SEMINARI TENUTI
Giovedì 7 Marzo 2024, 16.30- 17.30 aula Tricerri
Lorenzo Sacco (Firenze)
Titolo: Pythagorean-hodograph spline interpolation algorithms with applications to marine robotics
Abstract: A key feature in the field of motion robotics is the ability of a vehicle to move autonomously toward specific targets. One of the most used methods of motion planning requires the vehicle to be able to follow a specific trajectory. Advances in the state of the art have led to high-performance vehicles, opening up the possibility of performing complex trajectories. Consequently, the development of efficient algorithms capable of constructing curvilinear paths of different kind becomes an important feature for advanced path planning algorithms. One possible choice is to rely on Pythagorean-Hodograph (PH) curves, a specific class of polynomial curves with interesting computational properties.
The first part of the talk will focus on the basic concepts related to PH curves, with special emphasis on the possibility of an exact and explicit computation of certain quantities relevant for applications, including the curve length. I will also present a subclass of PH curves with a ration rotation minimizing adapted frame and, afterwards, a new geometric approach for the characterization of quintic RRMF curves.
I will finally introduce related algorithms for solving Hermite interpolation problems andconstructing PH spline paths with smooth continuity.
The second part of the talk will cover the concepts of guidance and control, with a focus on path following algorithms. In particular, I will show how to transform the spatial constraints of spline trajectories into kinematic references for a robotic vehicle. Finally, I will briefly present the application of algorithms based on PH spline construction for the development of an autonomous guidance software for marine surface vehicles, specifically designed for environmental monitoring purposes.
abstract.pdf
Michela Ascolese (Firenze)
Titolo: Polyominoes and Tilings
Abstract:
Giovedì 23 Novembre 2023, 16.30- 17.30 aula Tricerri
Titolo: Entropy for quandles
Abstract: How predictable is the multiplication table of a given binary algebraic structure? When the algebra is defined by specific identities, these equations impose restrictions on the table. Yet, to what extent can we challenge these constraints? This presentation delves into the spectrum of disorder in quandle tables, spanning from trivial cases to Latin squares. Additionally, it explores how this disorder behaves in the context of universal algebraic constructions such as subalgebras, products, and homomorphic images. The key analytical tool for this exploration is the recently developed concept of the entropy function, together with its distinctive properties.
Quanto è prevedibile la tabella di moltiplicazione di una data struttura algebrica binaria? Quando l'algebra è definita da identità specifiche, queste equazioni impongono restrizioni sulla tabella. Ma fino a che punto possiamo sfidare questi vincoli? In questa presentazione esploreremo lo spettro del disordine nelle tabelle di moltiplicazione dei quandle, spaziando dai casi più banali ai quadrati latini. Inoltre, analizzeremo come questo disordine si comporta nel contesto delle costruzioni algebriche universali come sottoalgebre, prodotti e immagini omomorfe. Lo strumento analitico chiave per questa esplorazione è il recentemente sviluppato concetto di funzione di entropia, insieme alle sue proprietà distintive.
Abstract_FS_Entropy_for_Quandles.pdfMartedì 26 Aprile 2022, 16.30-17.30 aula Tricerri
Angel Garcia Blazquez (Murcia)
Titolo: The Isomorphism Problem for Rational Group Algebras of Metacyclic Groups
Abstract: The Isomorphism Problem for group rings with coefficients in a ring R asks whether the isomorphism type of a group G is determined by its group ring RG. We will introduce this problem in general and we will discuss the particular case of rational group rings of metacyclic groups.
Martedì 17 Maggio 2022, 16.30-17.30 aula Tricerri
Lapo Cioni (Firenze)
Titolo: Preimages of sorting algorithms
Abstract: Bubblesort, Queuesort and Stacksort are well known sorting algorithms, which have interesting properties from a combinatorial point of view. We will talk about some of those properties, focusing in particular on the problem of studying the preimages of the functions associated to the sorting algorithms.
Martedì 31 Maggio 2022, 16.30-17.30 aula Tricerri
Giada Volpato (Firenze)
Titolo: Representation theory of the symmetric groups
Abstract: Representations of the symmetric groups are particularly interesting because there's a nice combinatorics theory that gives us several tools to work with. We will talk about these tools and we will introduce some research problems on this topic.
Giovedì 9 Giugno 2022, 14.30-15.30 aula Tricerri
Camilla Brizzi (Firenze)
Titolo: The optimal transport problem: the classical and the supremal setting
Abstract: In my talk, I will present the problem of Optimal Transport, the first formulation by Monge and then the relaxed version due to Kantorovich, trying to explain the main properties and results. I will then mention some fields of research, with particular attention at the formulation of OT in a "supremal" setting.
