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Algebra, Geometry, and Mathematical Logic
Associative rings and algebras – Calculus of variations and optimal control; optimization – Category theory; homological algebra – Mathematical logic and foundations – Theory of computation
standard compliant  ACM 2012
This research area concerns three of the fundamental fields in pure mathematics: algebra, geometry and logic. Roughly speaking, algebra is the study of symmetry via mathematical structures with algebraic operations; geometry is concerned with properties of space including the concepts of distance and shape; and mathematical logic investigates the formal properties of mathematical systems including syntax (formal languages and calculi) and semantics (structures and models). The research groups working in this area at the University of Verona organise regular seminars, research activities, and host academic visitors from all over the world. Our research in algebra focuses on the representation theory of algebras, in particular, finite-dimensional algebras and Leavitt path algebras, localization theory, approximation theory, homological algebra, triangulated categories, t-structures and hearts, and spaces of Bridgeland stability conditions. In geometry we specialise in geometric mechanics, symplectic geometry and topology, including the study of Kähler and hyperkähler manifolds (in particular polygon and hyperpolygon spaces), moduli problems such as moduli of parabolic and parabolic Higgs bundles, equivariant cohomology, geometric quantization, cobordism, Gromov width and related topics. The logic group works on constructive algebra and analysis, Bishop set theory and type theory, higher-type computability theory and category theory, proof theory, Hilbert's program in abstract mathematics, especially the computational content of classical proofs with transfinite methods, logical methods in computer science, languages and logics for quantum computing.


Algorithms, Logic, and Theory of Computing
Applied computing – Combinatorics – Computer science – Convex and discrete geometry – Operations research, mathematical programming – Theory of computation
standard compliant  ACM 2012
Our research on algorithms and data structures includes graph algorithms, temporal networks, approximation algorithms, distributed algorithms, computational complexity, combinatorial search, and algorithms on strings. Many of the algorithmic questions we attack originate from real world problems in bioinformatics and computational biology, as well as planning and optimization in the context of medical diagnosis and market investments. We also investigate decision tree and random forests based models for deep learning applications. Regarding strings and sequences, we work on pattern matching and mining, the design and analysis of compressed data structures, as well as on combinatorics on words, text compression, grammars, and string rewriting. Members of the area work on reactive synthesis from temporal logic specifications, complexity of properties for formal languages, and decidability of the model checking/satisfiability problem for interval temporal logic. Our research also includes formal methods applied to concurrent and distributed languages, in particular, process calculi for mobile systems, concurrent and distributed object-oriented languages, formalisation of distributed algorithms, and semantics foundations and security analysis of cyber-physical systems and smart devices in the context of the Internet of Things paradigm. Further topics are the extraction of algorithms from proofs in constructive analysis, the use of minimal logic in mathematical proofs, and the study of computability models in higher order computability theory from a categorical point of view. Finally, we study models for the representation of real-time concurrent systems that include stochastic as well as hybrid behavior, as well as unconventional models of computation (often bio-inspired), molecular algorithms, and self organization processes.


Bioinformatics and medical informatics
Applied computing – Computing methodologies
standard compliant  ACM 2012
The research areas of bioinformatics and medical informatics are essential for improving our understanding of living systems and enhancing healthcare delivery. Bioinformatics provides the tools and methodologies to decode and analyze biological information, enabling us to comprehend the complexity of living organisms. This involves the analysis of omics data (genome, proteome, transcriptome, and metabolome), generated by cutting-edge technologies such as spatial transcriptomics and single-cell sequencing, along with the definition and analysis of biological networks, and the development of efficient algorithms and data structures to process the vast amounts of biological sequence data being produced today. Medical informatics leverages technology to improve health outcomes and patient care by enhancing clinical support and healthcare delivery. Our goal is to develop new theories, algorithms, data structures, artificial intelligence models, and tools to address the ongoing innovations in these fields. By expanding the boundaries of efficient methodologies in bioinformatics and medical informatics, we contribute to the continuous evolution of personalized medicine, improve public health strategies, and ensure the efficient management and analysis of healthcare information systems. The main research areas include: Evolutionary biology Multimodal data integration Natural computing Omics analysis Personal genome analysis Dedicated data structures and algorithms Informatics for biomedical imaging Clinical decision support systems Models and management of clinical processes and guidelines


