Call for applications to the XLI Cycle is open.

The call for applications for 3 positions in the International PhD in Science, XLI Cycle, is now open:

• official announcement
• how to apply
• application form

The deadline for application is July 7, 2025, at 12 PM (Italian time).

More information about the PhD projects:

• New approaches for measuring dry deposition of nitrogen and trace elements using Particulate Matter biosensors
• Solving problems on cubic graphs and snarks using computational and theoretical methods
• Methods and models for pricing and managing financial risks related to climate change and the green transition

New approaches for measuring dry deposition of nitrogen and trace elements using Particulate Matter biosensors

Background and motivation

Atmospheric Particulate Matter (PM) is a well-known threat to human health, but its role in altering terrestrial ecosystems dynamics is still scarcely understood. PM can act as a vector for the dry deposition of nitrogenous compounds and trace elements, which can have detrimental effects on soil chemistry, plant physiology, and overall forest ecosystem health. While wet deposition processes are relatively straightforward to quantify through precipitation sampling and analysis, dry deposition remains poorly characterized due to the complexity of measurement techniques and the necessity for advanced instrumentation.

Dry deposition is influenced by numerous factors, including particle size distribution, meteorological conditions, surface characteristics, and land cover type. The most accurate methodology for assessing dry deposition fluxes is the Eddy Covariance (EC) technique, which provides high-resolution, continuous data on vertical fluxes of gases, matter and energy. However, EC requires specific, high-cost and high-frequency instrumentation, a stable power supply, and a sophisticated analytical approach, making its implementation challenging, particularly in remote or resource-limited regions (e.g. developing countries).

The primary objective of this research is to develop and validate novel techniques for assessing the dry deposition of nitrogenous species and trace elements associated with PM in forest ecosystems. Specifically, the research activity aims to:

• Perform vertical flux measurements of PM using the EC technique in different forest ecosystems to establish reference data on deposition rates;
• Develop and test biosensor-based methodologies utilizing moss bags and moss cubes as passive collectors for PM dry deposition;
• Investigate the spatial and temporal variability of PM-associated nitrogen and trace element deposition through biosensor exposure under controlled experimental conditions;
• Compare biosensor-derived deposition estimates with EC-based measurements to evaluate the reliability and accuracy of this alternative approach;
• Analyze biosensor deployment strategies to distinguish between lateral advection and vertical fluxes while eliminating the confounding effects of wet deposition.

This study will integrate traditional atmospheric physics techniques with innovative biosensor-based approaches for a comprehensive assessment of PM dry deposition. The research will be conducted in collaboration with the University of Navarra (Spain) taking advantage of their expertise in biological material preparation and advanced chemical analysis.

By providing a cost-effective and adaptable approach to PM deposition assessment, this research will support long-term environmental monitoring and inform mitigation strategies aimed at preserving forest health and biodiversity. The collaboration between the Università Cattolica del Sacro Cuore and the University of Navarra will ensure a multidisciplinary perspective, combining expertise in atmospheric physics, biogeochemistry, and ecological monitoring.

Opportunities

• Research participating to the international collaboration between Università Cattolica del Sacro Cuore and Universidad de Navarra Pamplona with at least one year spent in both institutions;
• Double degree opportunity;
• The candidate will benefit from a large existing network of collaborators whose expertise covers both atmospheric physics, biomonitoring, ecology and chemistry;
• Opportunity to obtain the Ph.D. title from Universidad de Navarra Pamplona and from Università Cattolica del Sacro Cuore.

Supervisors

Prof. Giacomo Gerosa, Università Cattolica del Sacro Cuore, Brescia campus, Italy, giacomo.gerosa@unicatt.it
Prof. David Elustondo, Universidad de Navarra Pamplona, Spain, delusto@unav.es
Prof. Riccardo Marzuoli, Università Cattolica del Sacro Cuore, Brescia campus, Italy, riccardo.marzuoli@unicatt.it

Solving problems on cubic graphs and snarks using computational and theoretical methods

Background and motivation

In this project we consider problems about the structure of graphs, which are objects consisting of a set of vertices and a set of edges. Graphs are often used to model real life objects such as road networks or molecules. Many important open problems and longstanding conjectures in Graph Theory (i.e., the study of graphs), which are stated for large families of graphs, can be reduced to cubic graphs (i.e., graphs where every vertex is incident with exactly three edges). That is: if these problems can be solved for cubic graphs, they are solved for all graphs.

One of the most emblematic examples where this is the case is the famous Four Color Theorem [1], but many other important conjectures like the Cycle Double Cover Conjecture [6,7] and the Tutte’s 5-flow Conjecture [8] can be reduced to the class of cubic graphs. This is one of the main reasons why the study of cubic graphs is one of the most active core topics in graph theory. Next to that, cubic graphs also have applications in other areas such as chemistry, where they can be used to model chemical molecules such as the Nobel-Prize winning fullerenes [5].

