15 Maggio, 2024 17:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

More about some geometric and algebraic aspects of Bicomplex Möbius Transformations

Elena Luna Elizarraras, Holon Institute of Technology

On-line (link: polimi-it.zoom.us/j/96642022726)

abstract

abstract

Although some authors have previously considered Möbius transformations in the bicomplex context, in this talk we will show some new aspects of them, which can only be understood using what could be called geometric-hyperbolic objects.

15 Maggio, 2024 11:00

MOX Seminar

Analysing multivariate densities in Bayes spaces with implications for functional data analysis

Karel Hron, University Olomouc

Aula Saleri - Seminari VI piano

abstract

abstract

Probability density functions can be embedded in the geometric framework of Bayes spaces which respect their relative nature and enable further modeling and analysis. Specifically, the Hilbert space structure of Bayes spaces (whereof compositional data are one specific instance) has several important implications for classical and Bayesian inference, as well as functional data analysis. In this contribution, an orthogonal decomposition of multivariate densities in Bayes spaces using a distributional analog of the Hoeffding-Sobol identity is constructed. The decomposition is based on a reformulation of the standard (arithmetic) margins into so-called geometric margins. These are orthogonal projections into one-dimensional space of information contained in multivariate densities and coincide with the arithmetic margins in case of independence. More generally, the decomposition contains an independent part and all possible interaction terms. The orthogonality of the decomposition results in an analog of Pythagoras' Theorem for squared norms of the decomposed densities and margin-free property of the interaction terms. Because the squared norms from the Pythagoras' decomposition are essentially compositional in nature, all tools of the log-ratio methodology can be used for their statistical processing. Theoretical results will be illustrated with empirical geochemical data. This talk is based on joint work with Christian Genest and Johanna Nešlehová from McGill University, Montréal, Canada.

14 Maggio, 2024 09:30

Laboratorio FDS

MATEC4Girls

Laboratorio FDS, Dipartimento di Matematica - Politecnico di Milano

Dipartimento di Matematica

abstract

abstract

In occasione della Giornata internazionale delle Donne nella Matematica, che si celebra il 12 maggio, il laboratorio FDS invita le studentesse di III, IV e V delle scuole secondarie di secondo grado all'evento MATEC4Girls.

Programma della giornata

9:30-10:15 Benvenuto e saluti istituzionali a cura di:
Prof.ssa Irene Sabadini, Direttrice del Dipartimento di Matematica
Prof.ssa Isabella Nova Prorettrice delegata
10:15-11:15 Seminario introduttivo sugli inquinanti e la marmitta catalitica, a cura della Prof.ssa Isabella Nova

11:30-16:00 Laboratorio - Modellistica e ottimizzazione di forma, a cura della Dott.ssa Caterina Bassi

14 Maggio, 2024 15:00

Sezione di Probabilità e Statistica Matematica

The macroeconomic effects of climate change and the green transition

Matteo Ciccarelli, Head of Forecasting and Policy Modelling at European Central Bank

Aula Seminari - III piano. Zoom link: polimi-it.zoom.us/j/92204941893?pwd=UlFyODBjbis4eWltaTJIZmsyR0NzQT09

abstract

abstract

Modelling interaction between climate change, the green transition and the macroeconomy requires empirically validated assumptions. The presentation will focus on a few questions of relevance from the perspective of central banks and on the importance to understand the business cycle effects of climate-related shocks and risks. Based on recent empirical and modelling work on the topic and through the lens of standard economic concepts and models, the presentation will shed light on the demand and supply channels of climate-related shocks, on the importance of appropriately choosing the variables and proxies to ‘identify’ the shocks and account for the transmission channels in empirical analysis, and on the asymmetric and heterogenous effects of weather shocks and climate policies across countries. The presentation will conclude with implications for modellers and policy makers.

14 Maggio, 2024 11:30

Sezione di Analisi

Existence and multiplicity of coexistence states in a heterogeneous predator-prey model with saturation

Eduardo Munoz Hernandez, Universidad Complutense de Madrid

Aula Seminari - III Piano

abstract

abstract

In this talk we analyze a predator-prey model coming from the heterogeneous counterparts of the classical Lotka-Volterra
and Holling-Tanner models by considering a non-negative saturation term that can vanish inside the domain. By the use of the maximum principle and bifurcation theory the regions of coexistence can be exactly determined. Furthermore, by varying the amplitude of the saturation different multiplicity results will be obtained. This is a joint work with Julián López-Gómez.

