## MAIN PhD Seminars 2024

Date | Speaker(s) |

March, 6th | Marco Casula |

March, 13rd | Luca Zedda |

March, 20th | Filippo Maria Cassanello |

March, 27th | Alessandro Iannella |

April, 3rd | Elisa Crabu |

April, 17th | Jacopo Mereu |

April, 24th | Alessandra Perniciano |

May, 8th | Antonio Sanna |

May, 15th | Giuseppe Demuru |

May, 22nd | Massimiliano Fadda Federico Meloni |

May, 29th | Andrea Cabriolu Giorgia Nieddu |

*All the seminars start at 5 PM.*

**Marco Casula: Bochner-Euclidean volume**

We will start with examples of calculating the volume of objects in three-dimensional space and then extend the definition to any manifold. Therefore we will introduce a new and different volume on complex manifolds, with particular attention to cases of finite and infinite volumes. The work is based on the article by Loi-Placini.

**Luca Zedda: Self-Supervised Learning: The Dark Matter of Artificial Intelligence**

In this seminar, we shall delve into the concept of Self-Supervised Learning, an intriguing and rapidly expanding branch of artificial intelligence. Fundamental concepts of this innovative approach will be introduced, demonstrating how it is possible to connect the process of human cognitive development to that of artificial within the context of deep learning. Through the analysis of self-supervised models, it will be explained how AI can autonomously learn, addressing the challenges posed by the lack of explicit annotations in data and the application of these technologies to real-world scenarios.

**Filippo Maria Cassanello: An alternative approach to the Hölder continuity of solution of the fractional p-laplacian**

In this seminar we will define the non-local operator “fractional p-laplacian” by also talking about his biological interpretation for describing the movement of population in hostile habitat. Then we will give a different proof of the Hölder continuity of weak solution of this operator by extending the approach that DiBenedetto developped for the p-laplacian. This work is based on the paper “An alternative approach to the Hölder continuity of solution of some elliptic equations” of Duzgun, Marcellini, Vespri and is in collaboration with Prof. Antonio Iannizzotto.

**Alessandro Iannella: The Transitional Space: Generative Artificial Intelligence as an Opportunity for Professional Growth for Teachers**

This seminar aims to illustrate the benefits, risks, and challenges of using Generative Artificial Intelligence in teaching, also drawing on concepts and metaphors from psychology and sociology. Particular attention will be paid to the different phases of the teaching process, from design to evaluation.

**Elisa Crabu: Mathematical tools for Computer Vision**

Photometric Stereo is a Computer Vision tecnique that leads to reconstructing the digital shape of an object from a set of images, obtained by lighting the object with a light source placed at different positions around it. The method, by estimating the surface normals, computes an approximation of the surface. In this talk we will describe the main steps of the solution method, presenting the mathematical tools that underlie it, including the singular value decomposition, least square problems and the numerical solution of partial differential equations.

**Jacopo Mereu: AI-supported End User Development in VR**

End-User Development (EUD) is a research field that aims to design and develop software or hardware technology (digital artifacts) such that their consumers (end users) should be able to adapt such artifacts according to their needs. End users are not a static category; the unique context of the application determines their identity, skills, and experience. In the context of this seminar, the end users are proficient programmers in Unity but lack expertise in constructing Extended Reality environments. The research aims to assist these end users in using a XR Development toolkit, the Mixed Reality Toolkit (MRTK), whose latest version has recently been released. Large Language Models (LLMs) have been chosen as the method to support the end users. These models are trained with extensive documents, allowing them to acquire knowledge across various domains. However, their knowledge has a temporal limitation, as the models lack information about events or developments occurring after a certain date. Consequently, an LLM may lack information about the MRTK3 library. This seminar thus presents a practical case of enhancing the performance of an LLM in a domain where it possesses limited or no prior knowledge.

