Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 27-01-2020 al 02-02-2020
Lunedì 27 gennaio 2020
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Erwin Topp (U. Santiago del Cile)
Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative
In this talk we present Hölder regularity estimates for an Hamilton-Jacobi with fractional time derivative of order α ∈ (0, 1) cast by a Caputo derivative.. Contrary to the classical time derivative case α = 1, the convergence of the solution on the so-called projected Aubry set is not straightforward. Indeed, a function with nonpositive Caputo derivative for all time does not necessarily converge . However, we establish partial results of convergence under some geometrical assumptions. Joint work with Olivier Ley (INSA-Rennes, France) and Miguel Yan- gari (EPN, Ecuador).
Lunedì 27 gennaio 2020
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Francesco Caravenna (Università di Milano-Bicocca)
On the two-dimensional KPZ and Stochastic Heat Equation
We consider the Kardar-Parisi-Zhang equation (KPZ) and the multiplicative Stochastic Heat Equation (SHE) in two space dimensions, driven by with space-time white noise. These singular PDEs are "critical" and lack a solution theory, so it is standard to consider regularized versions of these equations - e.g. convolving the noise with a smooth mollifier - and to investigate the behavior of the regularized solutions when the regularization is removed. Based on joint works with Rongfeng Sun and Nikos Zygouras, we show that these regularized solutions undergo a phase transition as the noise strength is varied on a logarithmic scale, with an explicit critical point. In the sub-critical regime, the regularized solutions of both KPZ and SHE exhibit so-called Edwards-Wilkinson fluctuations, i.e. they converge to the solution of the *additive* Stochastic Heat Equation (after centering and rescaling), with a non-trivial constant on the noise. We finally discuss the critical regime, where many questions are open.
Lunedì 27 - Venerdì 31 gennaio 2020
Aula B, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Diego Noja (Università di Milano Bicocca)
Nonlinear Schroedinger equation on graphs: linear and nonlinear
Calendario e orari
- lunedì 27 gennaio, ore 16-18
- martedì 28 gennaio, ore 14-16
- mercoledì 29 gennaio, ore 14-16
- giovedì 30 gennaio, ore 14-16
- venerdì 31 gennaio, ore 10-12
Martedì 28 gennaio 2020
Ore 10:00, Aula Dal Passo, Dipartimento di Matematica, Università di Tor Vergata
Seminario dei Giovani Ricercatori
Nicola Cavallucci (Sapienza Università di Roma)
Packing conditions on CAT(0) spaces
The study of metric spaces satisfying synthetic notions of curvature is an important topic in geometry. The aim of the talk is to motivate why these spaces are interesting using the special case of \( CAT(0) \) spaces satisfying a uniform packing condition.
Martedì 28 gennaio 2020
Ore 11:25, Aula Dal Passo, Dipartimento di Matematica, Università di Tor Vergata
Seminario dei Giovani Ricercatori
Mauricio Misquero (Università di Tor Vergata)
Some rigorous results on the 1:1 resonance of the spin-orbit problem
Consider the problem of an spinning oblate satellite (e.g. the
Moon) with respect to its center of mass when it is moving in a
Keplerian ellipse around a planet (e.g. the Earth). This is the
spin-orbit problem and it modeled by a pendulum-like equation. We study
the resonance 1:1 (e.g. the dark side of the Moon) from an analytical
point of view, with no requirements of smallness of the orbital
eccentricity and taking into account dissipative forces. The problem
depends on \( e \), the eccentricity of the orbit, and on \( \Lambda \), the
oblateness of the spinning body. Our main concern is the capture into
the 1:1 resonance for points of the \( (e,\Lambda) \)-plane. First, we find
a region of uniqueness of the 1:1 resonance, which is the continuation
from the solution for \( e=0 \). Then, a subregion of linear stability is
estimated. We also study a separatrix close to the line \( e=e_*\approx
0.682 \), beyond which the resonance is unstable. Finally, we study the
dissipative case by estimating regions of asymptotic stability of the
solution (capture into resonance) depending on the strength of the
dissipation applied.
Martedì 28 gennaio 2020
Ore 14:30, Aula C, Dipartimento di Matematica, Sapienza Università di Roma
Discussione tesi di dottorato (esame finale)
H. A. Mimun (Sapienza)
Percolation in the Miller-Abrahams random resistor network
The Miller-Abrahams random resistor network is used to study electron transport in amorphous solids. This resistor network is given by the complete random graph built on a marked homogeneous Poisson point process on R^d and each edge {x,y} is associated to a filament with conductance depending on the temperature, the distance between the points x,y and their associated marks. In this talk we consider the subgraph containing only edges with lower bounded conductances and, using the method of randomized algorithms developed by Duminil-Copin et al. and the renormalization argument proposed by Grimmett and Marstrand, we analyze the connection probabilities and the left-right crossings in appropriate regimes. These percolation properties are key ingredients for understanding the asymptotic behavior at low temperature of the effective conductivity of the Miller-Abrahams random resistor network. Joint work with Alessandra Faggionato (Sapienza University, Rome).
Martedì 28 gennaio 2020
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Vivina Barutello (Università di Torino)
Some aspects of the anisotropic Kepler problem
Anisotropic Kepler-like potentials have been introduced and studied by Gutzwiller and Devaney in the '70 and '80 and they turns out to be a useful toy-model in the comprehension of some complex singular Hamiltonian systems. In this talk we start presenting some results concerning collision motions (i.e., trajectories interacting with the singularity) which take advantage of a change of coordinates due to McGehee. In this coordinates the singularity at the origin is regularized and replaced by a smooth manifold on which a phase space analysis can be carried out. Finally we show an application of these results in the construction of a symbolic dynamic for the multiple anisotropic center problem. Note: This talk is part of the activity of the MIUR Department of Excellence Grant 2018-2022, CUP E83C18000100006.