For many of the aforementioned conjectures it has been proven that they are true for cubic graphs admitting a 3-edge-coloring (i.e., a coloring of the edges of the graph with three colors in such a way that adjacent edges are colored differently), and that they are very hard to solve for cubic graphs not admitting a 3-edge-coloring. In particular, it has been shown that if such conjectures are not true, a smallest counterexample must be a snark, i.e., a cubic graph not admitting a 3-edge-coloring and having some other additional properties on the girth (i.e., length of a shortest cycle) and the cyclic edge-connectivity. This makes snarks a particularly interesting and important class of graphs.

In this project we therefore aim to study properties of snarks which are relevant in the research panorama of modern Graph Theory. To do this, a common and highly successful approach consists in defining parameters measuring how far a snark is from being 3-edge-colorable, see for example [3]. Such parameters are very important as they allow to fix substructures in the snarks which should help to prove statements. For example, the resistance of a snark G is the minimum number of edges that need to be removed from G to obtain a graph which admits a 3-edge-coloring. An open problem could now be investigated in a restricted subclass of snarks (for example snarks with resistance at most 2). As these subclasses have a more restricted structure, we have more tools at our disposal and the problem should be easier to solve. The proofs of these restricted problems could then be used as stepping stones to solve the original problems.

Another approach consists of tackling problems through computational techniques. For example, in [2] all snarks on up to 36 vertices are generated and many of their properties are verified through computer tests. Generation and computer tests on small snarks are very powerful tools for checking structural properties of small snarks and possibly finding counterexamples to conjectures (e.g., using the new lists of snarks from [2], 22 published conjectures were disproved).

The aim of this doctoral project, held in cooperation with KU Leuven, is to investigate snarks and their properties with respect to the major conjectures in the field. An example of an important open problem which we would like to look into is the Petersen Coloring Conjecture [4], claiming that every bridgeless cubic graph admits a normal 5-edge-coloring (i.e., a 5-edge-coloring with additional properties on the number of colors appearing around each vertex). The innovative approach that we have in mind consists of combining computational and theoretical techniques. Generation and computer tests on snarks are indeed great tools which help develop intuition and elaborate strategies to prove general theorems on snarks. We thus plan to perform computer tests on relatively small snarks and use the obtained insights to prove the existence of normal 5-edge-colorings in subclasses of snarks. Such results will be useful stepping stones for an eventual proof of the full conjecture. The candidate will therefore develop expertise both on the theoretical and the computational aspects of graph theory and will benefit from a large existing network of collaborators whose expertise covers both theoretical and computational graph theory.

Opportunities

• Research participating to the international collaboration between Università Cattolica del Sacro Cuore and KU Leuven with at least one year spent in both institutions.
• Double degree opportunity;
• The candidate will benefit from a large existing network of collaborators whose expertise covers both theoretical and computational graph theory;
• Opportunity to obtain the Ph.D. title from KU Leuven and from Università Cattolica del Sacro Cuore.

Supervisors

Prof. Dr. Marco Antonio Pellegrini, Università Cattolica del Sacro Cuore, Brescia campus, Italy marcoantonio.pellegrini@unicatt.it
Prof. Dr. Jan Goedgebeur, KU Leuven, Belgium jan.goedgebeur@kuleuven.be
Dr. Jorik Jooken, KU Leuven, Belgium jorik.jooken@kuleuven.be
Dr. Davide Mattiolo, KU Leuven, Belgium davide.mattiolo@kuleuven.be

Methods and models for pricing and managing financial risks related to climate change and the green transition

Background and motivation

Climate change and the green transition carry many risks that can undermine the stability of the financial system. Properly assessing and managing these risks and identifying ways to incentivize the green transition pose a major challenge. At the scientific level, this challenge requires new models and methods.

To this end, the PhD student will work on quantitative assessing the impact of climate-related financial risks encompassing physical risks (e.g., extreme weather events, rising sea levels) and transition risks (e.g., regulatory changes, technological shifts) associated with the transition to a low-carbon economy. Moreover, (s)he will also focus on the possible mechanisms and policies to encourage green transition and study their economic effects.

The project consists of two phases. The first phase, to be carried out at UCSC, is dedicated to the development and implementation of models—primarily asset pricing and credit risk models—as well as related methodologies. The second phase, based at KU Leuven, focuses on testing these financial models. The goal is to investigate model risk in the context of climate finance, with particular attention to identifying and evaluating assumptions that can significantly influence impact estimates. This phase also involves developing strategies to mitigate model risk.

Opportunities

• Experimental research participating to the international collaboration between Università Cattolica del Sacro Cuore and KU Leuven with at least one year spent in both institutions;
• Double degree opportunity (PhD in Science from Università Cattolica del Sacro Cuore and PhD in Mathematics from KU Leuven).

Supervisors

Prof. Davide Radi, Università Cattolica del Sacro Cuore, Milan campus, Italy davide.radi@unicatt.it
Prof. Wim Schoutens, KU Leuven, Belgium wim.schoutens@kuleuven.be