Graduate Seminar 20232024
List of Seminars
Video recordings at Unipd's portal "Mediaspace"
(Click on title for abstract)
 4 October 2023, h. 16:00, Martina Costa Cesari (Padova, Dip. Mat.), An Introduction to NonConnected Linear Algebraic Groups and their partition into Jordan Classes and Lusztig Strata video

8 November 2023, h. 14:30, Chiara Turbian (Padova, Dip. Mat.) A 2D Bin Packing Problem in the Sheet Metal Industry: models and solution approaches video

22 November 2023, h. 14:30, Khai Hoan NguyenDang (Padova, Dip. Mat.), “Groups and geometry: from algebraic varieties to Galois representations and vice versa" video

13 December 2023, h. 14:30, Amna Mohsin (Padova, Dip. Mat.), Wasserstein Generative Models video

20 December 2023, h. 15:30, Pietro Sabelli (Padova, Dip. Mat.), “Doublenegation in the Foundation of Constructive Mathematics" video

24 January 2024 h. 14:30, Laura Rinaldi (Padova, Dip. Mat.), Digital twins: a general overview and the application to bread baking video

31 January 2024 h. 14:30, Luca Talamini (Padova, Dip. Mat.), PDE's and Conservation Laws: from the basics to current research video

15 February 2024 h. 14:30, Room 1BC45, Chiara Brambilla (Padova, Dip. Mat.), A differential game model for sponsored content video

28 February 2024 h. 14:30, room 2BC30, Marco Baracchini (Padova, Dip. Mat.), Classical Modular Forms and the ksquare problem video

13 March 2024 h. 14:30, room 2BC30, Pietro Vanni (Padova, Dip. Mat.), Padic numbers and characteristic p video

10 April 2024 h. 15:30, room 2BC30, Mariana Costa Villegas (Padova, Dip. Mat.), A sphere rolling on a plane: a journey into nonholonomic mechanics video

24 April 2024 h. 14:30, room 2BC30, Elisa Marini (Padova, Dip. Mat.), “Collective periodic behaviors in largevolume interacting particle systems" video

9 May 2024 h. 14:30, room 2BC30, Davide Francesco Redaelli (Padova, Dip. Mat.), “Differential games and large population limits beyond the classic MeanField setting" video

23 May 2024 h. 15:30, room 2BC30, Nicolò Crescenzio (Padova, Dip. Mat.), “Numerical Solution of Wave Propagation Phenomena in Viscoelastic Materials>" video

5 June 2024 h. 14:30, room 2BC30, Elena Danesi (Padova, Dip. Mat.), “Strichartz estimates for the Dirac equation in different settings" video

