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Dove / Data e Ora: Aula 1A150, Torre Archimede, il giorno 29/05/2018 alle ore 16:30

Relatore: Nicola Pagani (University of Liverpool)

Abstract: A recurring theme in mathematics is the problem of classifying certain objects modulo a suitable notion of isomorphism. In some cases the resulting set of equivalence classes can be naturally endowed with some geometric structure (a topological space, etc.). When this happens, the resulting geometric object is called a moduli space. In this talk we present some examples of this phenomenon starting from familiar objects such as spheres, triangles (modulo isometry) and linear subspaces of a given vector space (modulo automorphisms of the ambient vector space). We will then explore applications of this approach to problems in enumerative geometry and then try to give a hint of how and why moduli spaces are used in physics.

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La storia di Plimpton 322

Dove / Data e Ora: Aula 1AD100, il giorno 25/05/2018 alle ore 16:00

Relatore: Prof. Luigi Salce (Università di Padova)

Abstract: Si tratta della storia di una tavoletta babilonese che contiene tabelle numeriche variamente interpretate.

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Nastri, orologi e ciambelle: un viaggio nella ricerca ''matemusicale'' contemporanea

Dove / Data e Ora: Aula 1A150, Torre Archimede, il giorno 19/04/2018 alle ore 15:30

Relatore: Moreno Andreatta (CNRS IRCAM UPMC)

Abstract: La musica e la matematica hanno legami profondi le cui origini sono antichissime. In questa conferenza ci soffermeremo su alcune rappresentazioni geometriche a servizio della musica ed in particolare su quelle che sembrano particolarmente adatte a mettere in evidenza il ruolo della simmetria nell’organizzazione dello spazio armonico: la rappresentazione circolare, le cui origini coincidono con l’invenzione della combinatoria, e il Tonnetz o “reticolo delle note”, che segna la nascita della teoria dei grafi. Mostreremo numerosi esempi, anche con l’aiuto del pianoforte, di come talvolta i musicisti anticipino nelle loro composizioni l’emergenza di strutture algebriche e geometriche che i matematici avrebbero formalizzato solo successivamente.

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A gentle walk through SPDEs

Dove / Data e Ora: Aula 1A150, il giorno 08/03/2018 alle ore 16:30

Relatore: Marta Sanz-Solé (Universitat de Barcelona)

Abstract: The theory of stochastic partial differential equations (SPDEs) emerged about thirty years ago and since then, it has been undergoing a dramatic development. This new field of mathematics is at the crossroad of probability and analysis, combining tools from stochastic analysis and the classical theory of partial differential equations. Motivations for the study of SPDEs arise both within mathematics, as well as from applications to other scientific settings possessing an inherent component of randomness. This randomness can be, for example, in the initial conditions, in the environment, or as an external forcing. In the lecture, I will describe the mathematical approach to the most fundamental problems in the theory of SPDEs. For example, the underlying stochastic calculus, existence and uniqueness of solutions, and the properties of their sample paths. Aiming to be accessible to an audience ranging from graduate students to researchers not necessarily in the field of probability, the lecture will be of colloquium style, insisting on ideas rather than in technical details.

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Pieces of soap films

Dove / Data e Ora: Aula Magna, Palazzo Bo, il giorno 15/02/2018 alle ore 16:00

Relatore: Camillo De Lellis ((Universität Zürich, IAS Princeton) )

Abstract: The Plateau problem, named by Henry Lebesgue after the Belgian physicist, consists in finding the surface of least area which spans a given contour: Plateau discovered that soap films obey that simple energy principle. In order to investigate the question, generations of mathematicians have investigated the very fundamental notions of ``surface'', ``boundary'' and ``area'', proposing a variety of different theories. In this talk I will give a brief exposition of the so-called theory of currents, introduced by Federer and Fleming in the 60es after the pioneering work of De Giorgi in the case of hypersurfaces. I will then discuss an open question relating the shapes of the contour and that of the minimizer, posed by Almgren in the early eighties and recently solved in a joint work with Guido de Philippis, Jonas Hirsch and Annalisa Massaccesi.

CV Relatore: SHORT BIO: Camillo De Lellis was born in San Benedetto del Tronto (AP), and received his Ph.D. in Mathematics from the Scuola Normale Superiore at Pisa, in 2002. He is Full Professor of Mathematics at University of Zürich since 2005 and is going to be appointed on July 2018 as Professor of the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey. Camillo De Lellis is a world-renowned geometric analyst with a broad expertise in fluid dynamics, geometric regularity theory and calculus of variations. Camillo has given a number of remarkable contributions in central problems of these fields, introducing modern tools and innovative approaches that have resulted in new and monumental insights in these areas and have advanced fundamental understanding within the mathematical community. In particular, Camillo has worked on various aspects of the theory of hyperbolic systems of conservation laws and of incompressible fluid dynamics, where, together with Lászlo Székelyhidi, he has introduced the use of Mikhael Gromov’s convex integration methods, combined with the embedding theorems of John Nash, to analyse non-uniqueness issues for weak solutions to the Euler equation and the Onsager conjecture (about dissipative solutions of the Euler equation). Camillo, in collaboration with Emanuele Spadaro, has also utilized pioneering techniques, coupled with a novel approach, to craft an accessible proof of the 1.000-page result on partial regularity of minimal surfaces obtained by Frederick J. Almgren, thus providing a concise modern version of the theory that not only strengthened Almgren’s original assertion, but also presented many new insights opening new lines to inquiry. Camillo’s groundbreaking achievements in fluid dynamics and in the regularity of minimal surfaces earned him the prestigious Fermat Prize in 2013. His original and transformative work in the field has also resulted in the Stampacchia Gold Medal in 2009; the SIAG/APDE Prize in 2013 (shared with Lászlo Székelyhidi); the Cacciopoli Prize in 2014 and the Amerio Gold Medal Prize in 2015. Camillo De Lellis has been invited speaker at the International Congress of Mathematicians (ICM) at Hyderabad, in 2010, and plenary speaker at the European Congress of Mathematics (ECM ) at Krakow, in 2012. He has also been awarded an ERC grant in 2012. Camillo serves in the editorial boards of many leading pubblications in the field, including: Annals of PDE, the Archive for Rational Mechanics and Analysis, Calculus of Variations and Partial Differential Equations, Inventiones Mathematicae and Journal of Differential Geometry.

