Maths bites trento

Seminario periodico del Dipartimento di Matematica

Versione stampabile

Luogo: PovoZero - Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula seminari - Sala Seminari "-1"
Ore: 15.30

Il prossimo appuntamento

Giovedì 31 gennaio 2019

  • Annalisa Massaccesi, Università degli Studi di Verona

 

13 settembre 2018

 

  • Jean-Michel Coron (Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie)

How to use the nonlinearities to control a system

A control system is a dynamical system on which one can act thanks to what is called the control. For example, in a car, one can turn the steering wheel, press the accelerator pedal etc. These are the control(s). One of the main problems in control theory is the controllability problem. It is the following one. One starts from a given situation and there is a given target. The controllability problem is to see if, by using some suitable controls depending on time, the given situation and target, one can move from the given situation to the target. We study this problem with a special emphasis on the case where the nonlinearities play a crucial role. In finite dimension in this case a key tool is the use of iterated Lie brackets as shown in particular by the Rashevski-Chow theorem. This key tool gives also important results for some control systems modeled by means of partial differential equations. However we do not know how to use it for many other control systems modeled by means of partial differential equations. We present methods to avoid the use of iterated Lie brackets. We give applications of these methods to the control of fluids modeled by various equations (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg-de Vries equations).

4 ottobre 2018

  • Alessandra Bernardi, Università degli Studi di Trento

La moltiplicazione

Lʼuso delle tabelline per la moltiplicazione dei numeri arriva in Italia con Fibonacci nelle scuole di Abaco e resiste allo Sputnik (URSS 1957) ma non allo sbarco degli USA sulla Luna (1969): prima lʼalgoritmo di Karatsuba (1960) poi la scoperta di Cooley e Turkey della Fast Fourier Transform (1965) rivoluzionano completamente la storia della programmazione informatica mondiale. La complessità di questi algoritmi va da O(n2), O(nlog(3)/log(2)) a O(n log(n)) e può essere misurata con il rango dei tensori associati. Lo stesso tipo di misura mostra che lʼalgoritmo di Strasser (1969) per moltiplicare due matrici 2x2 con 7 moltiplicazioni invece di 8 è il metodo più efficiente per moltiplicare matrici 2x2. Quale sia la complessità effettiva della moltiplicazione di matrici nxn è ancora un problema aperto. Le sue applicazioni vanno oltre la moltiplicazione dei numeri e sono presenti ad esempio nella riproduzione di ogni file audio o nella ricostruzione di immagi... Google ha annunciato di puntare alla supremazia quantistica e intende farlo prima del 2027 anno previsto dalla NASA per il primo computer quantistico con un considerevole numero di q-bits. Se questo avverrà la cybersecurity dovrà cambiare completamente struttura. La versione quantistica della FFT potrebbe essere alla base di questa possibile rivoluzione.

25 ottobre 2018

  • Guido De Philippis, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

Boundary regularity for mass minimizing currents

The Plateau problem consists in finding the surface of minimal area spanning a given boundary. Since the beginning of the 50ʼs the study of this problem led to the development of fundamental tools in Geometric Analysis and in the Calculus of Variations. The aim of the talk is to give an overview of the problem and of the techniques used to solve it. In the end I will also present some recent results concerning boundary regularity.

14 novembre 2018

  • Massimiliano Sala, Università degli Studi di Trento

An open problem in vectorial Boolean functions: do bijective APN functions exist in even dimension?

For the construction of the so-called "block ciphers", vectorial Boolean function are used as S-Boxes. The S-Boxes that offer the best resistance to differential cryptanalysis are called APN functions (Almost Perfect Nonlinear functions). For practical reasons in the constructions of circuits, it would be optimal to have APN functions in even dimension which are bijective. Their existence was widely believed to be impossible, but in 2009 Dillon gave the first construction of such function, although limited to the case n=6. After that no new such functions have been found. If just one 8-bit APN permutation would be found, it would be a result having a massive practical impact. We will discuss some results that limit strongly the shape and degree of these other putative counter-examples.

6 dicembre 2018

  • Peter Gritzmann, Technische Univesität München

Constrained clustering and diagrams for the consolidation of farmland

In many regions farmers cultivate a number of rather small (and discontiguous) lots that are distributed over a wider   area. This results in a non-favorable cost-structure for the production. Since the classical form of land consolidation is typically too expensive, too time-consuming and too rigid voluntary lend-lease agreements have been suggested as a legally simple, economically convincing and extremely flexible alternative. In the past, the practical relevance of this approach was severely limited by the mathematical complexity of finding good (let alone optimal) reassignments.
We developed a new mathematical clustering approach establishing a close relation between constrained clustering and diagrams which leads to practically very efficient tools which are now used in practice.
The analysis of the mathematical structure of the model provides proof of its favorable properties (existence of feasible power diagrams) and allows the derivation of efficient approximation algorithms (based on the approximation of certain semi-norm level sets by polytopes) with a provably small worst-case error bound.

31 gennaio 2019

  • Annalisa Massaccesi, Università degli Studi di Verona

Referenti: Ana Maria Alonso Rodriguez  - Eduardo Luis Sola Conde