20 June 2024 h. 15:30, room 2BC30, Cinzia Bandiziol (Padova, Dip. Mat.), "Topological Data Analysis: basic concepts and applications" video
Martina Costa Cesari, "An Introduction to NonConnected Linear Algebraic Groups and their partition into Jordan Classes and Lusztig Strata"
Abstract. Linear algebraic groups are a class of mathematical structures that combine concepts from algebra and geometry. This suggests that algebraic groups can be approached from different perspectives, such as Group Theory, Algebraic Geometry, and Combinatorics. They have applications in several directions (Invariant Theory, Physics). Linear algebraic groups are affine varieties with a compatible group structure. They were introduced in the late 1800s to study continuous symmetries of differential equations. An important class of algebraic groups consists of non connected algebraic groups. In the first part of the talk I will introduce basic notions and examples of linear algebraic groups, and in particular of non connected linear algebraic groups. The last part of the presentation is devoted to explore some partition of these objects, in particular Jordan classes and Lusztig strata, and investigating their geometric properties.
Chiara Turbian, "A 2D Bin Packing Problem in the Sheet Metal Industry: models and solution approaches"
Abstract. The Bin Packing Problem (BPP) is a wellstudied problem in Operations Research, and, in its basic formulation, it aims at packing a set of items into a finite set of bins by minimizing the number of used bins. Due to its wide range of applications, several variants of the problem have been proposed during the last decades, which differ from each other by dimensionality, additional constraints, and characteristics of the items or the bins. We consider a TwoDimensional Bin Packing Problem (2DBPP) arising in Salvagnini Italia, a multinational corporation working in the sheet metal industry. In our problem, the basic 2DBPP is enriched by the presence of technological constraints emerging from the context, such as precedence relations between groups of items and conditional safety distances between items. We present exact and heuristic approaches to solve the problem, both based on Mixed Integer Linear Programming (MILP), and we show related computational results.
Khai Hoan NguyenDang, "Groups and geometry: from algebraic varieties to Galois representations and vice versa"
Abstract.Since a very long time ago, there has been an effective approach to study geometry via group theory. In this talk, we will focus on objects given by sets of solutions of a system of polynomial equations, called algebraic varieties. Galois theory makes a bridge between the geometry of algebraic varieties and group theory in terms of Galois representations. The talk will survey some basic but still interesting aspects of these connections and provide several examples. We will also provide a uniform way to investigate a certain class of algebraic varieties, named Abelian varieties.
Amna Mohsin, "Wasserstein Generative Models"
Abstract.In this seminar firstly, I will present an introduction about optimal transport. Nowadays optimal transport importance extends to diverse domains, ranging from mathematics and computer science to economics and image processing. Subsequently, I will talk about the Wasserstein distance, particularly the W1 distance, which is a powerful metric for measuring the dissimilarity between probability distributions and it provides a more stable and meaningful measure than traditional metrics like the KullbackLeibler divergence. This metric is used in particular within generative models, which are modern deep learning techniques that may be used to generate objects such as images, text, or any other structure. I will introduce these models and explain their application domain and discuss their properties, especially in relation to the limitation in their use of the W1 distance. Then, I will talk about the main objective of the thesis, which builds upon prior work which introduce a dynamics based method that allows us to obtain very accurate computations of the Wasserstein distance. The objective is to apply this method effectively within generative models to overcome the limitations in the traditional methods used to compute the W1 distance, and how we expect this method to improve the models performances.
Pietro Sabelli, "Doublenegation in the Foundation of Constructive Mathematics"
Abstract. In this talk, we will first introduce the fundamental ideas of Constructive Mathematics through basic examples taken from ordinary mathematical practice and focus on its computational aspect. Secondly, we will review how the logical principle of the Excluded Middle, dating back to Aristotle, and, more generally, the concept of negation play a crucial role in distinguishing Constructive Mathematics from Classical Mathematics. Finally, we will give a nontechnical overview of Gödel’s doublenegation interpretation of arithmetic and present our new result, which generalises it to the “Minimalist Foundation”, a foundation for constructive mathematics designed in Padua by M.E. Maietti and G. Sambin.
Laura Rinaldi, "Digital twins: a general overview and the application to bread baking"
Abstract.A digital twin is composed of two existing systems: the tangible system of physical reality and its virtual and numerical replica which is enabled by real data and underling models through the underlying use of digital technologies. The presence of digital twins is motivated by the necessity of obtaining some information about the real system questioning the virtual one by a nonintrusive manner. Such technology helps us to monitor the real system, to carry out maintenance tasks or optimize some process. In this talk, I will present an industrial application which consists in the building of an embedded digital twin of the bread baking process to the end of monitoring the energy consumption to avoid waste.
Luca Talamini, "PDE's and Conservation Laws: from the basics to current research"
Abstract. In this talk I will try to introduce you to the world of PDE's in general and conservation laws in particular. In the first part of the talk we will focus on rather classical topics. Via a lot of examples I will try to give you a feeling of what a PDE is really about and what it means "to solve it". In the last part we take a look at conservation laws (a particular class of PDE's). Besides being my current main research topic, conservation laws provide me with a great tool to illustrate modern challenges in the field of nonlinear PDE's.
Chiara Brambilla, "PA differential game model for sponsored content"
Abstract. Let us consider a communication platform distinguished for its highquality content, where advertising can take two different forms: traditional and sponsored (also known as native advertising in the marketing literature). Native advertising is a widely used marketing tool that aims to mimic the regular topics of the platform on which it is placed. Due to this striking resemblance, native advertising may be very effective, but at the same time, it may negatively influence the perceived credibility of the media outlet. In our model, a firm allocates investments to both traditional and native advertising on such a platform. Meanwhile, the media outlet must grapple with the tradeoff between the profit accrued from publishing native advertising and the ensuing decline in credibility. We formalise this problem as a hierarchical infinitetime horizon linear state differential game, played a` la Stackelberg, where the media outlet acts as the leader while the firm is the follower. Finally, we characterise a timeconsistent openloop equilibrium and obtain the conditions that make it optimal for the media outlet to accept native advertising.
