Didattica Seminario di Matematica del Dottorato

Seminario di Matematica del Dottorato

• Roberta Fabbri: "Nonautonomous dynamical systems with some applications"
  Abstract:
  The talk wants to illustrate how nonautonomous ordinary differential equations can be studied using techniques of topological dynamics and of ergodic theory.
  Some of the most basic of these techniques are described and some applications are discussed.
  When/Where: Thursday, March 12nd, 2024, Aula Tricerri - DIMAI, 14:00
  
  
• Samuele Antonini: "Explanatory frameworks in mathematics education"
  Abstract:
  Studies in mathematics education have led to the construction of various theoretical lenses to identify and explain crucial didactical phenomena in the learning and teaching of mathematics. In this seminar, through the analysis of students' processes involved in mathematical activities, I will introduce some explanatory frameworks based on a duality of mathematical concepts that can be a source of cognitive gaps for students. The importance of considering the intertwining of different perspectives - epistemological, cognitive and didactic - will be highlighted.
  When/Where: Monday, Dec 18th, 2023, Aula 207 - DIMAI, 17:00
  
  
• Caterina Stoppato: "Hypercomplex function theory"
  Abstract:
  During the last century, several function theories have been introduced over quaternions and over other alternative algebras. The idea behind these constructions is recovering in higher dimensions the refined tools available in the theory of holomorphic functions of one complex variable. The resulting theories, nonetheless, reflect the peculiar properties of the higher-dimensional algebras considered.
  A relatively recent breakthrough was the definition, in 2006, of the notion of slice regular function of one quaternionic variable by Gentili and Struppa. This notion, generalized to alternative *-algebras by Ghiloni and Perotti in 2011, has rapidly grown into a full-fledged theory.
  The talk will overview the general problem of function theory in one hypercomplex variable and the main features of the theory of slice regular functions, mentioning applications to open problems from other areas of mathematics.
  When/Where: Thursday, May 04th, 2023, 14:15, Aula Tricerri
  
  
• Carolina Vallejo Rodriguez: "Finite Group Representation Theory: The Global-Local Principle"
  Abstract:
  Groups are the mathematical object formally describing our intuitive idea of symmetry. For this reason "wherever groups disclose themselves or can be introduced, simplicity crystallizes out of comparative chaos". But how do we study groups? We can focus on their inherent combinatorics or look at their images into groups of matrices. This latter point of view is known as group representation theory. In this seminar I will discuss some important open problems in group representation theory.  I will also discuss the global-local principle by focusing on two of the main global-local conjectures in the area. 
  When/Where: Wednesday February 01st, 2023, 14:30, Aula Tricerri
  
  
• Cesare Bracco: "Surface reconstruction from unstructured data"
  Abstract:
  We will consider two aspects concerning the reconstruction of surfaces from unstructured distributed data. The first is detecting the discontinuities the surface may have in order to reproduce them as accurately as possible. Finding the discontinuity curves, usually called faults (or gradient faults when gradient discontinuities are considered), is actually an important and non-trivial issue in itself, with several applications, for example in image processing and geophysics.
  The second aspect is obtaining the continuous model describing the surface from the set of scattered points: the lack of structure in the data requires approximation methods which automatically adapt to the distribution and shape of the data themselves. We will discuss an adaptive approach to this issue based on spline spaces.
  When/Where: Thursday December 01st, 2022, 15:00, Aula Tricerri
  
  
• Angela Slavova: "Applications of Cellular Neural Networks (CNN) for Studying Differential Equations"
  Abstract:
  In this seminar we shall present the derivation of the CNN implementations through spatial discretization, which suggests a methodology for converting the differential equations (DE) to CNN templates and vice versa. The CNN solution of the DE has four basic properties, which are:
  i) continuous in time;
  ii) continuous and bounded in value;
  iii) continuous in interaction parameters;
  iv) discrete in space.
  First, we shall present some basic theory of CNN including the main types of equations that describe these networks, as well as some results about their dynamics and stability.
  Then, we shall demonstrate how an autonomous CNN can serve as a unifying paradigm for active wave propagation and several well-known examples chosen from different disciplines will be modeled. Moreover, we shall show how the three basic types of DE: the diffusion equation, the Laplace equation, and the wave equation, can be solved via CNN.
  Finally, several equations arising in biology, physics and ecology will be modeled through the CNN approach and their dynamics will be studied.
  When/Where: Wedesday October 12th, 2022, 16:00, Aula Tricerri
  
  
• Luigi De Pascale: "Optimal transport, Wasserstein distances and Machine Learning"
  Abstract:
  I will introduce the general optimal transport problem and, in this general framework, the Wasserstein distances. I will also give a formulation of some Machine Learning problems which allows for the applications of Wasserstein barycenters.
  Some open problems will be described and discussed.
  When/Where: Wedesday May 25th, 2022, 15:00, Aula Tricerri
  
  
• Luigi Barletti: "Il problema di Mott"
  Abstract: Se la natura segue le leggi della meccanica quantistica, perché ne abbiamo una percezione "classica"? Questa domanda, sorta fin dagli albori della teoria quantistica, è ben sintetizzata nel cosiddetto problema di Mott: una particella viene emessa all'interno di una camera a nebbia sotto forma di una funzione d'onda con perfetta simmetria sferica, eppure la particella lascia nella camera una traccia rettilinea, seguendo quindi una traiettoria classica. E' possibile inquadrare e spiegare questo fenomeno, apparentemente contraddittorio, all'interno della stessa meccanica quantistica? Il seminario intende presentare la  formulazione matematica del problema e illustrare i risultati che sono stati ottenuti, da quelli dello stesso Mott fino agli sviluppi più recenti.
  When/Where: Wedesday March 23rd, 2022, 15:00, Aula Tricerri
  
  
• Marco Maggesi: "Matematica Artificiale"
  Abstract: Fino ad anni recenti, la Matematica era una attività svolta dagli esseri umani per gli esseri umani.  Nel seminario verrà discussa una nuova prospettiva, in cui la Matematica diventa un'attività che esseri umani e macchine svolgono per esseri umani e macchine.
  When/Where: Wednesday January 19, 2022, 14:30, Aula Tricerri