Martedì 28 Giugno 2022, 16.30-17.30 aula Tricerri
Alice Dell'Arciprete (University of East Anglia, Norwich UK)
Titolo: Decomposition numbers of the symmetric group and related algebras
Abstract: Representations of the symmetric group are quite well understood, mainly thanks to James who developed the use of combinatorial tools, such as diagrams, tableaux and abacuses. This constructive approach can be generalised to give techniques for studying representations of related algebras including the Ariki-Koike algebras.
In particular, we will talk about the decomposition numbers of the symmetric group and sketch how we can generalise some results for the Ariki-Koike algebras.
Martedì 12 Luglio 2022, 16.30-17.30 aula Tricerri
Luca Briani (Pisa)
Titolo: Is there an optimal shape?
Abstract: How to construct a rod of maximum rigidity? Which body moves in a fluid with the least resistance? Among sets of given area, which has the smallest perimeter? In a shape optimization problem, the objective is to deform and modify the shape of a given object to minimize (or maximize) a cost function.
From a mathematical point of view, the most intriguing feature is that the competing objects are shapes (i.e. subsets of R^N) rather than functions. We will discuss some classical problems (some of which are still open) and introduce the mathematical framework that can be used to obtain existence results.
Martedì 27 Settembre 2022, 14.30-16.00 aula Tricerri
Ettore Teixeira Turatti (Firenze)
Titolo: Multilinear spectral theory
Abstract: The spectral theory of matrices is a classical concept that has many applications in image processing, signal processing, biodiversity estimation, etc. The extended notion of eigenvectors to higher order tensors has been introduced recently in 2005, we will study this concept and understand its similarities and differences to the matrix case.
Martedì 11 Ottobre 2022, 14.30-16.00 aula Tricerri
Lorenzo Putignano (Firenze)
Titolo: Something about Representation Theory
Abstract: In this talk I will introduce basic concepts and ideas about representation and character theory of finite groups. My focus will be in particular on the case of symmetric groups where combinatorics plays a fundamental role. In the final part I briefly present the concept of centralizer algebra arised in order to attack important conjectures in representation theory. Again I will put the attention on symmetric groups touching the heart of my research project and showing first improvements on it.
Martedì 25 Ottobre 2022, 14.30-16.00 aula Tricerri
Lorenzo Sacco (Firenze)
Titolo: Interpolazione di flussi di dati 3D tramite spline quintiche PH ed applicazione alla pianificazione di traiettorie.
Martedì 8 Novembre 2022, 16.30-18.00 aula Tricerri
Bernardo Nannini (Firenze)
Titolo: Induzione matematica e catene di inferenze logiche: un'analisi cognitivo-didattica.
Martedì 22 Novembre 2022, 14.30-16.00 aula Tricerri
Niccolò Di Marco (Firenze)
Titolo: The null label problem and its relation to the 2-intersection graph
Abstract: A 3-uniform hypergraph H consists of a set V of vertices, and a subset of triples of V, called set of edges E. Let a null labeling be an assignment of +1 or -1 to the triples such that each vertex has a signed degree equal to zero. If a null labeling exists, we say that the hypergraph is null. Assumed as necessary condition the degree of every vertex of H to be even, the Null Labeling Problem consists in determining whether H has a null labeling. It is remarkable that null hypergraphs arise considering two hypergraphs with the same degree sequence. In particular, the symmetric differences of these two hypergraphs give a new hypergraph that is null. From a discrete tomography point of view, null hypergraphs arise from matrices with the same projections, i.e. solutions of the same reconstruction problem. Therefore they allow modeling of switching components, a very used notion in this field of research.
Although the problem is NP-complete, the subclasses where the problem turns out to be polynomially solvable are of interest. We defined the notion of 2-intersection graph related to a 3-uniform hypergraph and we prove that if it is Hamiltonian then the related 3-hypergraph has a null labeling. Then we aimed to deepen the knowledge of the structural properties of 2-intersection graphs. Going into details, we studied when, given a graph G, it is possible to find a 3-hypergraph such that its 2-intersection graph is G. If it is possible, we say that G is reconstructable or equivalently, it has the 2-intersection property. It’s easy to see that the question is relatively straightforward for some classes. However, using some suitable gadgets, we proved that the problem in its general form is NP-Complete.
Martedì 13 Dicembre 2022, 14.30-16.00 aula Tricerri
Corentin Henriet (IRIF, Université de Paris)
Titolo: A swim with fighting fish
Abstract: In this talk, I will propose you an excursion into the world of bijective combinatorics. This is an area of mathematics where we find a variety of discrete objects arising in other mathematical domains, and try to establish bijective links between them in order to understand better their structure and their relations. The central objects of my PhD are an exotic generalization of parallelogram polyominoes called fighting fish : I will present them to you, draw their connections with planar maps, intervals in a lattice of Dyck paths (and maybe more, if time allows), and what we can learn from that.