Weekly Bulletin (it)

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

Settimana dal 16-05-2022 al 22-05-2022

Lunedì 16 maggio 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Eduard Fereisel (Charles U. Prague)
On Rayleigh-Benard problem in the framework of compressible fluid flows
We consider the physically relevant fully compressible setting of the Rayleigh-Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to the gravitational force. Under suitable restrictions imposed on the constitutive relations we show that this open system is dissipative in the sense of Levinson, meaning there exists a bounded absorbing set for any global-in-time weak solution. In addition, global-in-time trajectories are asymptotically compact in suitable topologies and the system possesses a global compact trajectory attractor. The standard technique of Krylov and Bogolyubov then yields the existence of an invariant measure - a stationary statistical solution sitting on the global attractor. In addition, the Birkhoff--Khinchin ergodic theorem provides convergence of ergodic averages of solutions belonging to the attractor a.s. with respect to the invariant measure.

Martedì 17 maggio 2022
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Lezione di analisi numerica
Simone Cacace

Martedì 17 maggio 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Dipartimento
Simone Cacace
Modeling and optimal control of a tentacle-like soft-manipulator
Soft-robotics is an emerging branch of robotics, focused on the design, construction and control of articulated manipulators (even with a large number of degrees of freedom) composed of elastic and soft materials, able to perform complex tasks and to adapt to the working environment. The main objective, compared to more classical rigid manipulators, is to ensure the safety of human-machine interactions, especially in the industrial, but also in the medical field, with futuristic applications to invasive surgery and rehabilitation of patients with limited mobility. In this seminar, I will present a mathematical model for a soft-robot inspired by an octopus tentacle, obtained using the theory of calculus of variations and studied through some tools of optimal control theory for partial differential equations. It is a two-dimensional model, which aims to capture the dynamics emerging from the biological structure of the tentacle. The reference theory is the Euler-Bernoulli beam, in particular its nonlinear formulation which includes an inextensibility constraint and a bending moment. To these properties a curvature constraint has been added, which prevents the tentacle from bending beyond a certain threshold, and also a distributed control term, which locally prescribes the curvature and models the voluntary contraction of the muscular system of the tentacle. I will also present the results obtained by numerically solving some typical optimal control problems in this field: reaching a point with the free-end of the tentacle, avoiding obstacles in the working environment, and grasping objects, guaranteeing stability at the contact points with respect to external perturbations. This is a joint work with A.C. Lai and P. Loreti at the Department of Basic and Applied Sciences for Engineering (SBAI), Sapienza University of Rome.

Martedì 17 maggio 2022
Ore 15:30, Sala di Consiglio e via zoom ID riunione: 867 4440 2839 Passcode: MDN, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Luca Bonaventura (Politecnico di Milano)
A deeper look at shallow waters
Geophysical fluid dynamics considers domains with horizontal length scales much larger than the vertical ones. In this regime, simplified mathematical models based on the hydrostatic approximation can be derived rigorously, such as the classical shallow water equations. Furthermore, vertically averaged or multi-layer non-hydrostatic models can also be derived in order to reproduce dispersive effects. In this talk, the classical derivation of shallow water models will be reviewed critically, with special focus on the role of turbulence modelling, on the choice of the proper time scales, on the treatment of boundary conditions at the free surface and on the correct asymptotic procedure to be followed, in order to provide a more solid foundation to the rigorous derivation of simplified models including non-hydrostatic pressure terms.
Per informazioni, rivolgersi a: carlini@mat.uniroma1.it

Martedì 17 maggio 2022
Ore 16:00, Aula "Dal Passo" and online on this link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Chaona Zhu (Chinese Academy of Sciences and Roma "Tor Vergata")
Prescribing scalar curvatures: the negative case
The problem of prescribing conformally the scalar curvature on a closed manifold of negative Yamabe invariant is always solvable, if the function to be prescribed is strictly negative, while sufficient and necessary conditions are known in the case that function is non positive. Still in the case of a negative Yamabe invariant, Rauzy (Trans. Amer. Math. Soc. 1995) showed solvability, if the function to be prescribed is not too positive, as quantified by Aubin-Bismuth (J. Funct. Anal. 1997) later on. In this talk we will review these results variationally and shed some light on the case, when Rauzy’s conditions fail. This talk is joint work with Martin Mayer.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it

