Graduate Seminar 2023-2024

 

List of Seminars

Video recordings at Unipd's portal "Mediaspace"

(Click on title for abstract)

 
Martina Costa Cesari, "An Introduction to Non-Connected 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.
 

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Chiara Turbian, "A 2D Bin Packing Problem in the Sheet Metal Industry: models and solution approaches"

Abstract. The Bin Packing Problem (BPP) is a well-studied 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 Two-Dimensional 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.

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Khai Hoan Nguyen-Dang, "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.

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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 Kullback-Leibler 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.

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Pietro Sabelli, "Double-negation 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 non-technical overview of Gödel’s double-negation 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.

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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 non-intrusive 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.

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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 non-linear PDE's.

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Chiara Brambilla, "PA differential game model for sponsored content"

Abstract. Let us consider a communication platform distinguished for its high-quality 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 trade-off between the profit accrued from publishing native advertising and the ensuing decline in credibility. We formalise this problem as a hierarchical infinite-time 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 time-consistent open-loop equilibrium and obtain the conditions that make it optimal for the media outlet to accept native advertising.

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Marco Baracchini, "Classical Modular Forms and the k-square 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.

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