Notiziario Scientifico

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

Settimana dal 17-06-2024 al 23-06-2024

Lunedì 17 giugno 2024
Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università degli studi di Roma "Tor Vergata"
Seminario di Analisi Numerica
Tan Bui-Thanh (University of Texas at Austin)
Learn2Solve: A Deep Learning Framework for Real-Time Solutions of Forward, Inverse, and UQ Problems
Digital models (DMs) are designed to be replicas of systems and processes. At the core of a digital model (DM) is a physical/mathematical model that captures the behavior of the real system across temporal and spatial scales. One of the key roles of DMs is enabling "what if" scenario testing of hypothetical simulations to understand the implications at any point throughout the life cycle of the process, to monitor the process, to calibrate parameters to match the actual process and to quantify the uncertainties. In this talk, we will present various (faster than) real-time Scientific Deep Learning (SciDL) approaches for forward, inverse, and UQ problems. Both theoretical and numerical results for various problems including transport, heat, Burgers, (transonic and supersonic) Euler, and Navier-Stokes equations will be presented.
Per informazioni, rivolgersi a: speleers@mat.uniroma2.it


Martedì 18 giugno 2024
Ore 14:30, Aula Piano Terra, CNR-IAC, via dei Taurini 19, 00185 Roma
Seminari Generali dell'IAC
Lorenzo Balzotti (Dipartimento di Ingegneria Informatica Automatica e Gestionale Antonio Ruberti, Sapienza.)
Knowledge Graphs: embeddings, link prediction and explanation
Knowledge Graphs (KGs) are data structures that integrate information into a network of entities and relations. They are essential for organizing and retrieving knowledge in various domains, from search engines to recommendation systems. In this seminar, we will introduce the fundamentals of KGs and examine some of the key challenges they present. In the first part, we will discuss methods to address their incompleteness, exploring methodologies for predicting missing links. In the second part, the seminar will delve into the emerging field of AI explanation, emphasizing its importance in enhancing the transparency and trustworthiness of KG embedding systems.
Per informazioni, rivolgersi a: roberta.bianchini@cnr.it


Martedì 18 giugno 2024
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Tan Bui-Tanh (University of Texas at Austin)
Learn2Solve: A Deep Learning Framework for Real-Time Solutions of forward, inverse, and UQ Problems
Digital models (DMs) are designed to be replicas of systems and processes. At the core of a digital model (DM) is a physical/mathematical model that captures the behavior of the real system across temporal and spatial scales. One of the key roles of DMs is enabling “what if” scenario testing of hypothetical simulations to understand the implications at any point throughout the life cycle of the process, to monitor the process, to calibrate parameters to match the actual process and to quantify the uncertainties. In this talk, we will present various (faster than) real-time Scientific Deep Learning (SciDL) approaches for forward, inverse, and UQ problems. Both theoretical and numerical results for various problems including transport, heat, Burgers, (transonic and supersonic) Euler, and Navier-Stokes equations will be presented.


Martedì 18 giugno 2024
Ore 16:00, Aula 1B , Dipaertimento SBAI
Wolfgang Woess (TU Graz)
Polyharmonic potential theory on the Poincaré disk
We consider the open unit disk \(\mathbb{D}\) equipped with the hyperbolic metric and the associated hyperbolic Laplacian \(\mathcal{L}\). For \(\lambda \in \mathbb{C}\) and \(n \in \mathbb{N}\), a \(\lambda\)-polyharmonic function of order \(n\) is a function \(f: \mathbb{D} \to \mathbb{C}\) such that \((\mathcal{L} - \lambda \, I)^n f = 0\). If \(n =1\), one gets \(\lambda\)-harmonic functions. Based on a Theorem of Helgason on the latter functions, we prove a boundary integral representation theorem for \(\lambda\)-polyharmonic functions. For this purpose, we first determine \(n^{\text{th}}\)-order \(\lambda\)-Poisson kernels. Subsequently, we introduce the \(\lambda\)-polyspherical functions and determine their asymptotics at the boundary \(\partial \mathbb{D}\), i.e., the unit circle. In particular, this proves that, for eigenvalues not in the interior of the \(L^2\)-spectrum, the zeroes of these functions do not accumulate at the boundary circle. Hence the polyspherical functions can be used to normalise the \(n^{\text{th}}\)-order Poisson kernels. By this tool, we extend to this setting several classical results of potential theory: namely, we study the boundary behaviour of \(\lambda\)-polyharmonic functions, starting with Dirichlet and Riquier type problems and then proceeding to Fatou type admissible boundary limits. In collaboration with Maura Salvatori and Massimo Picardello, JFA 2024.
Per informazioni, rivolgersi a: fabio.scarabotti@sbai.uniroma1.it