Physics
Applied physics – Condensed matter physics
The research activity of the Physics area is carried out in the following fields: - The study, manufacturing, and characterization of thin-film photovoltaic cells and sensors, where the layers are deposited in lab with the techniques of vacuum thermal evaporation (4 machines), radio frequency sputtering (1), pulsed electron beam deposition (1), spin coating (2), chemical bath (2) and subsequently treated through the use of furnaces (5) in a controlled atmosphere. The characterizations of the individual layers and the finished devices are applied with techniques of microscopy and atomic force profilometry, current-voltage, and capacity-voltage measurements with a solar simulator. - the implementation and use of optical techniques for non-destructive diagnostics of works of art including multi-modal imaging in infrared and thermal bands, multi-spectral imaging, surface analysis with conoscopic laser micro profilometry, infrared spectroscopy - the application of X-ray and infrared spectroscopy and atomic force microscopy to the study of biological systems - the foundations, history, and teaching of physics with particular regard to the teaching of modern physics at the university level and the training of primary and secondary school teachers.


Software Engineering and Formal Verification
Security and privacy – Software and its engineering – Theory of computation
standard compliant  ACM 2012
The software engineering and formal verification area conducts research on novel methodologies and tools for the design, development, and validation of software systems. Research on software design is concerned with smart contracts and blockchain architectures, focusing on solid and secure architectural patterns, and on semantic foundations of wireless systems. Software verification research adopts multiple perspectives: (i) static analysis and abstract interpretation, also in reference to properties (e.g., intensional/extensional) that affect the analysis’ precision and the design of (im)precision measures; (ii) automatic generation of test cases to reveal implementation defects and vulnerabilities; (iii) investigation of models for the design and the formal verification of concurrent, distributed systems and with mobile components; and (iv) deductive approaches to automated software verification using satisfiability modulo theories. These research activities are applied to a variety of kinds of software systems, including blockchain, smart contracts, REST APIs, smartphone apps, IoT, edge-computing, cyber-physical systems, quantum programs, software developed using dynamic programming languages or with multiple programming languages.


Artificial Intelligence
Computing methodologies
standard compliant  ACM 2012
Artificial Intelligence (AI) research aims at developing algorithms, models, and technologies that enable machines to operate autonomously, adapting to new situations, and improving over time through experience. AI focuses on creating systems capable of performing tasks that typically require human intelligence, such as problem-solving, learning, reasoning, perception, understanding visual scenes and natural language, and interacting with the environment. Our area spans the following interdisciplinary subfields of AI: Automated reasoning and intelligent systems include knowledge representation, theorem proving, model building, satisfiability modulo theories, temporal reasoning, intelligent agents, multi-agent systems, and search methodologies with emphasis on discrete space search. Machine learning methods and approaches encompass supervised learning, unsupervised learning, reinforcement learning, and deep learning, along with advanced methodologies such as continual learning, self-supervised learning, data generation, domain adaptation, and generalisation. Natural language processing primarily leverages statistical, linguistic, and deep learning techniques for text understanding, language generation, sentiment analysis, and machine translation. Computer vision enables machines to interpret and understand visual information through tasks such as image classification, object detection, image segmentation, 3D reconstruction, biometric and human behaviour recognition, motion analysis, image and video understanding and generation, and scene understanding, which are essential for applications including autonomous vehicles, medical imaging, augmented reality, and surveillance systems. Combining visual and language processing modalities, computer vision and natural language processing present solutions for several multimodal applications, such as cross-modal retrieval, visual question answering, enhanced human-computer interactions, and multimodal content creation. Multimodal systems are not limited to vision and language, but other modalities can be involved for the sake of (scene) understanding or (data) generation. Computer graphics applies geometric and physically-based theories to various tasks, including object modelling, shape analysis, visualisation, texture mapping, rendering, animation, and simulation. It encompasses techniques for creating realistic images, virtual environments, and interactive graphics in applications such as video games, film production, virtual reality, and scientific visualisation. In medical bioinformatics, the studies involve the development of advanced network-based AI algorithms and deep learning algorithms to analyse heterogeneous personal data such as genomes and integrate them, to extract the important features to stratify patients based on disease subtypes, environmental interactions, and personalising treatment responses. In multi-dimensional signal processing, the studied techniques regard advanced filtering, feature extraction and segmentation methods, multiresolution and sparse signal representations, time(space)/scale methods, including wavelets, compressive sensing, large-scale image characterisation and retrieval tools, related to both optical and multimodal images. Social and affective computing involves creating systems that recognise and respond to human emotions and understand social interactions and dynamics. This field leverages data from various sources, such as facial expressions, voice tone, body language, and physiological signals, to interpret users' emotional states and social contexts. The aim is to enhance human-computer interactions by enabling systems to adapt to both individual emotional and psychological conditions and broader social environments. By integrating these insights, social and affective computing seeks to create more intuitive, empathetic, and context-aware technology, improving user experiences in areas such as virtual assistants, social media, customer service, and collaborative platforms. Autonomous agents and multiagent systems: Design and development of autonomous agents (e.g., robotic platforms) that can sense, model, and interact with the environment in which they operate and with other agents (including humans) to carry out complex tasks (e.g., deliver items in a logistic scenario). Main research topics include task assignment, distributed constraint optimization, decentralised optimization, Multi-Agent reinforcement learning, cooperative perception. Reinforcement learning and planning under uncertainty: Design and development of algorithms for learning policies in unknown environments. Specific topics concern safe reinforcement learning (e.g., learning policies in safety-critical environments such as autonomous driving), deep reinforcement learning, model-based reinforcement learning, offline reinforcement learning (e.g., learning policies from pre-acquired data in mobile robotics, Industry 5.0 and environmental sustainability applications), bridging learning and planning, planning under uncertainty in partially observable environments, and reasoning in the face of uncertainty. Explainable and neuro-symbolic planning: Design and development of algorithms that merge symbolic methods - i.e., high-level symbolic (human-readable) representations of problems, logic, and search - with neural network-based techniques to address the weaknesses of each approach, providing a robust and explainable AI capable of reasoning, learning, and cognitive modeling (e.g., learning interpretable policies and allow agents to explain their decisions in autonomous driving and industrial plant control).


