Notiziario Scientifico

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

Settimana dal 18-03-2024 al 24-03-2024

Lunedì 18 marzo 2024
Ore 13:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Vittoria Silvestri (Università di Roma La Sapienza)
Introduction to Random Geometry
This course wants to give an overview of active research topics in the field of Random Geometry, with a focus on growth models. We will start by discussing discrete growth models such as the Eden model, Diffusion Limited Aggregation and Internal DLA. We will then move to the continuum for the remaining part of the course. After discussing conformal invariance of Brownian motion, we will focus on the class of randomly growing domains on the complex plane which can be described via Loewner dynamics. We will introduce several random aggregation models on the complex plane, which go under the name of Hastings-Levitov models and Aggregate Loewner Evolutions, of which we will study the large-scale features, presenting existing results and several open questions.


Lunedì 18 marzo 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Xavier Lamy (Università di Tolosa)
On the stability of Möbius maps of the n-sphere
A classical theorem of Liouville asserts that if a map from the sphere to itself is conformal, then it must be a Möbius transform: a composition of dilations, rotations, inversions and translations (identifying sphere and euclidean space via stereographic projection). There is a long history of studying stability of this rigidity statement: if a map is nearly conformal, must it be close to a Möbius transform? One can also ask what happens if the image of the map is only nearly spherical. I will present optimal stability estimates obtained with André Guerra and Kostantinos Zemas, which generalize to higher dimensions recent results for the 2-sphere (where, unlike higher dimensions, the problem can be directly linearized). 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.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it


Lunedì 18 marzo 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Gianmarco Bet (Università di Firenze)
Detecting a late changepoint in the preferential attachment model
Motivated by the problem of detecting a change in the evolution of a network, we consider the preferential attachment random graph model with a time-dependent attachment function. Our goal is to detect whether the attachment mechanism changed over time, based on a single snapshot of the network at time \(n\) and without directly observable information about the dynamics. We cast this question as a hypothesis testing problem, where the null hypothesis is a preferential attachment model with a constant affine attachment parameter \(\delta_0\), and the alternative hypothesis is a preferential attachment model where the affine attachment parameter changes from \(\delta_0\) to \(\delta_1\) at an unknown changepoint time \(\tau_n\). For our analysis we assume that the changepoint occurs close to the observation time of the network, which corresponds to the relevant scenario where we aim to detect the changepoint shortly after it has happened. We present two tests based on the number of vertices with minimal degree. The first test assumes knowledge of \(\delta_0\), while the second does not. We show that these are asymptotically powerful when \(n-\tau_n \gg n^{1/2}\). Furthermore, we prove that the test statistics for both tests are asymptotically normal, allowing for accurate calibration of the tests. If time allows, we will present numerical experiments to illustrate the finite sample test properties.
Per informazioni, rivolgersi a: faggiona@mat.uniroma1.it


Martedì 19 marzo 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Agnese Pacifico (Sapienza University of Rome)
Control and identification of unknown PDEs
In this talk we address the control of Partial Differential equations (PDEs) with unknown parameters. Our objective is to devise an efficient algorithm capable of both identifying and controlling the unknown system. We assume that the desired PDE is observable provided a control input and an initial condition. Given an estimated parameter configuration, we compute the corresponding control using the State-Dependent Riccati Equation (SDRE) approach. Subsequently, we observe the trajectory and estimate a new parameter configuration using Bayesian Linear Regression method. This process iterates until reaching the final time, incorporating a defined stopping criterion for updating the parameter configuration. The systems arising from the discretization of PDEs are high dimensional, therefore we also focus on the computational cost of the algorithm. The Proper Orthogonal Decomposition (POD), a Model Order Reduction technique, is applied to the system in order to reduce the computational cost of the control computation step, and this provides impressive speedups. We present numerical examples to show the accurateness of the proposed method.


Martedì 19 marzo 2024
Ore 14:30, aula 1° piano, CNR-IAC, via dei Taurini 19, Roma
Seminari Generali dell'IAC 2024
Matteo Paoluzzi (CNR-IAC )
Collective Behavior in Living Materials
Active Materials are collections of self-propelled particles that serve as model systems for several biological systems ranging from epithelial tissues to bacterial microfilms. Because of their non-equilibrium dynamics, active systems can show condensed phases that are prevented by fluctuations at equilibrium. For instance, active particles can condense even in the absence of any attractive force, develop collective long-ranged polar order in two spatial dimensions, and produce spontaneous currents once embedded into complex environments. In this talk, I will show how most of the peculiarities of scalar active systems can be rationalized in terms of persistent random walks. I will explore the impact of such non-equilibrium dynamics on a coarse-graining scale where it is possible to observe a phase separation driven by the noise. Link streaming QUI: https://www.iac.cnr.it/matteo-paoluzzi-i-seminari-generali-delliac-2024
Per informazioni, rivolgersi a: roberta.bianchini@cnr.it


