Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 03-05-2021 al 09-05-2021
Martedì 04 maggio 2021
Ore 14:15, link, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Michele Palladino (Gran Sasso Science Institute)
Linear Quadratic Optimal Control and Reinforcement Learning
Starting from the general framework presented in Lecture 4, we will show convergence results for the value functions and the optimal controls when the experience that an agent has on the underlying physical system increases. Then Mr. Andrea Pesare will show an algorithm which makes partial use of the results previously presented.
Martedì 04 maggio 2021
Ore 14:15, indirizzo streaming su zoom, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Francisco J. Silva (Université de Limoges, Francia)
(titolo da comunicare)
Martedì 04 maggio 2021
Ore 14:30, Canale Youtube Cnr-Iac https://www.youtube.com/watch?v=_1eWvlqvXyI, Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche
AIM: Artificial Intelligence and Mathematics, fundamentals and beyond
Prof. Yu Guang Wang (Max Planck Institute for Mathematics in the Sciences & University of New South Wales, Leipzig - Germany & Sidney - Australia)
How Framelets Enhance Graph Neural Networks (Seminar in English)
This work presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Martedì 04 maggio 2021
Ore 15:00, Il Colloquio sarà tenuto in modalità telematica, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre, Largo San Leonardo Murialdo 1
Colloquio di Fisica
Aires Ferreira (Department of Physics - University of York)
Spin-orbit coupling phenomena in van der Waals materials: perspectives from theory and experiment
Spin-orbit coupling (SOC)—a relativistic interaction which entangles a particle’s motion with its quantum mechanical spin—is fundamental to a wide range of physics phenomena, spanning from the formation of topological insulators to the spin Hall effect of light. Recent years have seen remarkable progress in probing, enhancing and tailoring SOC effects in atomically thin materials and their interfaces. From the electrical control of spin-valley coupling in bilayer graphene [1] to reversible spin-charge conversion in graphene on transition metal dichalcogenides at room temperature [2], these discoveries challenge our previous notions of the possible behaviour of spin-orbit coupled electrons at interfaces. In this talk, I will discuss recent results of van der Waals heterostructures and new proposals for probing and exploiting the rich interplay of spin and lattice-pseudospin spin degrees of freedom triggered by SOC [3]. References: [1] “Anisotropic spin currents in graphene”, Link https://physics.aps.org/articles/v11/s108 [2] “Optimal charge-to-spin conversion in graphene on transition-metal dichalcogenides”, M. Offidani, M. Milletarì, R. Raimondi, and A. Ferreira, Phys. Rev. Lett. 119 (2017); “Proposal for unambiguous electrical detection of spin-charge conversion in lateral spin valves”, S. A. Cavill, C. Huang, M. Offidani, Y.-H. Lin, M. A. Cazalilla and A. Ferreira, Phys. Rev. Lett. 124 (2020); “Gate-tunable reversible Rashba−Edelstein effect in a few-layer Graphene/2H-TaS2 heterostructure at room temperature“, L. Li, et al, ACS Nano 14 (2020) [3] “Skew-scattering-induced giant antidamping spin-orbit torques: Collinear and out-of-plane Edelstein effects at two-dimensional material/ferromagnet interfaces“, F. Sousa, G. Tatara and A. Ferreira, Phys. Rev. Res. 2 (2020); “Effect of proximity-induced spin-orbit coupling in graphene mesoscopic billiards”, A. L. R. Barbosa, J. Ramos, and A. Ferreira, Phys. Rev. B 103 (2021)
Per informazioni, rivolgersi a: Davide Meloni, Davide.meloni@uniroma3.it
Mercoledì 05 maggio 2021
Ore 14:00, Seminario telematico via Google Meet all'URL http://meet.google.com/jjt-toji-skw, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Zsolt Patakfalvi (École polytechnique fédérale de Lausanne)
Replacing vanishing theorems in mixed characteristic and the Minimal Model Program for 3-folds over excellent schemes
Kodaira and Kawamata-Viehweg vanishing is frequently used to lift sections of adjoint bundles, a crucial part of many arguments in the classification theory of algebraic varieties, notably in many proofs of the Minimal Model Program. These vanishing theorems fail in mixed characteristic situations, for example for 1.) proper, flat schemes over the p-adic numbers, or 2.) proper birational models of mixed characteristic local rings. I present a work that remedies this situation to some extent. In particular, we are able to a.) show Kodaira and Kawamata-Viehweg vanishing in many situations, b.) prove the 3-dimensional Minimal Model Program for excellent schemes, and c.) draw geometric corollaries of point b.) to the existence of the moduli space of stable surfaces in mixed characteristic. This is a joint work with Bhargav Bhatt, Linquan Ma, Karl Schwede, Kevin Tucker, Joe Waldron and Jakub Witaszek.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Mercoledì 05 maggio 2021
Ore 14:30, https://meet.google.com/pip-kvzt-fkz, Dipartimento di Fisica, Sapienza Università di Roma
Seminario delle Meccaniche
Anna De Masi (Università dell'Aquila)
Non equilibrium stationary states and interfaces
The context is the Fick’s law where a stationary current flows in a system driven by the boundaries which are put in contact with suitable reservoirs. This is a much studied problem but only recently together with Olla and Presutti I have obtained results in stochastic Ginzburg-Landau types of models with phase transition. I will present these models where the stationary non equilibrium distribution is known explicitly and exploit this to study the stationary fluctuations of the interface. It is well known since the work by Gallavotti, 1972, that in the \(2d\) Ising model at thermal equilibrium the interface fluctuates by the order of \(\sqrt N\), \(N\) the size of the system. We will see that in the presence of a stationary current produced by reservoirs at the boundaries the interface is much more rigid as it fluctuates only by the order \(N^{1/4}\). Actually with Merola and Olla we proved this \(N^{1/4}\) result only for the SOS approximation. Beyond the SOS approximation new interesting and surprising phenomena appear, I will discuss some preliminary results obtained with Ioffe, Merola, Presutti and Sholsman (in different combinations).
