Magnitude homology, as introduced by Hepworth and Willerton, is a bigraded homology theory of metric spaces that categorifies Leinster's notion of magnitude. The definition of magnitude was motivated, and naturally arose, from considerations on Euler characteristic in enriched category theory, and it has found many interesting connections with other areas of mathematics; such as differential geometry, graph theory, category theory, entropy, and even biological diversity. Magnitude homology satisfies all reasonable axioms of homology theories: Mayer-Vietoris and Kunneth theorems are prominent examples. The goal of the thesis is to study the magnitude homology of metric spaces in general, and its relation with reachability homology using the magnitude-path spectral sequence. 

Hochschild cohomology plays a central role in the study of algebraic structures, representation theory and investigations of associative algebras, capturing both algebraic and homotopical properties. It has been extensively studied in contexts ranging from representation theory to algebraic geometry and topology. To each simplicial complex X, one can consider the so-called incidence algebra I(X) of the face poset of X. Then, a classical theorem of Gerstenhaber and Schack shows that Hochschild cohomology of I(X) is isomorphic to the homology of X. Goal of the thesis is to study the diagrammatic Hochschild homology of algebras and prove the theorem of Gerstenhaber and Schack using path homology of graphs. 

Sam and Snowden have recently introduced the notion of (quasi)-Grobner categories, that is categories satisfying "good" combinatorial conditions. The advantage of the framework developed by Sam and Snowden is that one can study representation theory of categories and talk about Noetherianity of functors in a way that generalizes the classical notions. The goal of the thesis is to explore the theory of(quasi)-Grobner categories and explore its applications; such as a criterion for a “rationality” result for Hilbert series of representations, connecting it to the theory of formal languages. 

The goal of the thesis is to study homological stability properties of mapping class groups. We will be generally interested in homological invariants of families of groups, and in their “stable” homology. In fact, homological stability has shown that, for certain families such as the mapping class groups, it is easier to compute infinitely many homology groups at once - rather than computing single homology groups of the family. The proof of homological stability uses a spectral sequences argument, known as the Quillen argument, and in the case of mapping class groups of 3-manifolds this is due to Hatcher and Wahl. 

At the crossroads between geometry, algebra, model theory, and the computer science, the Tarski-Seidenberg theorem deals with subsets of the Euclidean space, showing that a projection of such a set on a hyperplace is still of this form. This project aims at exploring this fascinating result and its implications in logic, algebraic geometry, or computational complexity, just to name a few of the possibilities.

Does there exist an explicit criterion to determine whether a given Diophantine equation admits integer solutions? This problem, formalized in the context of computability theory, was shown to have a negative solution. The aim of this project is to unravel the proof of this deep result and explore similar decidability problems in number theory.

The goal of this project is to consider (quasicoherent?  perverse?) sheaves in classical algebraic topology, and investigate how they can be recast in the definable context, where spaces of sections are endowed with the structure of (phantom) Polish spaces

Schauder bases are a fundamental notion in Banach Space theory. In this project their fundamental properties will be studied, and higher-order generalizations indexed by walks on ordinals will be constructed using methods from analysis and set theory.

TBA

TBA

• Diamond and all things Suslin

• Szemeredi past and present

• Stefano Bonatesta: Logiche modali non-normali, 2026

• Francesco Noventa: Un calcolo dei sequenti etichettati per la logica modale al primo ordine, 2026

• Pietro Bacchetta, Applicazioni dei teoremi di Gödel: Teorema di Goodstein e Reverse Mathematics, UNIBO, Bachelor Thesis in Mathematics, 2026

• Matteo Gabrielloni, Teoria dei Modelli e Teorema di Ax-Kochen, UNIBO, Bachelor Thesis in Mathematics, 2026

• Lorenzo Baldinini, Infinito-Categorie e Omotopia Simpliciale, UNIBO, Bachelor Thesis in Mathematics, 2026

• Maria Caterina Arpinati: Pensiero simbolico logico e matematico in Leibniz, UNIBO, Master Thesis in Philosophy, 2026

• Cecilia Di Florio, Towards a logic-based approach to legal case-based reasoning, UNIBO, PhD Thesis, 2026

• Andrea Gentile: Un calcolo di sequenti etichettato per il futuro lineare discreto, 2025

• Ivan Caporale: Embedding della logica intuizionistica nella logica di Grzergorczyk. I calcoli di sequenti etichettati G3Grz e G3I e l’embedding di G3I in G3Grz, 2025

• Matteo Casarosa, Set Theory of Derived Functors, UNIBO and Université Paris-Cité, PhD Thesis, 2025

• Lorenzo Lipparini, Constructive Models of Homotopy Type Theory in Cubical Sets, UNIBO, Master Thesis, 2025

• Riccardo De Santis: Logica del paradosso e dialeteismo: il valore di una contraddizione, UNIBO, Bachelor Thesis in Philosophy, 2025

