Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 22-01-2024 al 28-01-2024
Lunedì 22 gennaio 2024
Ore 14:00, Aula E, Dipartimento di Matematica, Sapienza Università di Roma
Minicorso dottorato
Alberto Cogliati (Università di Pisa)
Storia della geometria iperbolica (V)
Lunedì 22 gennaio 2024
Ore 14:00, Aula Seminari, RM004, Dipartimento SBAI:
Esami finali del dottorato di ricerca in Modelli Matematici per l'Ingegneria, Elettromagnetismo e Nanoscienze
-- Yuri Cacchiò - Geophysical Fluid Dynamics: 2D Navier-Stokes Equations on Rotational Frame, Well-Posedness and Enstrophy Cascade -- Maria Lucia Cardinali - Wavelet Scattering Transform for Signal Approximation and Classification -- Fausto Colantoni - Non-local Boundary Value Problems for Brownian motions
Per informazioni, rivolgersi a: lorenzo.giacomelli@uniroma1.it
Lunedì 22 gennaio 2024
Ore 14:30, Aula 24, Ed. CU002 (iv piano) - Zoom link, Dip. Scienze Statistiche, Sapienza
Seminario di Probabilità
Wolfgang Bock (Linnaeus University (Sweden))
Recent Results on the Generalized Grey Brownian Motion
Grey Brownian motion was introduced by Schneider in 1990. In his work Schneider showed that indeed the process fulfills a Feynman-Kac like formula for the solution of the fractional heat equation. In the 2000s the process was generalized by Mainardi et al. In 2016 the group of Grothaus established a White Noise like calculus for the process, also introducing spaces of test and generalized functions. In this talk, we will review this recent development and give an overview of the analysis and the most recent results. In an outlook, we give a strategy how to introduce spaces of regular distributions to obtain a form of regularity theory.
Per informazioni, rivolgersi a: luisa.beghin@uniroma1.it
Lunedì 22 gennaio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Nicola Visciglia (Università Degli Studi di Pisa)
Global well posedness for the generalized derivative NLS
The gDNLS equation in the periodic setting has been extensively studied in the literature. By standard compactness argument the associated Cauchy problem is well-known to be locally well posed. Our aim is to show that the local solutions can be globalized for small data, hence answering to a question raised by Ambrose-Simpson. This is a joint work with Masayuki Hayashi. This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 23 gennaio 2024
Ore 14:00, Aula E, Dipartimento di Matematica, Sapienza Università di Roma
Minicorso dottorato
Alberto Caglioti (Università di Pisa)
Storia della geometria iperbolica (VI)
Martedì 23 gennaio 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Michele Pernice (KTH (Stockholm))
A stacky Castelnuovo's contraction theorem
In this talk, we are going to discuss a generalization to weighted blowups of the classical Castelnuovo' contraction theorem. Moreover, we will show as a corollary that the moduli stack of n-pointed stable curves of genus 1 is a weighted blowup. This is a joint work with Arena, Di Lorenzo, Inchiostro, Mathur, Obinna.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 24 gennaio 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Charles Young (University of Hertfordshire)
Raviolo vertex algebras, higher current algebras, and raviolo conformal blocks
Vertex algebras formalise the properties of what physicists would call operator product expansions (OPEs) in chiral conformal field theories (CFTs). One way to motivate the axioms of vertex algebras is by first defining conformal blocks in genus zero, and then studying their limits in which marked points collide. One would like to generalise this story to higher settings: "higher" in the sense of higher dimensions, but also in the sense of higher/homotopy/differential graded (dg) algebras. In recent months, an elegant and comparatively accessible instance of such higher vertex algebras has been introduced by Garner and Williams. They are called raviolo vertex algebras, and are associated to manifolds of real dimension three admitting a transverse holomorphic foliation; that is, roughly, manifolds having one complex-holomorphic and one topological direction. I will describe these raviolo vertex algebras, and go on to show that they, too, arise from the limiting behaviour of certain raviolo conformal blocks, which I will introduce in the talk. In particular I will describe a certain configuration space of ravioli, and a model in dg commutative algebras of the derived sections of its structure sheaf. This talk is based on work in preparation, joint with Luigi Alfonsi and Hyungrok Kim.
