere, is a classical subject that has been studied for well over a century. It is remarkable that even the iteration of quadratic polynomials, a seemingly simple family of maps, has led to a surprisingly deep theory, with several important open questions still unsolved. Naturally the field of holomorphic dynamical systems has expanded into many directions. Since the late 1980's there has been considerable interest in the iteration of rational functions in higher dimensions. In recent years it has become clear that already in two complex variables phenomena arise that are unlike anything that can occur in one variable. In this course we will consider some of the most striking results in this direction of research. In particular we consider the construction of wandering domains, and we finish by discussing the most pressing open questions regarding the classification of invariant Fatou components. Programma 1. Crash course in 1D complex dynamics. Classification of invariant Fatou components and non-existence of wandering domains. Discussion of fixed points. 2. Parabolic bifurcations. Mane-Sad-Sullivan result. Lavaurs Theorem 3. Wandering domains in higher dimensions: skew products. Detailed proof of the construction of wandering domains. Discussion of very recent results. 4. Fatou components of polynomial automorphisms, and open questions.

Giovedì 17 gennaio 2019
Ore 14:30, Aula 311 - Pal. C, Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre Largo San Leonardo Murialdo,1
Seminario di Geometria
Fabrizio Anella (Universita' Roma Tre)
Rational curves on elliptic fiber spaces
Rational curves play an important role in many different fields, which ranges from algebraic and hyperbolic geometry to theoretical physics. A key piece in the theory is the existence of such curves on varieties with trivial canonical class. It is well-known that an abelian variety does not contain rational curves, and it is conjectured that this is the only case. This is completely proved only in dimension two by the works of Bogomolov and Mumford. There are many partial results in dimension three, but very little is known in higher dimension. In this talk we will give a constructive proof for the existence of uniruled divisors in varieties with an elliptic fiber space structure with some technical hypothesis. We will discuss, with some examples, which hypothesis are necessary and which ones can be relaxed.

Giovedì 17 gennaio 2019
Ore 14:30, Aula F, Dipartimento di Matematica e Fisica, Universita' degli Studi Roma Tre, Largo San Leonardo Murialdo,1
Seminario di Fisica Matematica
Prof. S. Miracle-Sole (CNRS Marseille)
Wulff shape associated to the Ising model.
I will review some aspects of the theory of the Wulff shape in the context of the Ising model. According to the Wulff construction the shape of the equilibrium crystal is determined by the surface tension considered as a function of the interface orientation. We present some (conjectured) approximate solutions and some rigorous results concerning this function, in the case of a lattice gas, and apply them to study the shape of the equilibrium crystal and, in particular, the shape of the facets of this crystal.

Giovedì 17 gennaio 2019
Ore 15:00, Aula D’Antoni, Dipartimento di Matematica, Universita' di Roma "Tor Vergata", Via della Ricerca Scientifica 1
Corso di Dottorato
Prof. Han Peters (University of Amsterdam)
Holomorphic dynamics: Wandering Fatou Components
The iteration of rational functions, acting on the Riemann sphere, is a classical subject that has been studied for well over a century. It is remarkable that even the iteration of quadratic polynomials, a seemingly simple family of maps, has led to a surprisingly deep theory, with several important open questions still unsolved. Naturally the field of holomorphic dynamical systems has expanded into many directions. Since the late 1980's there has been considerable interest in the iteration of rational functions in higher dimensions. In recent years it has become clear that already in two complex variables phenomena arise that are unlike anything that can occur in one variable. In this course we will consider some of the most striking results in this direction of research. In particular we consider the construction of wandering domains, and we finish by discussing the most pressing open questions regarding the classification of invariant Fatou components. Programma 1. Crash course in 1D complex dynamics. Classification of invariant Fatou components and non-existence of wandering domains. Discussion of fixed points. 2. Parabolic bifurcations. Mane-Sad-Sullivan result. Lavaurs Theorem 3. Wandering domains in higher dimensions: skew products. Detailed proof of the construction of wandering domains. Discussion of very recent results. 4. Fatou components of polynomial automorphisms, and open questions.

Venerdì 18 gennaio 2019
Ore 11:00, Aula 311 - Pal.C, Terzo piano, Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre Largo San Leonardo Murialdo,1
Seminario di Logica Matematica
Giulio Guerrieri e Luc Pellissier
1)Types by Need (joint work with Beniamino Accattoli and Maico Leberle). 2)Linear Implicative Algebras, a Brouwer-Heyting-Kolmogorov interpretation of linear logic
1)Giulio Guerrieri A cornerstone of the theory of λ-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational models. Since the seminal work of de Carvalho in 2007, it is known that multi types (i.e. non-idempotent intersection types) refine intersection types with quantitative information and a strong connection to linear logic. Typically, type erivations provide bounds for evaluation lengths, and minimal type derivations provide exact bounds. De Carvalho studied call-by-name evaluation, and Kesner used his system to show the termination equivalence of call-by-need and call-by-name. De Carvalho's system, however, cannot provide exact bounds on call-by-need evaluation lengths. In this paper we develop a new multi type system for call-by-need. Our system produces exact bounds and induces a denotational model of call-by-need, providing the first tight quantitative semantics of call-by-need. 2) Luc Pellissier Implicative Algebras were recently introduced by Alexandre Miquel as a unified framework for forcing and realisability, whose particularity is to interpret terms and formulæ uniformly. In this ongoing work, we show how linear logic fits in this picture: we present a notion of model of intuitionnistic linear logic in which sits both syntactic models and a localized phase semantics ; and show how to transform such a model into an algebra allowing to interpret faithfully all the connectives of classical linear logic.