• Romeo Novali: Il potenzialismo in Matematica. Due processi generativi potenzialisti: le gerarchie cumulative degli insiemi e le free choice sequences, UNIBO, Bachelor Thesis in Philosophy, 2025

• Riccardo Malagoli: Computabilità e Complessità. Un’analisi storica e teoretica, UNIBO, Bachelor Thesis in Philosophy, 2025

• Benedetta D’Astolto: La Logica Infinitaria. Aspetti semantici e loro utilizzo in Teoria dei Modelli, UNIBO, Master Thesis in Philosophy, 2025

• Alessandro Chiaradia, Model-Theoretic Stability and its application to the Szemerédi Regularity Lemma, UNIBO, Bachelor Thesis in Mathematics, 2025

• Valerio Francesco Mangiacotti: Un calcolo dei sequenti per le logiche rilevanti, 2024

• Nicolay Lanzi: Descrizioni Definite e l'Operatore ι in Logica formale: Una Teoria Senza Cut, 2024

• Margherita Violi: Un calcolo di sequenti etichettato per la logica inquisitiva, 2024

• Jurij Lanfranco, An Introduction to Sheaf Theory and the Foundations of Condensed Mathematics, UNIBO, Bachelor Thesis, 2024

• Luca Marchiori, Homological Algebra for pro-Lie and Locally Compact Polish groups, UniTrento, Master Thesis, 2024

• Andrea Magi, Caratteristiche Cardinali del Continuo e Teorema di Bell, UNIBO, Bachelor Thesis, 2024

• Edoardo Bianchini, Introduzione alla Teoria Dei Modelli e sue Applicazioni ai Campi Algebricamente Chiusi, UNIBO, Bachelor Thesis, 2024

• Gloria Fantuzi, Sistemi deduttivi in teoria della dimostrazione e didattica, UNIBO, Master Thesis, 2024

• Fabio Altadonna, Logica di Hoare applicata su un linguaggio procedurale: implementazione Matita, UNIBO, Bachelor Thesis in Computer Science, 2024

• Marco Russo, Il lambda-calcolo con la strategia Call-by-Value, UNIBO, Bachelor Thesis in Computer Science, 2024

• Orazio Andrea Capone, Una webapp per dimostrazioni in deduzione naturale per la logica del primo ordine, UNIBO, Bachelor Thesis in Computer Science, 2024

• Jonathan Donini: Calcoli di sequenti annidati per le logiche modali, 2023

• Silvia Panza: Il calcolo dei sequenti per la logica GL, 2023

• Gabriele Giancola: Super-strict implication and non-normal logics. Labelled sequent calculus for the logic of super-strict implication S1, 2023

• Lorenzo Cappelletti: Calcolo dei sequenti annidati per logiche modali, 2023

• Davide Cavalli: Logica modale del prim'ordine: l'approccio possibilista ed attualista a confronto, 2023

• Alessandro Gentili, Introduzione alla Teoria Descrittiva degli Insiemi Effettiva, UNIBO, Bachelor Thesis, 2023

• Elena Maltoni, Rango di Morley, Forking e Indipendenza, UNIBO, Master Thesis, 2023

• Vincenzo Borriello: Una formalizzazione delle costruzioni comparative mediante la logica dei predicati, Master Thesis in Linguistics, UNIBO, 2023

• Melissa Antonelli, Towards a logical foundation of randomized computation, UNIBO, PhD Thesis, 2023

• Claudia Aimi: Implicazione super stretta e logiche non normali. Un calcolo di sequenti etichettato dell'implicazione super stretta per le logiche riflessive e transitive non normali S2 e S3, 2022

• Guido Boccali: Curry-Howard Isomorphism, Bachelor Thesis in Philosophy, UNIBO 2022

• Pietro Faustini: Razionalità ed errori: un approccio filosofico all’Economia. Modelli, metodi, prospettive, Master Thesis in Philosophy, UNIBO, 2022

• Grazia Sibilio: Critica alle flussioni ne L’Analista di Berkeley, Master Thesis in Mathematics, UNIBO, 2022

• Gabriele Vanoni, On Reasonable Space and Time Cost Models for the λ-Calculus, UNIBO, PhD Thesis, 2022

• Niccolò Martini: Calcolo dei Sequenti per un Sistema Formale della Logica Temporale, 2021

• Lorenzo Venieri, Prove di consistenza e indipendenza nella Teoria degli insiemi, UNIBO, Bachelor Thesis in Mathematics, 2021

• Cecilia Di Florio: Assioma di Scelta, Forcing e misura di Lebesgue, Master Thesis in Mathematics, UNIBO, 2020 (restricted full text)

• Guido Fiorillo, Casualità algoritmica e dimensione effettiva, UNIBO, Master Thesis in Mathematics, 2020

• Andrea Condoluci, Beta-Conversion, Efficiently, UNIBO, PhD Thesis, 2020

• Federico Cappelli, I Grundlagen der Geometrie, UNIBO, Master Thesis in Mathematics, 2019