Mercoledì 19 giugno 2024
Ore 10:30, Aula seminari IAC- CNR (1 piano), IAC-CNR, Via dei Taurini 19, Roma
seminario di matematica applicata
Prof. Michael Vynnycky (University of Limerick (Ireland))
Practical asymptotics in applied science
Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced; asymptotics also provides a fuller understanding of the underlying problems. In this talk, I will give some examples of applications where this approach helped me: electrochemical pickling of steel, vanadium redox flow cells, pharmaceutical freeze-drying and moving-bed reactors
Per informazioni, rivolgersi a: Giuseppe Pontrelli (giuseppe.pontrelli@gmail.com)


Mercoledì 19 giugno 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Andrea Petracci (Università di Bologna)
On moduli spaces of Fano varieties and their singularities
Fano varieties are projective varieties with “positive curvature”. Examples of Fano varieties are projective spaces, products of projective spaces, Grassmannians and hypersurfaces in projective spaces of low degree. Recently, K-stability (which is the algebro-geometric version of Kähler-Einstein metrics in complex-differential geometry) has been used to construct compact (actually projective) moduli spaces of Fano varieties. In this talk I will explain how to use combinatorial methods (e.g. Minkowski sums of polytopes and toric geometry) to produce singular points on moduli spaces of Fano varieties. This is based on work with Anne-Sophie Kaloghiros. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.


Mercoledì 19 giugno 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario Algebre di Operatori
Nicola Pinamonti (University of Genova)
Secular growths and their relation to Equilibrium states in perturbative Quantum Field Theories
During this talk we discuss the emergence of secular growths in the correlation functions of interacting quantum field theories when treated with perturbation methods. It is known in the literature that these effects are present if the interaction Lagrangian density changes adiabatically in a finite interval of time. If this happens, the perturbative approach cannot furnish reliable results in the evaluation of scattering amplitudes or in the evaluation of various expectation values. We show, during this talk, that these effects can be avoided for adiabatically switched-on interactions, if the spatial support of the interaction is compact and if the background state is suitably chosen. In particular, this is the case when the background state is chosen to be at equilibrium and when thermalisation occurs at late time. The same result holds also if the background state is only invariant under time translation or if the explicit time dependence is not too strong, in a precise sense which will be discussed in the talk. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0


Giovedì 20 giugno 2024
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Gabriele Mondello (Sapienza)
Sottovarietà compatte massimali di A_g
Riporterò i risultati di un lavoro in collaborazione con Grushevsky, Salvati Manni e Tsimerman. In tale lavoro classifichiamo le sottovarietà olomorfe compatte massimali di A_g e determiniamo la massima dimensione di una sottovarietà compatta di A_g passante per un punto molto generico.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it


Giovedì 20 giugno 2024
Ore 14:30, Aula 1B1, Via Scarpa 16, Dipartimento SBAI, Sapienza Università di Roma
Seminario "PDE a Tutto SBAI"
Abdelrazek Dieb (Ibn Khaldoun University of Tiaret (Algeria))
Existence and non-existence results for non-linear elliptic systems involving Hardy potential
We discuss existence and non-existence results for non-negative super-solution to a class of gradients-potential systems with Hardy terms. In particular the existence of optimal critical curves that separates the existence and the non-existence regions is proved
Per informazioni, rivolgersi a: isabella.ianni@uniroma1.it


Venerdì 21 giugno 2024
Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario Algebre di Operatori
Adam Dor-on (Haifa University)
Arveson's hyperrigidity conjecture is false
A classical result in approximation theory due to Korovkin asserts that a sequence of positive unital maps on C([0,1]) converges pointwise to the identity if they merely converge to the identity on the functions 1,x,x^2. This result was later generalized by Saskin, who showed that convergence to the identity on a generating function system implies convergence to the identity everywhere if and only if the system has full Choquet boundary. Arveson's last open conjecture in his seminal work on non-commutative boundary theory predicts that a non-commutative analogue of Saskin's result holds. We refute Arveson's conjecture with an elementary counterexample. All notions will be explained during the talk. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0


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