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Algebra, Geometry, and Mathematical Logic
Associative rings and algebras – Category theory; homological algebra – Mathematical logic and foundations
standard compliant  MSC
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
Combinatorics – Computer science – Convex and discrete geometry – Operations research, mathematical programming
standard compliant  MSC
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
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
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) aims to develop algorithms, models, and technologies that enable machines to perform complex tasks, interact with the environment and people, adapt to new situations, and improve over time through experience. This research area integrates deep knowledge that includes formal methods, optimization techniques, modelling, and analysis of multimodal signals. The research is developed through numerous international and national collaborations and focuses on both methodological and applied aspects of AI. In particular, the research primarily concentrates on the following interdisciplinary fields of AI: automated reasoning and intelligent systems, autonomous agents and multi-agent systems, reinforcement learning and planning under uncertainty, explainable and neuro-symbolic planning, machine and deep learning, natural language processing, computer vision, multimodal applications, computational graphics, application of AI for bioinformatics and medical informatics, processing of multidimensional signals, and computational methods for the analysis of social and affective behaviour concerning virtual/augmented/mixed/extended reality and social robotics.


Mathematical methods and models
Calculus of variations and optimal control; optimization – Numerical analysis – Partial differential equations – Probability theory and stochastic processes
standard compliant  MSC
Research in this area is oriented towards the mathematical modelling of a variety of phenomena in science, engineering, business, and industry. Typical applications include 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 surfaces, motion by mean curvature), image processing, mathematical finance (stochastic differential equations, Lévy processes, stochastic control), stochastic models for complex systems, stochastic machine learning, classical and quantum mechanics. This area is characterised by multidisciplinary skills in Analysis of 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 collaborations, networks, and projects both at national and international levels. This area can be further divided into sub-areas. Analysis of PDEs and Calculus of Variations: 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: 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: 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
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
The Information Systems and Data Analytics research area focuses on developing and experimenting with innovative approaches to information representation, manipulation, and processing across various application domains. It encompasses theoretical studies in spatial, temporal, and semistructured databases, as well as process modeling with emphasis on data and process integration. The area has expanded to include advanced data analytics techniques, including data mining, predictive analytics, machine learning applications, and recommendation systems. It also covers big data technologies such as scalable architectures, distributed computing frameworks, and real-time analytics. Case studies and applications primarily center on healthcare information systems, geographical information systems, process-aware information systems, smart city and IoT data analytics, tourism recommendation engines, and business intelligence. This interdisciplinary approach aims to address complex challenges in data-driven decision-making, knowledge discovery, system optimization, and personalized user experiences, bridging the gap between traditional information systems and cutting-edge data technologies.


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