Didattica e formazione Seminario del Dottorato

Seminario del Dottorato

• Mirko Armillotta: "Copula Tensor Count Autoregressions"
  Abstract: This paper presents a novel copula-based autoregressive framework for multi-layer arrays of integer-valued time series with tensor structure. Our framework generalizes recent advances in tensor time series models for real-valued data to a context that accounts for the unique properties of integer-valued data, such as discreteness and non-negativity.
  The model incorporates feedback effects for the counts’ temporal dynamics and introduces new identification constraints. An asymptotic theory is developed for a Two-Stage Maximum Likelihood Estimator (2SMLE) for the model’s parameters. The estimator balances the challenges of high-dimensionality, interdependence of the different count series, and computational stability.
  Together, this substantially pushes the frontier for modeling high-dimensional, structured tensor time series of counts. An application to tensor crime counts demonstrates the practical usefulness of the proposed methodology.
  When/Where: Wednesday, November 19th, 2025, Viale Morgagni 59 - Room 205, 12:00
  
  
• Philip Koopman: "Embodied AI Safety: Reimagining safety engineering for artificial intelligence in physical systems"
  Abstract: Embodied AI (eAI) uses artificial intelligence based on machine learning to interact with the physical world. We are already seeing eAI deployed in the real world in robotaxis, smart medical devices, household robots, and other applications.
  However, everyone is struggling with the safety of these devices: how to design for safety, how to evaluate safety, and how to think about whether any particular eAI system is acceptably safe.
  This talk provides an overview of my new book on this topic, with robotaxi safety as a concrete example. Anyone working in this area needs a basic understanding of four core areas: safety engineering, cybersecurity engineering, machine learning technology, and human/computer interaction.
  The talk also discusses eAI safety issues in the wild, the complexities of establishing what risks might be acceptable, and open challenges in eAI safety.
  A proposal for reimagining safety engineering responds to the huge disruption that eAI technology creates when applying traditional computer-based system safety approaches.
  The talk finishes with a call to build justifiable trust in eAI safety.
  When/Where: Tuesday, September 16th, 2025, Aula Tricerri - DIMAI, 10:00
  
  
• Yunxiao Chen: "Piecewise Comparisons without Stochastic Transitivity: Model, Theory and Applications"
  Abstract: Most statistical models for pairwise comparisons, including the Bradley-Terry (BT) and Thurstone models and many extensions, make a relatively strong assumption of stochastic transitivity. This assumption imposes the existence of an unobserved global ranking among all the players/teams/items and monotone constraints on the comparison probabilities implied by the global ranking.
  However, the stochastic transitivity assumption does not hold in many real-world scenarios of pairwise comparisons, especially games involving multiple skills or strategies. As a result, models relying on this assumption can have suboptimal predictive performance.
  In this paper, we propose a general family of statistical models for pairwise comparison data without a stochastic transitivity assumption, substantially extending the BT and Thurstone models. In this model, the pairwise probabilities are determined by a (approximately) low-dimensional skew-symmetric matrix.
  Likelihood-based estimation methods and computational algorithms are developed, which allow for sparse data with only a small proportion of observed pairs. Theoretical analysis shows that the proposed estimator achieves minimax-rate optimality, which adapts effectively to the sparsity level of the data.
  The spectral theory for skew-symmetric matrices plays a crucial role in the implementation and theoretical analysis.
  The proposed method’s superiority against the BT model, along with its broad applicability across diverse scenarios, is further supported by simulations and real data analysis.
  This is a joint work with Sze Ming Lee (PhD student at LSE).
  When/Where: Friday, September 12th, 2025, Aula 205 - DISIA, 10:00
  
  
• Hartmut Prautzsch: "Honeycomb cutting for higher dimensional polyhedra"
  Abstract: Honeycomb cutting in 3D always generates smooth limiting surfaces, but never generates smooth limiting surfaces in 4D. Honeycomb cutting refers to an edge cutting scheme for convex polyhedra. For three-dimensional polyhedra, it is "parallel" to the honeycomb refinement scheme by Dyn, Levin and Liu. This means that the limiting surfaces are C¹ because the smoothness arguments for the refinement scheme also apply to the cutting scheme.
  However, I will show that a straightforward generalization of the cutting scheme to higher dimensional polyhedra cannot generate smooth limiting polyhedra. This, in return, also holds for the honeycomb refinement scheme for higher dimensional polyhedra.
  In my talk, I will embed these results in a discussion of general edge cutting schemes. In particular, I will mention the 4-6-8 scheme, as it may be a more promising candidate for a successful generalization to higher dimensions than simple honeycomb cutting.
  When/Where: Wednesday, June 4th, 2025, Aula Tricerri - DIMAI, 11:30
  