Mathematics methods and models
Calculus of variations and optimal control; optimization – Numerical analysis – Probability theory and stochastic processes
standard compliant  MSC
Research in this area is oriented towards the mathematical modelling, both from a theoretical and a numerical point of view, of a variety of phenomena arising in different areas of science, engineering, business, and industry. Typical applications include, for instance, quantum and classical fluid dynamics (nonlinear Schrödinger equations, advection-diffusion-reaction equations, nonlinear hyperbolic systems), complex multi-agent systems (kinetic equations, particle methods, multi-scale models), superconductivity and materials science (Ginzburg-Landau equations), evolution of interfaces in physics and biology (minimal surface equations, motion by mean curvature), image processing (total variation-based methods), optimal control (Hamilton-Jacobi equations), mathematical finance (stochastic differential equations, Lévy processes, stochastic control), statistical mechanics (interacting particle systems, stochastic systems with many degrees of freedom), classical and quantum mechanics. This area is characterised by a sophisticated integration of multidisciplinary skills in Analysis of nonlinear PDEs, Calculus of Variations, Optimal Control, Numerical methods for PDEs, Scientific Computing, Stochastic Analysis, Probability Theory, Mathematical Physics, and Differential Geometry. The research is carried out through several collaborations, partnerships, networks, and projects both at national and international levels. This area can be further divided into sub-areas, which are recognisably different but interact with one another. Analysis of PDEs and Calculus of Variations Keyphrases: nonlinear partial differential equations, geometric measure theory, optimal transport, variational models in superconductivity theory and materials science, control theory, mean field games. Numerical Analysis and Scientific Computing Keyphrases: numerical methods for hyperbolic systems, Finite Volume and Discontinuous Galerkin schemes, exponential integrators and matrix function approximation, numerical methods for nonlinear Schrodinger equations, numerical methods for kinetic equations, modelling of multi-agent systems. Probability and Mathematical Physics Keyphrases: complex systems, interacting particle systems, stochastic dynamics, mean field games, stochastic partial differential equations, mathematical finance, neural networks and applications, integrable systems, geometric methods in mechanics.


Cybersecurity
Security and privacy – Software and its engineering
standard compliant  ACM 2012
The Department’s research focuses on designing, analyzing, verifying, and testing software and systems to address critical cybersecurity and privacy challenges faced by industry, society, and individuals in a technology-driven world. The research is both theoretical and applied, covering areas such as digital identity management, access control, web and mobile app privacy, GDPR compliance, cyber security risk assessment, black-box penetration testing, vulnerability detection, malware detection, obfuscation, and watermarking techniques for software protection, attack and defense tools for ICS, formal security analysis of ICS systems, formal models for automatic security properties and security protocols verification. The research is applied to various domains, including blockchain, cyber-physical systems, cloud systems, web and mobile apps, and the Internet of Things.


Information Systems and Data Analytics
Information systems
standard compliant  ACM 2012


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