Mercoledì 05 maggio 2021
Ore 16:00, Online seminar, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Aleksei Bykov (University of Rome Tor Vergata)
Hamiltonian approach to QFT on quantum spacetime and its adiabatic limits
It is a common place that in quantum gravity at high energies the smooth manifold of spacetime must be replaced by its quantized version, and non-commutative quantum spacetimes are among the most promising candidates for this replacement. However, the construction of a quantum field theory on such a spacetime seems to be a non-trivial and ambiguous task. One of the approaches to this problem was proposed and developed by Bahns, Doplicher, Fredenhagen and Piacitelli for the Doplicher-Fredenhagen-Roberts quantum spacetime. I will start by briefly reviewing this approach in a somewhat more general perspective and presenting its main advantages and disadvantages. I will expose my results on the existence of the weak adiabatic limit and my ongoing work on the strong adiabatic limit. If time permits, I will also discuss the ambiguities that arise in the process of finite renormalization required to fulfill the necessary conditions for the existence of the strong adiabatic limit. This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006. Link
Per informazioni, rivolgersi a: v.morinelli@gmail.com
Mercoledì 05 maggio 2021
Ore 16:00, https://meet.google.com/fxd-vqrv-gyj, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Fisica Matematica
Davide Fermi (Sapienza Università di Roma)
Semiclassical limit with zero-range potentials in one dimension
According to Bohr's correspondence principle, non-relativistic quantum mechanics should reproduce the classical Newton theory when the Planck constant is small, compared to the dimensional parameters characterizing the system of interest. In a series of works begun in 1980, Hagedorn showed that the Schroedinger dynamics of sharply localized coherent states is well approximated by the classical Hamiltonian evolution of their average positions and momenta, whenever the potential is sufficiently regular. Imitating Hagedorn's approach, we discuss the semiclassical limit for rescaled coherent states on the line in presence of delta and delta-prime singular potentials concentrated at a point. The quantum dynamics is approximated using singular perturbations of the free Liouville operator on classical phase space, constructed via standard resolvent techniques. We derive quantitative error estimates for the time evolution of the said coherent states, as well as for the associated wave operators and scattering matrix. Analogous results for a quantum star graph with Kirchhoff conditions at the vertex are briefly mentioned as well. Joint work with Claudio Cacciapuoti and Andrea Posilicano (University of Insubria). Refs.: Annali di Matematica (2020); Anal. Math. Phys. (2021); arXiv:2012.12735.
Giovedì 06 maggio 2021
Ore 14:00, On-line seminar (via MS Teams), Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Margherita Nolasco (Università degli Studi dell"Aquila)
A variational principle for a charge-normalized solitary wave for the Maxwell-Dirac equations
In the context of classical field theory, the solitary wave solutions of the Euler-Lagrange equations describe "extended" particles. The existence of a charge-normalized solitary wave solution of the coupled Maxwell-Dirac equations, describing the spin-1/2 charged particle (electron) with self-interaction, has been an open problem for a long time. The first existence result of (not necessarily normalized) solitary waves was given by Esteban, Georgiev and Séré (Calc.Var. PDE (1996)) by using a variational method, as critical points of an energy functional which is strongly indefinite and presents a lack of compactness. In this talk we discuss the existence of a charge-normalized solitary wave obtained with a different variational principle inspired by the min-max characterization of eigenvalues of Dirac operators. In particular, we provide a variational characterization of the normalized solitary wave as a minimizer of an effective "renormalized" energy functional. Note: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 MS Teams Link for the streaming
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Giovedì 06 maggio 2021
Ore 16:00, Streaming via Zoom and Youtube channel, Web site for information: https://www.dinamici.org/dai-seminar/
DinAmicI: Another Internet Seminar (DAI Seminar)
Selim Ghazouani (Université Paris-Sud (France))
Piecewise affine homeomorphisms of the circle and dilation surfaces
In this talk I will consider the following question: if one picks a piecewise affine map of the circle “at random”, what dynamical behaviour are we likely to observe? The case of standard circle diffeomorphisms has been studied by Herman in the 80s; in this emblematic case the problem can be reduced to theorems close to KAM theory. For the piecewise affine case, we put forward a geometric approach, inspired by methods from both Teichmüller theory and hyperbolic geometry. Note: The zoom link to the seminar will be posted on https://www.dinamici.org/dai-seminar/ and on https://mathseminars.org/seminar/DinAmicI. Moreover, it will be streamed live on youtube via the DinAmicI channel: https://www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Giovedì 06 maggio 2021
Ore 18:00, Il Seminario sarà tenuto in modalità telematica, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre, Largo San Leonardo Murialdo 1
Seminario di Geometria
Max Lieblich (Washington)
Topological reconstruction theorems for varieties
Per partecipare al seminario cliccare sul seguente link
Venerdì 07 maggio 2021
Ore 15:00, Seminario Telematico, link
Online Representation Theory Seminar
Thorge Jensen
Cellularity of the p-Kazhdan-Lusztig Basis for Symmetric Groups
After recalling the most important results about Kazhdan-Lusztig cells for symmetric groups, I will introduce the p-Kazhdan-Lusztig basis and give a complete description of p-cells for symmetric groups. After that I will mention important consequences of the Perron-Frobenius theorem for p-cells which provide one of the last missing ingredients for the proof of the cellularity of the p-Kazhdan-Lusztig basis in finite type A.
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