13 Maggio, 2024 15:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

On the intersection cohomology of vector bundles

Camilla Felisetti, Università di Modena e Reggio Emilia

Aula seminari MOX VI piano

abstract

abstract

Intersection cohomology is a topological notion adapted to the description of singular topological spaces, and the Decomposition Theorem for algebraic maps is a key tool in the subject. The study of the intersection cohomology of the moduli spaces of semistable bundles on Riemann surfaces began in the 80’s with the works of Frances Kirwan. Motivated by the work of Mozgovoy and Reineke, in joint work with Andras Szenes and Olga Trapeznikova, we give a complete description of these structures via a detailed analysis of the Decomposition Theorem applied to a certain map from parabolic vector bundles. We also give a new formula for the intersection Betti numbers of these moduli spaces, which has a clear geometric meaning. In the talk, I will give an introduction to the subject, and describe our results.

9 Maggio, 2024 16:30

Laboratorio FDS

The road to zero: escape room matematica

Laboratorio FDS, Dipartimento di Matematica, Politecnico di Milano

Online

abstract

abstract

Il laboratorio Effediesse del Politecnico di Milano invita il pubblico al gioco-didattico "The road to zero", un'escape room in modalità online (via Zoom) consistente in sfide matematiche a tema cambiamento climatico.

La prova è rivolta a un ampio pubblico (sopra i 14 anni) e avrà la durata di un'ora. Per i minori è previsto l'accompagnamento dei genitori e/o un loro consenso informato in fase di iscrizione al gioco.

"The road to zero" ha come tema principale il cosidetto "net zero". L'obiettivo del gioco sarà trovare un equilibrio tra pozzi e sorgenti di anidride carbonica. Le sfide avranno prevalentemente carattere logico-matematico, con un livello di competenze matematiche presupposte pari a quello di una studentessa o uno studente del primo anno di scuole superiori. Per gli studenti, il gioco sarà quindi un modo per applicare le nozioni apprese a scuola in un contesto di grande attualità, mentre per i più adulti sarà un modo per testare i propri ricordi e, magari, (re-)innamorarsi della matematica.

Al termine della prova sarà offerto un breve seminario di carattere divulgativo per discutere le strategie di risoluzione degli enigmi proposti.

Come gioco di divulgazione scientifico-matematica, "The road to zero" sostiene l'Agenda 2030 per lo sviluppo sostenibile, in particolare in riferimento al Goal 4 "Istruzione di quslità" e Goal 13 "Lotta al cambiamento climatico".

Ingresso libero con prenotazione
Link di iscrizione all'evento: forms.office.com/e/fq52fhiEdk

9 Maggio, 2024 16:30

Sezione di Analisi

On the long-time behaviour of solutions to unforced evolution Navier-Stokes equations under Navier boundary conditions

Alessio Falocchi, Politecnico di Milano

Aula Seminari - III Piano

abstract

abstract

We study the asymptotic behaviour of the solutions to Navier-Stokes unforced equations under Navier boundary conditions in a wide class of merely Lipschitz domains of physical interest that we call sectors. The main motivations come from the celebrated results by Foias-Saut related to the long time behaviour of the solutions to Navier-Stokes equations under Dirichlet conditions.
Here the choice of the boundary conditions requires carefully considering the geometry of the domain, due to the possible lack of the Poincaré inequality in presence of axial symmetries. In non-axially symmetric domains we show the validity of the Foias-Saut result about the limit at infinity of the Dirichlet quotient, in axially symmetric domains we provide two invariants of the flow which completely characterize the motion and we prove that the Foias-Saut result holds for initial data belonging to one of the invariants.
This is a joint work with Prof. Elvise Berchio (Politecnico di Torino, Italy) and Clara Patriarca (Université libre de Bruxelles, Belgium).