Martedì 17 maggio 2022
Ore 16:00, Sala del Consiglio, Facoltà di Ingegneria Civile e Industriale
Miles Rubin (Technion - Israel Institute of Technology)
Modeling a smooth elastic-inelastic transition with a strongly objective numerical integrator needing no iteration
Large deformation evolution equations for elastic distortional deformation and isotropic hardening/softening have been developed that model a smooth elastic-inelastic transition for both rate-independent and rate-dependent response with no need for loading-unloading conditions. A novel special case is a rate-independent overstress model. Specific simplified constitutive equations are proposed that capture the main effects of elastic-plastic and elastic-viscoplastic materials with only a few material parameters. Moreover, a robust and strongly objective numerical integrator for these simplified evolution equations has been developed which needs no iteration. Examples show the response of the rate-independent overstress model.
Per informazioni, rivolgersi a: jacopo.ciambella@uniroma1.it

Mercoledì 18 maggio 2022
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Dipartimento
Vittoria Silvestri
Modelli di crescita aleatoria sul piano
Lo studio dei meccanismi che regolano la formazione di strutture complesse in natura è da tempo oggetto di intensa ricerca in diverse aree della fisica e della matematica. In questo seminario presenterò diversi modelli di crescita aleatoria introdotti in tale ambito, sia discreti che continui, discutendone proprietà asintotiche come limiti di scala, fluttuazioni e mixing.

Mercoledì 18 maggio 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Giacomo Micheli (University of South Florida)
An Equivariant Isomorphism Theorem for Arboreal Galois Representations
In this talk we first recall the notion of arboreal Galois representation and then we develop a method to effectively determine the set of primes p for which certain arboreal Galois representations are surjective modulo p. Our method is based on a combination of height bounds on integral points on elliptic curves over function fields in positive characteristic and the ABC theorem for function fields. Using this technique we prove Jones' conjecture on the surjectivity of the arboreal Galois representation attached to f=x^2+t [Conjecture 6.7, Compositio Math. 43 (5) (2007)]. This is a recent joint work with Andrea Ferraguti.
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it

Mercoledì 18 maggio 2022
Ore 14:00, aula C, Dipartimento di Matematica
mini-corso (3 lezioni)
François Hamel (Aix-Marseille Université)
Travelling fronts and spreading properties for reaction-diffusion equations
mini-corso di dottorato, rivolto anche a ricercatori e professori, composto da 3 lezioni di 2 ore. Programma del corso disponibile su https://phd.uniroma1.it/web/pagina.aspx?i=3519&l=IT&p=478 Possibilità di seguirlo da remoto su https://uniroma1.zoom.us/j/89445477607 ID riunione: 894 4547 7607
Per informazioni, rivolgersi a: l.rossi@uniroma1.it

Mercoledì 18 maggio 2022
Ore 14:30, Aula 211 - Pal. C - Largo S. Leonardo Murialdo 1, Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre
Seminario di Analisi Matematica
Antonio J. Fernandez (ICMAT Madrid)
Singular limits for a half-Laplacian Liouville type equation.
We consider the nonlocal Liouville type equation (-Delta)^(1/2)u = epsilon * k(x) e^u, u > 0 in I u = 0 in R \ I where I is a union of d >= 2 disjoint bounded intervals, k is a smooth bounded function with positive infimum and epsilon > 0 is a small parameter. For any integer 1 <= m <= d, we construct a family of solution u_\epsilon which blow-up at m distinct points of I and for which epsilon *(integral of k(x) e^u) --> 2m*pi as epsilon --> 0. Moreover, we show that, when d = 2 and m is suitably large, no such construction is possible. The talk is based on a joint work with Matteo Cozzi (Milano, Italy).
Per informazioni, rivolgersi a: lbattaglia@mat.uniroma3.it

Mercoledì 18 maggio 2022
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabililtà
Michele Aleandri (Sapienza Università di Roma)
Opinion dynamics: conformist and nonconformist interacting agents
We study two models of binary decisions in a connected network of interacting agents. Individual decisions are determined by social influence, coming from direct interactions with neighbours, and a group level pressure that accounts for social environment. We study the convergence of the mean field variables associated to the processes as the number of agents goes to infinity and we show that propagation of chaos occurs. In the first model, we have a family of conformist or nonconformist agents that interact with each other. When the number of agents is large but fixed, we study the amount of time spent by the mean field variables associated to the process around the stable points of the macroscopic dynamics. In a nonconformist environment, there is a persistent disordered phase where no majority is formed: We show how in this case the introduction of a delay mechanism in the agent’s detection of the global average choice may drastically change this scenario, giving rise to a coordinated self sustained periodic behavior. In the second model, the population is divided into two social groups, each one characterized by its attitude with respect to the other. Agents of the same group interact with each other, while the other group exerts on them a social influence, that may also be null or even negative. We focus in particular on models with Lotka-Volterra type interactions, i.e., models with conformist vs. nonconformist groups. For these models, although the microscopic system is driven a.s. to consensus within each group, a periodic behaviour arises in the macroscopic scale. In order to describe fluctuations between the limiting periodic orbits, we identify a slow variable in the microscopic system and, through an averaging principle, we find a diffusion which describes the macroscopic dynamics of such variable on a larger time scale.