Martedì 28 gennaio 2020
Ore 15:00, Sala Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Modellistica Differenziale Numerica
Michael Herty (RWTH Aachen University)
Hyperbolic Transport on Graphs
The broad research thematic of flows on networks was addressed in recent years by many researchers, in the area of applied mathematics, with new models based on partial differential equations. The latter brought a significantcant innovation in a field previously dominated by more classical techniques from discrete mathematics or methods based on ordinary differential equations. In particular, a number of results, dealing with vehicular traffic, supply chains and data networks, have been presented recently. The field seems still to flourish and a considerable number of papers devoted to the subject is published every year, also because of the wide and increasing range of applications: from blood flow to air traffic management. The aim of the present survey talk is to present a view on large number of themes, results and applications related to this broad research direction. These techniques can be applied to different fields from mathematical modeling, analysis, numerics, optimization. We will provide an overview as well as some in-depth results.
Mercoledì 29 gennaio 2020
Ore 14:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Corso di dottorato
Roberto Peirone (Università di Roma Tor Vergata)
Analysis on Fractals - I
We will study energies on finitely ramified self-similar fractals. In particular, we will discuss the problem of the existence of such energies, and also of their uniqueness. The detailed program could depend on the interests of the audience
Mercoledì 29 gennaio 2020
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Algebra & Geometry Seminar
Gaëtan Borot (Max Planck Institut Bonn)
Topological recursion(s) for Masur-Veech volumes
Statistics of the simple length spectrum of bordered hyperbolic surfaces define functions on the moduli space. Andersen, Orantin and myself showed recently that they satisfy a recursion on the Euler characteristic, which implies a topological recursion for their averages over the Weil-Petersson measure. This can be seen as a generalization of Mirzakhani's identity and her proof of a topological recursion for the Weil-Petersson voulmes. We show how this result implies topological recursion (here taking the form of Virasoro constraints) for the Weil-Petersson averages of the asymptotic growth of the number of long curves. By invoking the relation between Weil-Petersson measure on the Teichmuller space, Thurston measure on the space of measured laminations, and Masur-Veech measure on the space of quadratic differentials, this gives a recursion to compute polynomials P_{g,n}(L_1,...,L_n) whose constant term are the Masur-Veech volumes of the principal stratum. This retrieves and generalizes a result of Delecroix et al. obtained via different (combinatorial) methods. If time permits, I will present a second topological recursion computing different polynomials R_{g,n}(L_1,...,L_n) whose constant terms is the same Masur-Veech volume, and which is a consequence of an intersection-theoretic approach of Chen, Moeller and Sauvaget. This is based on joint works with Jorgen Ellegaard Andersen, Severin Charbonnier, Vincent Delecroix, Alessandro Giacchetto, Danilo Lewanski, Campbell Wheeler.
Giovedì 30 gennaio 2020
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Incontro Scientifico per il lancio del premio "Levi Civita"
Tullio Levi Civita: un matematico poliedrico
Programma
- 14.30 Saluti Istituzionali a cura dell’Università La Sapienza, dell’Associazione Alumni dell’Università di Padova e di Corvallis Holding
- 15.00 Presentazione del premio e ricordo di Levi Civita, Franco Rampazzo, docente di Analisi Matematica, Università degli Studi di Padova
- 15.30 Note storiche sull’opera di Levi Civita, Enrico Rogora, docente di Storia della Matematica, Università di Roma “La Sapienza”
- 15.50 Calcolo tensoriale, calcolo differenziale e Big Data, Valeria Simoncini, docente di Analisi Numerica, Università di Bologna
- 16.10 Parallelismo di Levi-Civita e olonomia riemanniana, Paolo Piccinni, docente di Geometria, Università di Roma “La Sapienza”
- 16.30 Conclusioni, Maurizio Falcone, docente di Analisi Numerica, Università di Roma “La Sapienza”
Venerdì 31 gennaio 2020
Ore 12:00, sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario MoMA
Roberto Navigli (Università di Roma La Sapienza)
Multilingual Natural Language Understanding: how can a machine understand (not just transform) text in any language?
Natural Language Processing (NLP) has seen an explosion of interest in recent years, with many industrial applications relying on key technological developments in the field. However, Natural Language Understanding (NLU) – which requires the machine to get beyond processing strings and involves a semantic level – is particularly challenging due to the pervasive ambiguity of language. In this talk I will first introduce NLP and NLU and the key issues in the field, and will then move on to present recent research in my group on multilingual NLU, including work on BabelNet, our multilingual encyclopedic dictionary, and tasks such as multilingual word sense disambiguation and semantic role labeling. The key goal we aim at is to scale across languages easily and achieve state-of-the-art performance thanks to the integration of deep learning and explicit knowledge. I will also show several demos and discuss the technological transfer to Babelscape, a successful Sapienza startup company which brings to the market innovative tools for multilingual concept and entity extraction, enterprise knowledge graph creation and multilingual semantic search.
Venerdì 31 gennaio 2020
Ore 14:00, Aula D'Antoni, Dipartimento di Matematica, Università Tor Vergata
Seminario di Geometria Algebrica
Enrico Arbarello
Applicazioni della Teoria di Bridgeland sulle superfici K3: Brill-Noether (secondo A.Bayer), programma di Mukai (secondo S. Feyzbakhsh).
Venerdì 31 gennaio 2020
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per insegnanti (PLS)
Paolo Maroscia (Sapienza Università di Roma)
Matematica e letteratura: proposte concrete di laboratorio
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