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The Isoperimetric Problem with Density

Dove / Data e Ora: 1A150, il giorno 06/04/2017 alle ore 16:30

Relatore: Frank Morgan (Williams College, USA)

Abstract: The classical isoperimetric theorem says that the round sphere is the least-perimeter way to enclose given volume in R^n. Since their appearance in Perelman's proof of the Poincare conjecture, there has been great interest in enhancing space with a positive density that weights both perimeter and volume. Even if the density is radial, spheres about the origin usually no longer minimize weighted perimeter for given weighted volume. We discuss some open problems and recent results, some by undergraduates. All math students are welcome.

CV Relatore: Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. His proof with colleagues and students of the Double Bubble Conjecture is featured at the NSF Discoveries site. He has six books: Geometric Measure Theory: a Beginner's Guide (5th ed. 2016); Calculus Lite 2001, republished as Calculus 2012; Riemannian Geometry: a Beginner's Guide 1998; The Math Chat Book 2000, based on his live, call-in Math Chat TV show and Math Chat column; Real Analysis 2005; and Real Analysis and Applications 2005. He has a personal blog and a blog at the Huffington Post. More info available at math.williams.edu/morgan

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Presentare la tesi di laurea

Dove / Data e Ora: Aula 1A150, il giorno 23/03/2017 alle ore 14:30

Relatore: Cristina Rigutto

Abstract: Questo breve seminario è strutturato per offrire agli studenti dei suggerimenti pratici per prepararsi alla discussione della tesi. Si illustrerà come strutturare la presentazione, come esporla chiaramente e con sicurezza, come far fronte agli imprevisti più comuni: dal blocco di memoria alle domande inaspettate.

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How to optimally stir your coffee: Challenges in Differential Equations (Seminario per studenti)

Dove / Data e Ora: 1A150, il giorno 30/11/2016 alle ore 16:30

Relatore: Gianluca Crippa (Departement Mathematik und Informatik of the University of Basel)

Abstract: Mixing of different fluids is an ubiquitous phenomenon in sciences, technology, and everyday life. Nevertheless it is fair to say that we are quite far from a clear mathematical understanding of its analytical properties. In this talk I will present my perspective on this problem by describing a suitable mathematical framework for mixing phenomena and by proving a ''toy theorem'' in a simplified setting. The role of measure theory in the analysis of irregular partial differential equations will be emphasised.

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Matematica ed ecologia: le nuove frontiere della modellistica (seminario per studenti)

Dove / Data e Ora: 1A150, il giorno 17/05/2016 alle ore 11:30

Relatore: Prof. Marino Gatto (Politecnico di Milano)

Abstract: L'ecologia e' lo studio scientifico dei sistemi biologici ad alta complessita': popolazioni, comunita', ecosistemi. La matematica ha quindi giocato un ruolo fondamentale in ecologia fin dagli albori di questa disciplina scientifica, che ora procede ad un ritmo veloce attirando grande attenzione. Vito Volterra e Alfred J. Lotka sono considerati i padri fondatori della ecologia matematica e il loro lavoro è ancora fonte di ispirazione per i moderni ecologi e i moderni matematici. Nel seminario mostrero' come i modelli matematici possono effettivamente influenzare il lavoro di laboratorio e di campo dei biologi. Il piu' bell' esempio e' la lunga serie di esperimenti condotti da G.F. Gause con diverse specie di protozoi e ispirati al lavoro di Volterra su sistemi di equazioni differenziali non lineari che descrivono la competizione interspecifica. Poi, mostrero' come la matematica puo' essere di enorme importanza per l'ecologia applicata. A tal fine, illustrero' alcuni problemi di gestione ottimale delle risorse rinnovabili (principalmente risorse ittiche e foreste). Controllo ottimo e teoria dei giochi sono i principali strumenti che sono stati utilizzati per capire come gestire razionalmente i nostri ecosistemi. Infine, illustrero' alcuni nuovi problemi ecologici che richiedono l'uso di tecniche matematiche di recente sviluppo: lo studio delle dinamiche temporali complesse in ecologia (teoria delle biforcazioni e caos deterministico), l'analisi della persistenza ed estinzione in popolazioni frammentate (mediante processi di Markov) e l'uso di modelli su reti complesse per lo studio della ecologia dei parassiti e delle malattie.

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Dove / Data e Ora: 2BC60, il giorno 10/05/2016 alle ore 16:00

Relatore: Alessandro Languasco (Dipartimento di Matematica -Padova)

Abstract: - - -

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Uno sguardo a 4 dimensioni

Dove / Data e Ora: Aula 1C150, il giorno 22/01/2016 alle ore 16:00


Abstract: Potrebbe sembrare che per indagare forme e costruzioni geometriche nello spazio a 4 (e più) dimensioni, sia necessario appoggiarsi esclusivamente a un'interpretazione analitica, rinunciando a priori alla visione sintetica e a quel di più che ci viene dalle nostre capacità di visualizzazione . Questo però non è del tutto vero e si discuteranno nella conferenza degli esempi per illustrare questa tesi.

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