Giovedì 19 maggio 2022
Ore 14:15, Aula M3, Dipartimento di Matematica, Università di Roma Tre
Seminario di Geometria
Alessio Caminata (Genova)
Phylogenetic Trees, Tropical Geometry, and Rational Normal Curves
In 2004 Pachter and Speyer introduced the dissimilarity maps for phylogenetic trees and asked two important questions about their relationship with tropical Grassmannian. Multiple authors answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. In this talk, we present a negative answer to this second question. Then, we introduce a weighted variant of the dissimilarity map and show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. This tropical variety has a geometric interpretation in terms of point configurations on rational normal curves. The talk is based on a joint work with Noah Giansiracusa, Han-Bom Moon, and Luca Schaffler.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it

Giovedì 19 maggio 2022
Ore 15:00, Aula E - Sarà possibile partecipare al seminario anche in modalità telematica., Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica e Storia della Matematica
Ornella Robutti (Università di Torino)
Comunità di insegnanti di matematica in formazione: le loro prasseologie di design

Coloro che sono interessati a partecipare in modalità telematica possono contattare Annalisa Cusi (annalisa.cusi@uniroma1.it)

Venerdì 20 maggio 2022
Ore 14:30, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Fabio Gavarini (Università degli Studi di Roma "Tor Vergata")
Multiparameter quantum groups: a unifying approach
The original quantum groups – in particular, quantized universal enveloping algebras, in short QUEA’s – have been introduced as depending on just one “continuous” parameter. Later on, multiparameter quantum groups – in particular, multiparameter QUEA’s - have been introduced in differente ways, with the new, “discrete” parameters either affecting the coalgebra structure or the algebra structure (while leaving the dual structure unchanged). Both cases can be realized as special type deformations – namely, either by twist, or by 2-cocycle deformation – of Drinfeld's celebrated QUEA Uh(g). In this talk I will introduce a new, far-reaching family of multiparameter QUEA’s that encompasses and generalizes the previous ones, while also being stable with respect to both deformation by twists and deformations by cocycles. Taking semiclassical limits, these new multiparameter QUEA’s give rise to a new family of multiparameter Lie bialgebras, that in turn is stable under both by twist and deformations by 2-cocycles (in the Lie bialgebraic sense). This is a joint work with Gastón Andrés García – cf. arXiv:2203.11023 (2022).
Link per vedere seminario in streaming

Venerdì 20 maggio 2022
Ore 16:00, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Iain Gordon (University of Edinburgh)
(Joint with A.Brochier and N.White.) A few years ago, Bonnafé-Rouquier defined 'Calogero-Moser cells' through the representation theory of rational Cherednik algebras. These cells partition the elements of a complex reflection group, G, but are currently difficult to calculate except in small rank examples. In the special case when G is a finite Coxeter group, the cells are conjectured to be the same as Kazhdan-Lusztig cells. In other words, conjecturally 'Calogero-Moser cells' generalise Kazhdan-Lusztig cell theory from Coxeter groups to complex reflection groups. I will discuss a confirmation of this conjecture for G being the symmetric group. The proof uses ideas from integrable systems (Gaudin algebras), algebraic geometry (moduli of points on genus zero curves), and combinatorics (crystals). N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
Link per seguire seminario in streaming

Venerdì 20 maggio 2022
Ore 16:00, Aula III, Dipartimento di Matematica, Sapienza Università di Roma
MATH talks
Antonio Veredice (Sapienza Università di Roma)
La rinascita della Logica in Italia nella seconda metà del '900
La logica matematica ha in Giuseppe Peano uno dei maggiori rappresentanti a livello internazionale fra '800 e '900; quando gli interessi di Peano si spostano verso altre questioni (interlingua) gli studi di logica vengono abbandonati in Italia, proprio in un momento in cui la ricerca internazionale nel campo faceva importanti progressi sotto la spinta propulsiva dei teoremi limitativi di Godel. Solo negli anni '60 la ricerca in logica matematica rinasce in Italia ad opera di Ludovico Geymonat, Roberto Magari e altri studiosi che operano in un contesto pluridisciplinare tra matematica, filosofia e, più tardi, informatica teorica. Nella prima parte del seminario vedremo una ricostruzione storica di questo importante momento nella storia del pensiero scientifico Italiano. Nella seconda parte ci concentreremo invece sul controverso rapporto tra logica matematica e informatica teorica in Italia negli anni '70.
Per informazioni, rivolgersi a: mathtalks@uniroma1.it

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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