Martedì 19 marzo 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Leo HerrLeo Herr (University of Utah)
The rhizomic topology and tropical abelian varieties
The log etale topology is a natural analogue of the etale topology for log schemes. Unfortunately, very few things satisfy log etale descent -- not even vector bundles or the structure sheaf. We introduce a new rhizomic topology that sits in between the usual and log etale topologies and show most things do satisfy rhizomic descent! As a case study, we look at tropical abelian varieties and give some exotic examples.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com


Mercoledì 20 marzo 2024
Ore 10:00, Aula E, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke


Mercoledì 20 marzo 2024
Ore 10:30, Aula Dal Passo, Dipartimento di Matematica, Università degli studi di Roma "Tor Vergata"
corso di dottorato
Hartmut Prautzsch (Karlsruhe Institute of Technology)
Rational Curves and Surfaces for Geometric Modelling
Rational parametrization of quadrics: Week 4 o Stereographic projection and its generalization o Triangular patches on quadrics o Tensor-product patches on quadrics and Miquel’s theorem o Canal and pipe surfaces
Il materiale del corso è raccolto in un canale teams dedicato a cui gli interessati possono essere aggiunti scrivendo a manni@mat.uniroma2.it


Mercoledì 20 marzo 2024
Ore 11:30, Aula C, Dipartimento di Matematica e Fisica (Via della Vasca Navale, 84), Università di Roma Tre
Seminario di Logica e Informatica Teorica
Noa Lavl (Università degli Studi Roma Tre)
Factorization in generalized power series
A classical tool in the study of real closed fields are the fields \(K((G))\) of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field \(K\) of characteristic 0 and exponents in an ordered abelian group \(G\). We generalize previous results about irreducible elements and unique factorization in the subring \(K((G\leq0))\).


Mercoledì 20 marzo 2024
Ore 13:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Vittoria Silvestri (Università di Roma La Sapienza)
Introduction to Random Geometry
This course wants to give an overview of active research topics in the field of Random Geometry, with a focus on growth models. We will start by discussing discrete growth models such as the Eden model, Diffusion Limited Aggregation and Internal DLA. We will then move to the continuum for the remaining part of the course. After discussing conformal invariance of Brownian motion, we will focus on the class of randomly growing domains on the complex plane which can be described via Loewner dynamics. We will introduce several random aggregation models on the complex plane, which go under the name of Hastings-Levitov models and Aggregate Loewner Evolutions, of which we will study the large-scale features, presenting existing results and several open questions.


Mercoledì 20 marzo 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Claudio Procesi (Sapienza Università di Roma)
Algebre di Cayley-Hamilton e pseudocaratteri
Il titolo si riferisce al teorema di Cayley-Hamilton che esprime il fatto che una matrice n x n su un anello commutativo A soddisfa il suo polinomio caratteristico. La Teoria delle algebre di Cayley-Hamilton è una assiomatizzazione di questo fatto. Gli pseudocaratteri sono funzioni su un gruppo a valori in un anello commutativo che generalizzano i caratteri, appaiono in Teoria dei Numeri per studiare deformazioni di rappresentazioni. Un risultato recente su tali deformazioni potrebbe dare un esempio mancante nella teoria delle algebre di Cayley-Hamilton in caratteristica positiva.


Mercoledì 20 marzo 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Jacopo Bassi
How far is SL(3,Z) from being hyperbolic?
Motivated by the problem of determining whether biexactness, the (AO)-property and von Neumann solidity are equivalent properties for a discrete countable group, I will discuss few recent results regarding analytic properties of SL(3,Z), related to hyperbolicity. I will focus on the role of measurable dynamics and proximality arguments in this context. Partly based on joint works with F. Radulescu and T. Amrutam. Some references: https://arxiv.org/abs/2305.16277 https://arxiv.org/abs/2111.13885 https://arxiv.org/abs/2403.05948 The Operator Algebra Seminar schedule here: https://sites.google.com/view/oastorvergata/home-page


Mercoledì 20 marzo 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Carlo Presilla (Sapienza Università di Roma)
Puzzling pyramidal molecules: solved problems that raise new questions
The mere existence and the spectroscopic behavior of pyramidal molecules like ammonia have remained unsolved problems since the early developments of quantum mechanics. A possible solution can be found on the idea of spontaneous symmetry breaking. I discuss a model proposed some years ago with G. Jona-Lasinio and C. Toninelli and its more recent developments. Despite the simplicity of the model, results are obtained which are in quantitative agreement with experiments and provide predictions for the behavior of general chiral gases and their mixtures in fields from cold atoms to astronomical data. However, many open questions remain including whether this model can be considered a step to understanding homochirality.
Per informazioni, rivolgersi a: basile@mat.uniroma1.it, domenico.monaco@uniroma1.it