Venerdì 18 gennaio 2019
Ore 11:30, Aula 211, Pal. C, Dipartimento di Matematica e Fisica, Universita' degli Studi Roma Tre, Largo San Leonardo Murialdo 1
Seminario di Probabilita'
Prof. Yinon Spinka
Finitely-dependent processes are finitary
Consider a translation-invariant process $$X$$ indexed by $$\mathbb{Z}^d$$. Suppose that $$X$$ is finitely-dependent in the sense that its restrictions to sets which are sufficiently separated (at least some fixed distance apart) are independent. We are concerned with the following question: How "close" is $$X$$ to being an i.i.d. process? One natural notion of closeness, called block factor, was suggested by Ibragimov and Linnik over 50 years ago. It took roughly 30 years until Burton, Goulet and Meester constructed an example which showed that this notion is too strong. That is, $$X$$ may not be close to being i.i.d. in this sense. We show that $$X$$ is close in a slightly weaker sense -- it is a finitary factor of an i.i.d. process. This means that $$X=F(Y)$$ for some i.i.d. process $$Y$$ and some measurable map F which commutes with translations of $$\mathbb{Z}^d$$, and moreover, that in order to determine the value of $$X_v$$ for a given $$v$$, one only needs to look at a finite (but random) region of $$Y$$. The result extends to finitely-dependent processes indexed by the vertex set of any transitive amenable graph.

Venerdì 18 gennaio 2019
Ore 12:00, aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario MoMA
Andrea Puglisi
Granular Brownian Motion
Granular materials are made of macroscopic particles, called grains: sand, rice, sugar and powders are typical examples. They are important in our everyday life, in many industrial applications and in the prevention of geophysical hazards. In physics, mainly in the realm of non-equilibrium statistical mechanics, granular systems are an inspiring source of phenomena and questions. The simplest model of granular material is a "fluid" made of inelastic hard spheres. For such a system - in the dilute limit - the classical program of kinetic theory (Boltzmann equation, Chapman-Enskog-based hydrodynamics, and much more) has been developed by physicists and mathematicians in the last decades. In this seminar, after recalling a few key results of such a theoretical activity, I will focus on a series of experiments made in my laboratory in the last 5 years. They concern the statistical properties of a massive probe immersed in a steady state granular fluid. The fluid is obtained by vibro-fluidization of a large number of hard spheres of different materials, while the probe is a rigid rotator whose angular displacement and angular velocity are the key observables. In the dilute limit one conjectures a Markovian approximation for the rotator's dynamics which explains many aspects of the experiment, including a qualitative understanding of "motor effects" in the presence of rotator's asymmetries. Further noticeable facts appear when the granular fluid is not dilute, mainly the violation of the mobility-diffusivity Einstein relation, and anomalous diffusion. For these phenomena a predictive theory is lacking and only phenomenological models are available.

Venerdì 18 gennaio 2019
Ore 14:00, Aula 25, Dipartimento di Matematica, Università di Roma Tor Vergata
Corso di dottorato
Christos Efthymiopoulos (Athens)
Hamiltonian Perturbation Theory and Applications in Celestial Mechanics
After a quick review of the basics of the Hamiltonian formalism, the course will focus on methods of canonical perturbation theory allowing to characterize by analytical means the dynamics in nearly-integrable Hamiltonian systems with few degrees of freedom. The cornerstones of perturbation theory (symplectic transformations, normal form theory) will be presented along with some central results in the field, outlined in a heuristic way. The applications refer to mainstream problems of modern celestial mechanics and astrodynamics. In questa lezione verrà anche fissato l’orario del corso

Venerdì 18 gennaio 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Esame finale di Dottorato
Erika Pieroni
Minimal Entropy of 3-manifolds

Venerdì 18 gennaio 2019
Ore 15:00, Aula D’Antoni, Dipartimento di Matematica, Universita' di Roma "Tor Vergata", Via della Ricerca Scientifica 1
Corso di Dottorato
Prof. Han Peters (University of Amsterdam)
Holomorphic dynamics: Wandering Fatou Components
The iteration of rational functions, acting on the Riemann sphere, is a classical subject that has been studied for well over a century. It is remarkable that even the iteration of quadratic polynomials, a seemingly simple family of maps, has led to a surprisingly deep theory, with several important open questions still unsolved. Naturally the field of holomorphic dynamical systems has expanded into many directions. Since the late 1980's there has been considerable interest in the iteration of rational functions in higher dimensions. In recent years it has become clear that already in two complex variables phenomena arise that are unlike anything that can occur in one variable. In this course we will consider some of the most striking results in this direction of research. In particular we consider the construction of wandering domains, and we finish by discussing the most pressing open questions regarding the classification of invariant Fatou components. Programma 1. Crash course in 1D complex dynamics. Classification of invariant Fatou components and non-existence of wandering domains. Discussion of fixed points. 2. Parabolic bifurcations. Mane-Sad-Sullivan result. Lavaurs Theorem 3. Wandering domains in higher dimensions: skew products. Detailed proof of the construction of wandering domains. Discussion of very recent results. 4. Fatou components of polynomial automorphisms, and open questions.

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