Topological ManifoldsMarzio De Corato
Research · Teaching · Writing

Marzio
De Corato.

Black-and-white photograph: practising yoga on a rock in a mountain landscape.

Cybersecurity · Explainable AI · Information Theory · Quantum Computing · Quantitative Finance

My work in cybersecurity and explainable artificial intelligence continues an inquiry into data, models and knowledge that began in computational physics. My interest in classical and quantum information theory accompanies this path alongside quantum computing and quantitative finance, shaping the questions I bring to research and teaching.

Course materials Research Profile and CV
Adjunct teaching

University of Milan
Università Cattolica del Sacro Cuore

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Research

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Laboratories

Two galaxies to explore: Quantum Lab and GeoStat Lab, from quantum computing to statistics for Earth sciences.

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A selected research reading

Questions and findings

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Carbon, geometry, research

Forms of carbon

Cages, ribbons and periodic surfaces: explore atomic bonds and the questions connecting geometry to materials research.

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C₆₀ fullerene

C₆₀ fullerene

Twelve pentagons allow a hexagonal carbon network to close into a cage, revealing how ring arrangement accompanies the curvature of a closed carbon surface.

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Graphene nanoribbons

Graphene nanoribbons

Cutting a graphene sheet leaves an atomic edge whose properties can be investigated through spectroscopy and calculations. The two views make armchair and zigzag terminations recognisable.

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From the blog

The War of False Perceptions

Alerts in European schools show how an unfounded threat can consume resources, change decisions and prolong its effects. This essay examines that pressure through cognitive overload, orientation and the OODA loop in John Boyd’s thinking.

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Readings, forms and experience

The profile and the page about the site’s name bring together the personal journey and readings that accompany the scientific work, while the atlas collects figures through which to explore the geometric relationships discussed in the texts.

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Graph theory and cyber-attacks

Unaffected nodeCompromised node

When devices, services and identities are described through their relationships, system security can be studied as a structural problem in which both a vulnerability and the paths through which it could expose other resources matter.

From connections to attack paths

A graph G = (V, E) consists of vertices V and edges E. In an asset network, vertices may represent devices or services, while edges describe connections, dependencies or trust relationships. An attack graph instead represents conditions, actions or system states, depending on the model, to examine how several steps can combine into a compromise.

G = (V, E)

The analogy with an epidemic helps illustrate how a compromise can spread between nodes, provided that the conditions for each transition are considered. Credentials, permissions, vulnerabilities and configurations determine which paths are feasible; a connection alone describes a possibility of communication.

How this supports defence

Path analysis helps identify the resources reachable from an initial position and the connections that form critical passages. Comparing the graph before and after a change shows how network segmentation, reduced privileges or a vulnerability fix can interrupt particular sequences. A node’s importance depends on its role and context, so its number of connections gives only a partial account of risk.

Reading this figure

Red nodes marked with a cross represent compromised systems in the scenario; green nodes remain unaffected, while pale pulses follow the propagation paths. The map provides a conventional geographical layout for an illustrative network whose links and timing are constructed to clarify the phenomenon. It does not show observed attacks or estimate compromise probabilities.

References

Sheyner et al. — Automated Generation and Analysis of Attack Graphs, Carnegie Mellon University

NIST IR 7788 — Security Risk Analysis of Enterprise Networks Using Probabilistic Attack Graphs

Natural Earth cartography — public-domain data

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Topological Manifolds

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Research · Teaching · Exploration

Topological
Manifolds

Marzio De Corato

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