  
• Valerio Melani: "Categories and infinity-categories"
  Abstract: Category theory provides a powerful framework for understanding abstract structures in mathematics, enabling us to identify structural similarities across seemingly unrelated areas by working at a high level of abstraction.
  Infinity-categories, an advanced extension of category theory, facilitate the study of mathematical structures with richer homotopical data. In this context, the morphisms between objects form not just a set, but a more intricate object such as a topological space or a chain complex.
  In this seminar, we will explore the motivations behind this shift to infinity-categories and examine their applications in areas like algebraic topology, algebraic geometry and homotopy theory.
  When/Where: Thursday, May 15th, 2025, Aula Tricerri - DIMAI, 11:30
  
  
• Fang Han: "Nearest neighbor matching"
  Abstract: In two landmark Econometrica papers, Abadie and Imbens proved that the nearest neighbor (NN) matching estimator of the average treatment effect, when using a fixed number of neighbors, is asymptotically normal but semiparametrically inefficient and bootstrap inconsistent.
  In this talk, I will show that the same NN matching estimator becomes asymptotically normal, doubly robust, semiparametrically efficient, and bootstrap consistent as long as we force the number of NNs to diverge with the sample size.
  When/Where: Wednesday, April 16th, 2025, Aula 205 - DISIA, 10:30
  
  
• Robert Platt: "Using machine learning for confounding control in pharmacoepidemiology"
  Abstract: Machine learning tools are used extensively for prediction, but they are not typically designed for causal inference. However, tools such as targeted learning have been developed to exploit the strengths of machine learning in causal inference.
  In this presentation I will describe machine learning and its use to infer causation in pharmacoepidemiology.
  I will discuss settings in which machine learning can be used together with appropriate methods for confounding control, when it is useful, and when it may be unnecessary.
  When/Where: Monday, March 24th, 2025, Aula 205 - DISIA, 12:00
  
  
• Alessandro Goffi: "Mean Field Games: a bridge between semilinear and advection-diffusion equations"
  Abstract: Mean Field Games theory has been developed since 2006 by J.-M. Lasry and P.-L. Lions to describe Nash equilibria in differential games involving a large population of similar rational agents, where the strategy of each agent depends on the collective behavior. This model is described by parabolic systems of partial differential equations, where a backward Hamilton-Jacobi-Bellman equation is coupled with a forward Kolmogorov-Fokker-Planck equation.
  This theory has stimulated an increasing interest due to the recent applications in Engineering, Finance and Social Sciences.
  In this talk, after a brief introduction to the model, I will present the main peculiarities of these PDE systems and discuss recent advances and open problems about their regularity theory.
  These led to new questions and answers about qualitative and quantitative properties of solutions of linear and nonlinear partial differential equations.
  When/Where: Wednesday, January 15th, 2025, Aula Tricerri - DIMAI, 11:30
  
  
• Conrado da Costa: "Superdiffusive planar random walks with polynomial space-time drifts"
  Abstract: Is the process by which particles spread out from a concentrated area to a less concentrated area. Given some regularity assumptions, classical diffusion is obtained thanks to the Central Limit Theorem and invariance principles.
  A signature of classical diffusion is the mean square displacement that scales linearly. However, upon closer examination, many diffusion processes with self-interaction or interaction with the medium present different scaling of the mean square displacement. This phenomenon is known as anomalous diffusion.
  In this talk we are going to consider a flexible model for anomalous diffusion on the plane. This model relies on polynomial space-time drifts as the mechanism that drives the anomalous diffusion.
  This model was motivated by an heuristic connection to a self-interacting, planar random walk which interacts with its own centre of mass via an excluded-volume mechanism, and is conjectured to be superdiffusive with a scale exponent 3/4.
  The main goal of the talk is to explain this heuristic connection.
  The talk is based on a joint work with Mikhail Menshikov, Vadim Shcherbakov, and Andrew Wade, for details see arXiv:2307.07458.
  When/Where: Monday, April 15th, 2024, Aula Tricerri - DIMAI, 16:00
  
  
• 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