**Venue**: PovoZero - Department of Mathematics, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"**At: **4.30 pm

## Next appointments

### 9 May 2019

**Stefano Bonaccorsi,**Università di Trento

### 30 May 2019

**Marino Gatto**, Politecnico di Milano

### 27 June 2019

**Patrizia Pucci,**Universita degli Studi di Perugia

## The full programme

### 13 September 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 October 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 October 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 November 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 December 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 January 2019

**Annalisa Massaccesi,**Università degli Studi di Verona

Mass-minimizing integral currents: regularity at the boundary

In this seminar I will review (a part of) the history of the Plateau problem and the main regularity theorems for mass-minimizing currents. In the last part of the seminar I will explain the content of a recent paper by De Lellis, De Philippis, Hirsch and myself establishing generic regularity for the boundary points of a mass-minimizing current.

### 21 February 2019

**Luca Rossi,**CNRS Researcher al Laboratoire CAMS, EHESS, Paris

Stability: a key for the classification of solutions of PDEs

We give an overview of several notions of stability in the framework of dynamical systems. We then focus on evolution PDEs, starting from problems set on bounded domains.

The case of an unbounded domain can be tackled using the notion of generalised principal eigenvalue, inspired by a series of works in collaboration with H. Berestycki.

As an application, we will derive the validity of the "invasion property" for the Fisher-KPP equation in uniformly smooth domains.

### 14 March 2019

**Paolo Stellari,**Dipartimento di Matematica Università degli Studi di Milano

Derived Categories in Algebraic Geometry - A first glance

Derived categories ﬁrst appeared in Grothendieck's work as ﬂexible categorical tools to deal with various dualities and adjunctions of geometric nature. Due to the seminal work of Kontsevich they also provide bridges between geometry and mathematical physics. In this talk, I will leave this on the background and focus on how to handle bounded derived categories of coherent sheaves and how to use them to prove new results in algebraic geometry. Along the way, the notion of stability will pop up and give an interesting twist to the story.

### 4 April 2019

**Carlo Mantegazza**, Università degli Studi di Napoli Federico II

Evolution by curvature of networks in the plane

I will present the state-of-the-art of the problem of the motion by curvature of a network of curves in the plane, discussing existence, uniqueness, singularity formation and asymptotic behavior of the ﬂow.

**Contact** **people**: Ana Maria Alonso Rodriguez - Eduardo Luis Sola Conde