Giovedì 21 marzo 2024
Ore 14:00, Aula D'Antoni, Dipartimento di Matematica, Università degli studi di Roma "Tor Vergata"
corso di dottorato
Hartmut Prautzsch (Karlsruhe Institute of Technology)
Rational Curves and Surfaces for Geometric Modelling
Rational parametrization of quadrics: Week 4 o Stereographic projection and its generalization o Triangular patches on quadrics o Tensor-product patches on quadrics and Miquel’s theorem o Canal and pipe surfaces
Il materiale del corso è raccolto in un canale teams dedicato a cui gli interessati possono essere aggiunti scrivendo a manni@mat.uniroma2.it


Giovedì 21 marzo 2024
aula INdAM, Dipartimento di Matematica, Sapienza Università di Roma
Seminari gruppo UMI-CliMath
Programma

  • 14:00-14:50 Piermarco Cannarsa (Università di Roma Tor Vergata) Metodi quantitativi nella scienza del clima: possibili apporti della matematica
  • 15:00-15:50 Carlo Massimo Casciola (Sapienza Università di Roma) Metastabilità, eventi rari e implicazioni (per il clima e non solo)
  • 16:00-16:30 Tavola Rotonda
Sito web https://umi.dm.unibo.it/gruppi-umi-2/gruppo-umi-climath/

Giovedì 21 marzo 2024
Ore 14:30, Aula 1B1, RM002, Via A.Scarpa 16, Dipartimento SBAI, Sapienza Università di Roma
Seminari "PDE a tutto SBAI"
Francesca Gladiali (Università di Sassari)
On the critical points of solutions of Pdes in non-convex settings: the case of concentrating solutions.
In questo seminario parlerò del numero dei punti critici delle soluzioni di Pdes ellittiche nonlineari in un dominio di R^2 non convesso contrattile oppure no. Proverò una stima sul numero dei punti critici per le soluzioni del problema di Gel’fand che si concentrano. Farò vedere che in alcuni casi la stima è ottimale. I risultati si basano su un lavoro in collaborazione con M. Grossi.
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it


Giovedì 21 marzo 2024
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke


Giovedì 21 marzo 2024
Ore 16:00, Sala di Consiglio (e anche online, tramite la piattaforma Zoom), Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica della Matematica
Marta Menghini (Sapienza Università di Roma)
I contenuti matematici per la formazione insegnanti. Un'analisi storica.

Per informazioni, rivolgersi a: annalisa.cusi@uniroma1.it


Venerdì 22 marzo 2024
Ore 13:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Vittoria Silvestri (Università di Roma La Sapienza)
Introduction to Random Geometry
This course wants to give an overview of active research topics in the field of Random Geometry, with a focus on growth models. We will start by discussing discrete growth models such as the Eden model, Diffusion Limited Aggregation and Internal DLA. We will then move to the continuum for the remaining part of the course. After discussing conformal invariance of Brownian motion, we will focus on the class of randomly growing domains on the complex plane which can be described via Loewner dynamics. We will introduce several random aggregation models on the complex plane, which go under the name of Hastings-Levitov models and Aggregate Loewner Evolutions, of which we will study the large-scale features, presenting existing results and several open questions.


Venerdì 22 marzo 2024
Ore 17:00, Aula D'Antoni, Dipartimento di Matematica, U Roma Tor Vergata
Seminario di Topologia
Manish Saggar (U Stanford)
Capturing Brain dynamics using Topological Data Analysis
Characterizing intrinsic and extrinsic transitions in cortical activity can provide an understanding of cognition, e.g., how the ebbs and flows of cognition are anchored in the transitions of neural activity. Further, such anchoring could facilitate better models for psychiatric disorders and provide novel avenues for cognitive enhancement. This talk explores how noninvasive neuroimaging, despite its inherent limitations, can be leveraged to anchor cognitive performance and psychiatric nosology into rich spatiotemporal dynamics. We propose using tools from Topological Data Analysis (TDA), especially Mapper, to tackle the inherent noise in noninvasive neuroimaging devices and for capturing and characterizing brain dynamics in healthy and patient populations.


Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente mediante apposita form da compilare online, entro le ore 24 del giovedì precedente la settimana interessata. Le comunicazioni pervenute in ritardo saranno ignorate. Per informazioni, rivolgersi all'indirizzo di posta elettronica seminari@mat.uniroma1.it.
Coloro che desiderano ricevere questo notiziario via e-mail sono pregati di comunicare il proprio indirizzo di posta elettronica a seminari@mat.uniroma1.it.

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