Mercoledì 24 gennaio 2024
Ore 14:30, Aula I piano e canale youtube dell'IAC https://www.youtube.com/cnriac, Istituto per le Applicazioni del Calcolo, Cnr, via dei Taurini 19, Roma
Seminario generale IAC
Shi Jin (Shanghai Jiao Tong University)
Dimension Lifting for Quantum Computation of partial differential equations and related problems
Quantum computers have the potential to gain algebraic and even up to exponential speed up compared with their classical counterparts, and can lead to a technology revolution in the 21st century. Since quantum computers are designed based on the quantum mechanics principle, they are most suitable to solve the Schrodinger equation, and linear PDEs (and ODEs) evolved by unitary operators. The most efficient quantum PDE solver is a quantum simulation based on solving the Schrodinger equation. It will be interesting to explore what other problems in scientific computing, such as ODEs, PDEs, and linear algebra that arise in both classical and quantum systems, can be handled by quantum simulation. We will present a systematic way to develop quantum simulation algorithms for general differential equations. Our basic framework is dimension lifting, which transfers nonlinear PDEs to linear ones, and linear ones to Schrodinger typo PDEs. For non-autonomous PDEs and ODEs, or Hamiltonian systems with time-dependent Hamiltonians, we also add an extra dimension to transform them into autonomous PDEs that have only time-independent coefficients, thus quantum simulations can be done without using the cumbersome Dyson’s series and time-ordering operators. Our formulation allows both qubit and qumode (continuous-variable) formulations, and their hybridizations.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Mercoledì 24 gennaio 2024
Ore 15:00, Aula E, Dipartimento di Matematica
Seminario di Storia e Cultura matematica
Carlo Toffalori (Università di Camerino)
La Matematica di Mantegna
Mercoledì 24 gennaio 2024
Ore 15:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario
Filippo A. E. Nuccio Mortarino Majno di Capriglio (Université Jean Monnet Saint-Étienne/Institut Camille Jordan)
How to enjoy a mathematical discussion with your laptop
In this talk I will illustrate how certain programs, of which Lean is an example, permit to interact with a computer about the logical soundness of mathematical arguments. I will go through the details of well-known proofs trying to understand the feedback provided by the computer and will try to share the fun involved in the process. This seminar is part of the program "Computer-verified proofs: 48 hours in Rome"; see https://www.mat.uniroma2.it/butterley/formalisation/ for more information.
Per informazioni, rivolgersi a: greenblatt@mat.uniroma2.it
Mercoledì 24 gennaio 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Stefano Olla (Università di Paris-Dauphine e GSSI)
Heat equation from a deterministic dynamics
We derive the heat equation for the thermal energy under diffusive space-time scaling from a purely deterministic microscopic dynamics satisfying Newton equations perturbed by an external chaotic force acting like a magnetic field. Joint work with Giovanni Canestrari and Carlangelo Liverani.
Per informazioni, rivolgersi a: basile@mat.uniroma1.it
Giovedì 25 gennaio 2024
Ore 12:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario
Floris van Doorn (Bonn)
The internals of Lean
In this talk I will describe what goes on behind the scenes of Lean. I will explain the logic of Lean, called dependent type theory, what Lean tactics are and explain why we can trust proofs that are checked by Lean. This seminar is part of the program "Computer-verified proofs: 48 hours in Rome"; see https://www.mat.uniroma2.it/butterley/formalisation/ for more information.
Per informazioni, rivolgersi a: greenblatt@mat.uniroma2.it
Giovedì 25 gennaio 2024
Ore 14:30, Aula 1B1, RM002, Via A.Scarpa 16, Dipartimento SBAI, Sapienza Università di Roma
Seminario "PDE a tutto SBAI"
Davide Buoso (Università degli Studi del Piemonte Orientale “A. Avogadro”)
Bulk-boundary eigenvalue problems: a review
Diffusion equations in their linearized versions naturally lead to the study of elliptic eigenvalue problems where the eigenvalue appears both in the interior and on the boundary. This kind of spectral problems have surged in the literature only recently and give rise to many appealing questions. In this talk we will review two such problems that showed to be particularly interesting: the first one comes from the Allen-Cahn equation and is associated with the Laplacian, and has already been used to prove interesting results in spectral geometry. The second one comes from the Cahn-Hillard equation and is associated with the bilaplacian. After introducing these two problems, we will recall some basic facts from Spectral Theory and Spectral Geometry to provide context, and then discuss major properties and open problems concerning their eigenvalues.