9 Maggio, 2024 14:30

Dipartimento di Matematica del Politecnico di Milano

Condemned to excellence? Double standards and gender inequalities in science and research

Camilla Gaiaschi, Università del Salento

abstract

abstract

Double standard: what does it mean? The term refers to the existence of different evaluation criteria applied to individuals who are in the same situation or have the same characteristics. In terms of gender, especially in the workplace, including in science and research, it refers to the often harsher judgment applied to women during evaluations processes. This results in disadvantages in recruitment, promotion, and compensation. Through the analysis of European and Italian data on the presence of women in the research sector, as well as through some case studies conducted in the academic, medical, and bio-scientific fields, this contribution aims to provide an overview of the explanatory factors underlying gender inequalities in the scientific world, focusing on the individual, organizational and institutional levels.

Camilla Gaiaschi è ricercatrice presso l’Università del Salento. Ha conseguito un dottorato in sociologia presso l’Università degli Studi di Milano dove è successivamente assegnista di ricerca e docente del corso “Pari Opportunità e Carriere Scientifiche”. Prima di arrivare a Lecce ha svolto una Marie Curie Individual Fellowship presso l’Università di Losanna con il progetto dal titolo WIRED – Women In Research and higher EDucation.

I suoi interessi di ricerca vertono sulle disuguaglianze di genere nel mercato del lavoro e nelle professioni scientifiche, in particolare accademiche, sulle trasformazioni universitarie, sulle politiche di welfare in ottica di genere, e sul genere nella scienza. È autrice di numerose pubblicazioni scientifiche italiane e internazionali.

Dal 2022 in libreria con "Doppio Standard. Donne e carriere scientifiche nell'Italia contemporanea", edito da Carocci.
www.camillagaiaschi.com

8 Maggio, 2024 15:00 in punto

Sezione di Geometria, Algebra e loro applicazioni

Topology of three-dimensional Ricci limits and RCD spaces

Alessandro Pigati, Università Bocconi

Aula Seminari - III piano

abstract

abstract

Starting from the second half of the nineteenth century, it was understood that curvature, which is infinitesimal (geo)metric information on a space, integrates to give global structure results (in spite of its nonlinear nature), specifically yielding topological rigidity of the space. It was further observed by Gromov that a lower bound on the Ricci curvature is the essential ingredient in order to control the number of degrees of freedom at a metric level as well, allowing to compactify (in a very weak sense) the set of n-dimensional Riemannian manifolds obeying a Ricci lower bound. It was later understood that singular spaces belonging to this compactification (Ricci limits), are special cases of a more general analytic notion (RCD spaces), more stable with respect to certain natural operations, and thus they also inherit a rich analytic structure, allowing to do calculus on them.

In this talk, based on joint work with Elia Bruè and Daniele Semola, we will review some previously known structural results for Ricci limits and RCDs in the non-collapsed case, as well as some instructive examples and counterexamples, and we will see a new, more elementary proof that Ricci limits of dimension three are generalized manifolds, enjoying in particular uniform contractibility. Our tools, together with some results in geometric topology, give an alternative proof that they are in fact topological manifolds. We will also see a new result for tangent cones in higher dimension. If time allows, we will also mention a new structural theorem for RCDs in dimension three.

Camilla Gaiaschi è ricercatrice presso l’Università del Salento. Ha conseguito un dottorato in sociologia presso l’Università degli Studi di Milano dove è successivamente assegnista di ricerca e docente del corso “Pari Opportunità e Carriere Scientifiche”. Prima di arrivare a Lecce ha svolto una Marie Curie Individual Fellowship presso l’Università di Losanna con il progetto dal titolo WIRED – Women In Research and higher EDucation.

I suoi interessi di ricerca vertono sulle disuguaglianze di genere nel mercato del lavoro e nelle professioni scientifiche, in particolare accademiche, sulle trasformazioni universitarie, sulle politiche di welfare in ottica di genere, e sul genere nella scienza. È autrice di numerose pubblicazioni scientifiche italiane e internazionali.

Dal 2022 in libreria con "Doppio Standard. Donne e carriere scientifiche nell'Italia contemporanea", edito da Carocci.
www.camillagaiaschi.com