**Alessandra Perniciano: Radiomics: the issue of high dimensional data**

Radiomics, a branch of Computer Vision, involves the extraction and analysis of quantitative features from medical imaging modalities such as MRI, PET, and CT scans. The central idea behind Radiomics is that imaging features specific to various diseases may offer valuable insights into predicting prognosis and treatment outcomes across different types of pathologies. Notably, these characteristics remain elusive through traditional visual inspection methods employed in current radiologic practice, yet they provide insights into the underlying biological processes. However, the quantitative extraction of features leads to a situation of high dimensionality where not all the extracted features are necessarily relevant. During this seminar, I will present the challenges related to high dimensionality in Radiomics, providing an analysis of the current state of knowledge and discussing some future development directions.

**Antonio Sanna: Harmonic and Biharmonic maps between Riemannian Manifolds**

The object of this seminar is the definition of harmonic maps and biharmonic maps between Riemannian manifolds. During the exposition we will introduce the energy functional for smooth maps between two Riemannian manifolds, and, deriving the corresponding Euler-Lagrange equation — in order to find its critical maps, we will define a certain vector field, called tension field, which is identically zero when the map is harmonic, i.e. critical. We will extend the notion of harmonic maps to that of biharmonic maps which are the critical points of the bienergy functional. We will see that harmonic maps are trivially biharmonic. Thus a crucial problem is to understand when the converse is also true, that is: under what conditions biharmonic maps are harmonic. Beyond this theoretical exploration, we will give some examples of biharmonic maps which are not harmonic. In particular, we will consider the geometrically interesting case of biharmonic isometric immersions.

**Giuseppe Demuru: An Introduction to Causal Inference**

Causal inference involves the study of cause-and-effect relationships among variables, based on experimental or observational data. Understanding these relationships in depth is essential for making informed decisions and solving complex problems. The well-known statement “Correlation does not imply causation” underscores that simple associations do not necessarily imply causality. Causal inference utilizes methods such as Potential Outcomes (PO) and Directed Acyclic Graphs (DAGs) to identify and quantify the true causal relationships among variables.

**Massimiliano Fadda: Translating HTML in proprietary JSON**

Growens is an integrated industrial group that creates technologies for content creation, predictive marketing, and mobile messaging, aimed at organizations wishing to communicate effectively with their customers. The seminar will introduce the reasons that led the company to develop this project. An overview of the technologies and methodologies identified for its resolution will then be provided, introducing the architecture of the system that allows the conversion of generic HTML pages into proprietary Json.

**Federico Meloni: Mesh generation in the volumetric domain**

Representing an object in the virtual world is becoming a frequent practice in fields like industries, entertainment, medicine. To digitally represent an object, the space is discretized due to the inability of a computer to represent space continuously. Therefore, we utilize a series of primitives such as points, segments, polygons, and eventually polyhedra to represent an object, called in this context a mesh. A three-dimensional mesh can be superficial if only the exterior of the object is represented, or volumetric if it includes a description of the volume within. The latter unlocks the possibility of performing a variety of operations such as physical simulations, fluid dynamics, and many others. In this context, algorithms for automatic generation of volumetric meshes are becoming increasingly important and valuable. This seminar will review the basic concepts before proceeding to present high-level algorithms for generating volumetric meshes.

**Andrea Cabriolu: A Bayesian approach to an optimization algorithm for the dynamic scheduling of astronomical observations**

In the context of the dynamic scheduling of observations with Sardinia Radio Telescope, a key role is played by Optimizer, a set of algorithms to optimize the sequence of the astronomical observations. The calculations are based on several parameters, like weather conditions, device availability, operator’s availability and others. In this talk I’ll introduce the architecture which allows the communication between Optimizer and the whole scheduling system, consisting of a central database and a bunch of other components. The core concepts of the Bayesian statistics will be introduced as well, since this is the main pillar of the computing performed by the algorithm, to optimize the parameters set regargind the observations to be scheduled.

**Giorgia Nieddu: State of art on the use of A.I. in mathematics education**

In this seminar the most recent results on the use of A.I. in mathematics education, its areas of application, limits and possibilities will be presented.