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Giovedì 25 gennaio 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario
Gihan Marasingha (University of Exeter)
The benefits and challenges of teaching proof with Lean
This presentation will explore the pivotal role of Lean in enhancing first-year undergraduates' understanding of mathematical proofs. I will share insights from my experiences and initial educational research on teaching a large first-year undergraduate cohort with Lean, focusing on how this tool can significantly impact student perception of proofs. Additionally, I will address the challenges encountered in teaching with Lean and the implications for learning and comprehension. This seminar is part of the program "Computer-verified proofs: 48 hours in Rome"; see https://www.mat.uniroma2.it/butterley/formalisation/ for more information.
Per informazioni, rivolgersi a: greenblatt@mat.uniroma2.it
Giovedì 25 gennaio 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario
Nana Liu (Shanghai Jiao Tong University)
Analog quantum simulation of partial differential equations
Quantum simulators were originally proposed to be helpful for simulating one partial differential equation (PDE) in particular - Schrödinger's equation. If quantum simulators can be useful for simulating Schrödinger's equation, it is hoped that they may also be helpful for simulating other PDEs. As with large-scale quantum systems, classical methods for other high-dimensional and large-scale PDEs often suffer from the curse-of-dimensionality (costs scale exponentially in the dimension D of the PDE), which a quantum treatment might in certain cases be able to mitigate. To enable simulation of PDEs on quantum devices that obey Schrödinger's equations, it is crucial to first develop good methods for mapping other PDEs onto Schrödinger's equations. In this talk, I will introduce the notion of Schrödingerisation: a procedure for transforming non-Schröodinger PDEs into a Schrödinger-form. This simple methodology can be used directly on analog or continuous quantum degrees of freedom - called qumodes, and not only on qubits. This continuous representation can be more natural for PDEs since, unlike most computational methods, one does not need to discretise the PDE first. In this way, we can directly map D-dimensional linear PDEs onto a (D + 1)-qumode quantum system where analog Hamiltonian simulation on (D + 1) qumodes can be used. I show how this method can also be applied to both autonomous and non-autonomous linear PDEs, certain nonlinear PDEs, nonlinear ODEs and also linear PDEs with random coefficients, which is important in uncertainty quantification. This formulation makes it more amenable to more near-term quantum simulation methods and enables simulation of PDEs that are not possible with qubit-based formulations in the near-term.
Venerdì 26 gennaio 2024
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario MoMA
Marco Scuderi (Sapienza Università di Roma)
The spectrum of fault slip behavior and precursor to failure, what can we (machine) learn on earthquake prediction?
Earthquakes and tectonic fault slip are among the most hazardous and unpredictable natural phenomena. Fluids play a key role in tectonic faulting and recent research suggests that fluids are central in both human induced seismicity and the mode of fault slip, ranging from episodic tremor and slip to slow earthquakes. However, the lack of accessibility to earthquake faults and the complexity of physical processes has limited our ability to develop holistic models for fault zone behavior. Geophysical observations have the potential for illuminating precursors to failure for the spectrum of tectonic faulting, however we lack key laboratory data to connect these observations with predictive, physics-based models. In the past 5 years we have developed two prototypes state-of-the-art rock deformation apparatuses that allows us to illuminate the details of fault behavior under a range of boundary conditions. On the ground of theoretical consideration we have been able to reproduce the full spectrum of fault slip behavior, from aseismic creep, slow earthquakes to elasto-dynamic rupture. We find systematic variation of elastic wave propagation and acoustic precursors to failure. We train machine learning models to successfully predict lab earthquakes.
Per informazioni, rivolgersi a: basile@mat.uniroma1.it, adriana.garroni@uniroma1.it
Venerdì 26 gennaio 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Colloquium di dipartimento
Kevin Buzzard (Imperial College London)
Formalising modern research mathematics
A few years ago, the idea of formalising modern research level mathematics seemed completely out of reach. Since then, more and more examples have appeared. I'll go through several examples (some related to the mathematics of Scholze, Tao and Gowers), and talk about how the process is evolving, enabling multiple people to collaborate in the formalisation of modern research in real time.
Per informazioni, rivolgersi a: greenblatt@mat.uniroma2.it
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