Marco Baracchini, "Classical Modular Forms and the ksquare problem"
Abstract. Modular forms are objects belonging to the world of complex analysis. They are holomorphic functions with some transformation properties. In this talk I will introduce two arithmetic problems that could be studied using the theory of modular forms. In the second part of the talk we will see the definition of modular forms and some classical results in this area.
Pietro Vanni, "Padic numbers and characteristic p"
Abstract. For each prime p, padic numbers form an extension of the rational numbers that, being topologically complete, allows one to use analytic methods in arithmetic. In this talk I will introduce padic numbers outlining their basic properties and the role they play in number theory. Then I will give an idea on how one can employ padic numbers to study algebraic varieties (i.e. systems of polynomial equations) in characteristic p.
Mariana Costa Villegas, "A sphere rolling on a plane: a journey into nonholonomic mechanics"
Abstract. The problem of the sphere rolling on a plane is one of the most classical examples of nonholonomic mechanical systems. I will use this example to give a brief introduction to this kind of systems, their properties, and the main tools that are used to study them which go from geometry and dynamics to symmetries and Lie groups. We will then consider classical and new affine variations of this problem and see that the dynamics ranges from integrable to chaotic depending on the specifics of the system. Finally, I will discuss some curious and surprising phenomena occurring in specific examples.
Elisa Marini, "Collective periodic behaviors in largevolume interacting particle systems"
Abstract. In the first part of this seminar, we will give an overview of collective periodic behaviors in large systems of interacting components. Loosely speaking, such phenomena consist in nearlyperiodic oscillations which characterize the longtime dynamics of some macroscopic quantity of the system, and which cannot be ascribed to any external periodic force applied to the system, nor to any oscillatory behavior of its components, but rather arise from the interaction among these latter. Although they are ubiquitous in realworld systems (they are observed for instance in neural networks, predatorprey dynamics, epidemiology), such behaviors are still poorly understood from a theoretical standpoint. In the second part of the seminar, we will present a toy model of interacting diffusions displaying collective oscillations. This will serve as an example of the mechanisms which may originate collective periodic behaviors and to give an idea of the mathematics involved in the rigorous study of such phenomena.
Davide Francesco Redaelli, "Differential games and large population limits beyond the classic MeanField setting"
Abstract. Differential game theory is a branch of mathematics that touches many fields such as control and game theories, probability, stochastic and partial differential equations. An interesting aspect of it is studying strategies of the players which are optimal in that they produce a situation of equilibrium, for example in the famous sense due to Nash, and also seeing what happens when the number of players grows and possibly becomes infinite. In this talk I will try to give a brief introduction to this theory aimed at a wide audience of mathematicians possibly unaware of the subject, with the final purpose of presenting the main topics which my doctoral research focused on.
Nicolò Crescenzio, "Numerical Solution of Wave Propagation Phenomena in Viscoelastic Materials"
Abstract. Many materials, such as plastics, wood, concrete and metals at high temperatures, exhibit a mechanical behaviour that is intermediate between the elastic and the viscous one. Consequently, these materials cannot be adequately described using the wellknown classical theories of elasticity and viscosity and it is therefore necessary to consider a more general theory that is capable of modelling the behaviour of these materials, also known as viscoelastic materials. In the first part of the talk, we will provide a brief overview of the theory of linear viscoelasticity, with a particular focus on the socalled KelvinVoigt rheology. Then, we will discuss the problem of viscoelastic wave propagation phenomena in a KelvinVoigt heterogeneous material and show numerical results obtained by means of a Galerkin spectral approach.
Elena Danesi, "Strichartz estimates for the Dirac equation in different settings"
Abstract. The Dirac equation is a first order partial differential equation. It was first derived by Paul Dirac in 1928 in order to describe the free motion of a spin 1/2 particle on R^3, in according with the principles of quantum mechanics and special relativity. In the following years its definition has been generalized in order to be adapted to curved backgrounds. From the mathematical side, it can be listed within the class of dispersive equations, together with the Schrödinger, wave and KleinGordon equations. In the years, because of the study of nonlinear systems, a lot of effort has been devoted to developing tools to quantify the dispersion of a system. Among these tools we find a priori estimates on the solutions, such as Strichartz or local smoothing estimates. In the first part of the talk I will focus on the Schrödinger and wave equations in order to present these kind of estimates as well as some classical tools to prove them. In the second part, I will first introduce the Dirac equation on R x R^3 and describe its connection with the above mentioned equations. I will then present the equation in curved spacetimes. To conclude, I will survey some recent results concerning the validity of Strichartz estimates for the “curved” Dirac equation in specific settings, in particular compact or asymptotically flat manifolds.
Cinzia Bandiziol, "Topological Data Analysis: basic concepts and applications"
Abstract. In the last two decades, with the ever higher increasing amount of data of many kinds and, usually, of high dimension, it has revealed meaningfull to be able to extract new and additional infomation from data, overall if it is related to intrinsic properties of themselfes. It has motivated the birth of a new field of research, the so called Topological Data Analysis. Thanks to the strong theoretical basis of algerabraic topology, it allows to extract qualitative information from dataset, as point clouds, images, graphs, time series, ecc…, related to the “shape of data”, and to use them into machine learning and deep learning frameworks. In this talk, first we will introduce the main tool of TDA called persistent homology with basic definitions and notions. Then, after the introduction of the classification problem, we will discuss how to use the new topological information in such a context..