Graduate Seminar 2024-2025

List of Seminars

Video recordings at Unipd's portal "Mediaspace"

(Click on title for abstract)

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Beatrice Ongarato, "Hawkes processes in cyber-risk analysis: modelization and optimal security investment"

Abstract. With the rapid growth of the digital economy in recent years, cyber-risk has emerged as one of the most relevant and rapidly growing sources of risk. We provide an overview of the main concepts related to cyber-risk and examine the challenges involved in its quantification and modeling. We introduce Hawkes processes and explain their applicability in capturing the dynamics of cyber-attacks. Lastly, we present an ongoing project aimed at determining the optimal cyber-security investment strategy for an organization facing cyber-attacks. The problem is framed as a stochastic control problem with jumps and is addressed using Hamilton-Jacobi-Bellman (HJB) techniques. We introduce the main tools needed to solve this type of problem and show some preliminary numerical results.

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Ishan Jaztar Singh, "Bridging Enumerative Geometry and Quantum Integrable Hierarchies"

Abstract. Enumerative geometry explores the use of combinatorial and intersection theory techniques to solve counting problems in algebraic geometry. Integrable hierarchies, in contrast, consist of infinite sequences of partial differential equations with symmetries that have significance in mathematical physics. Both fields have seen substantial developments over the past half-century. This talk will focus on the infamous Witten-Kontsevich theorem, which establishes a deep connection between topological invariants of the moduli space of curves and the Korteweg–de Vries hierarchy. I will attempt to offer intuitive motivation and a formal statement of the theorem, and, time permitting, discuss its generalizations and the role of quantum hierarchies in this context.

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Pietro De Checchi, "Dynamics of Environment-Embedded Quantum Systems: An Introduction"

Abstract. Closed quantum systems are an idealization, their time evolution described by the Schrödinger Equation, i.e. by the action of unitary operators. The physics of a realistic quantum system, on the other hand, is bound to be disturbed by the environment in which it is naturally embedded and with which it inevitably interacts. The dimension of the space needed to fully describe the composite system increases, as one would have to include all, possibly infinite, environments variables, leading to intractable problems. To reduce the system to a smaller subspace of interest and to describe its correct dynamics, many strategies have been developed. These systems have in general non-unitary dynamics and are known as Open Quantum Systems. During the talk, we will introduce some of the main approaches based on various techniques, from dynamical semigroup generators, stochastic unravellings and bottom-up modelling.

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Enrico Sabatini, "Representations of Quivers over Rings: Merging Commutative and Non-Commutative Results"

Abstract. In the vast universe of representation theory there are two very separate and different worlds: commutative rings and finite dimensional (non-commutative) algebras. The problem of characterising certain subcategories, like many other problems, has been solved in both fields. However, the main techniques used for one context are generally not transferable to the other. Recently, some authors have focused their interest on a special kind of algebras that partially merge the two fields. Here, the apparently different results have a surprising generalisation and a unifying proof. In this talk, I will give an overview of the two fields mentioned above, describe their main features and give an idea of what allows such characterisations; avoiding all the technicalities. Finally, I'll show how the generalisation works with the aid of some interesting examples.

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Erik Chinellato, "Deep Unfolding: Bridging Optimization and Neural Network Interpretability"

Abstract. Deep neural networks (DNNs) have revolutionized numerous fields due to their powerful ability to learn complex representations. However, their black-box nature and lack of interpretability in architecture and weight design remain significant challenges. After an introductory segment on DNNs and backpropagation learning, this seminar introduces the Deep Unfolding method as a promising alternative, bridging the gap between data-driven learning and model-based optimization. By unrolling iterative optimization algorithms into structured neural network architectures, Deep Unfolding provides a principled approach to network design, enabling interpretability and theoretical insights into their operation. We will explore how this method leverages domain knowledge, achieves faster convergence, and enhances performance in resource-constrained scenarios. The session will highlight many wide-ranging practical applications of Deep Unfolding, covering audio source separation and recognition, image denoising and state estimation.

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