• Michele Malpezzi, Teoria degli Insiemi in una logica paraconsistente, UNIBO, Bachelor Thesis in Mathematics, 2019

• Silvia Angiolini, La decidibilità del campo esponenziale reale, UNIBO, Master Thesis in Mathematics, 2019 (restricted full text)

• Elena Tassoni, On the Normativity and Plurality of Logical Consequence: Some Reflections on the Role of Logic in Our Epistemic System, UNIBO, PhD Thesis, 2019

• Cristiano Piemontese, Sviluppo di un interactive theorem prover in ELPI, UNIBO, Master Thesis in Computer Science, 2018

• Nicola Carissimi, P-punti nella compattificazione di Stone-Čech di ω, UNIBO, Bachelor Thesis in Mathematics, 2018

• Noemi Petrini, Un argomento di storia della logica: dal sillogismo alla logica monadica, UNIBO, Bachelor Thesis in Mathematics, 2018

• Giacomo Carpani, Cantor e l'aritmetica transfinita, UNIBO, Master Thesis in Mathematics, 2017 (restricted full text)

• Giuseppe Baudo, Macchina di Turing e Calcolabilità in una Prospettiva Storica, UNIBO, Bachelor Thesis in Computer Science for Management, 2017 (restricted full text)

• Vanessa Jacquier, Gli assiomi di Antifondazione nella teoria degli insiemi, UNIBO, Master Thesis in Mathematics, 2017

• Valeria Vignudelli, Behavioral Equivalences for Higher-Order Languages with Probabilities, UNIBO, PhD Thesis, 2017

• Anna Di Natale, L'assioma della scelta e il paradosso di Banach-Tarski, UNIBO, Bachelor Thesis in Mathematics, 2016

• Lorenzo Ruaro, Cardinalità di insiemi e numeri cardinali, UNIBO, Bachelor Thesis in Mathematics, 2016

• Antonella Tavaglione, La logica del secondo ordine e la prova ontologica di Gödel, UNIBO, Bachelor Thesis in Mathematics, 2015

• Chiara Bonacci, Enunciati indipendenti dagli assiomi dell'aritmetica di Peano, UNIBO, Master Thesis in Mathematics, 2015 (restricted full text)

• Claudia Vannelli, Introduzione alla logica e alla matematica intuizioniste, UNIBO, Master Thesis in Mathematics, 2015 (restricted full text)

• Lucia Scarfo, Errori nelle dimostrazioni: tra logica ed esperienza didattica, UNIBO, Master Thesis in Mathematics, 2015 (restricted full text)

• Rosa Colasuono, Il sillogismo e il “Gioco della Logica” di L. Carroll, UNIBO, Bachelor Thesis in Mathematics, 2015 (restricted full text)

• Benedetta Antognoli, Calcolo delle equazioni e ricorsività, UNIBO, Bachelor Thesis in Mathematics, 2014 (restricted full text)

• Daniele Fiore, Logica dell'identità e delle descrizioni, UNIBO, Bachelor Thesis in Mathematics, 2014

• Dora Pastore, L'assioma di scelta : Storia e influenza sulla matematica del novecento, UNIBO, Master Thesis in Mathematics, 2014

• Federica Frisoni, Algoritmi e ricorsività: macchine di Turing e algoritmi di Markov, UNIBO, Master Thesis in Mathematics, 2014

• Laura Gobbi, Una teoria degli insiemi non convenzionale: NFU, UNIBO, Master Thesis in Mathematics, 2014 (restricted full text)

• Lucia Casadei, Logiche proposizionali polivalenti, UNIBO, Bachelor Thesis in Mathematics, 2014 (restricted full text)

• Eugenio Orlandelli, Proof theory of quantified modal logics, UNIBO, PhD Thesis, 2014

• Giulio Pellitta, Extending Implicit Computational Complexity and Abstract Machines to Languages with Control, UNIBO, PhD Thesis, 2014

• Caterina Cammera, La Teoria delle classi NBG, UNIBO, Master Thesis in Mathematics, 2013

• Claudia Cicero, Logiche modali e teoria degli insiemi, UNIBO, Master Thesis in Mathematics, 2013

• Federica Guerra, Tavole semantiche e problemi di decidibilità, UNIBO, Bachelor Thesis in Mathematics, 2013

• Francesco Antonio Genco, Logiche modali e logiche independence friendly, UNIBO, Master Thesis in Philosophy, 2013

• Giacomo Gualandi, Modelli di teoria degli insiemi, UNIBO, Master Thesis in Mathematics, 2013

• Saverio Tassinari, Il problema della primalità in complessità computazionale, UNIBO, Bachelor Thesis in Mathematics, 2013

• Matthias Puech, Certificates for Incremental Type Checking, UNIBO, PhD Thesis, 2013

• Carlotta Bulgarelli, Numeri ordinali e cardinali nella teoria di Von Neumann-Bernays-Gödel, UNIBO, Bachelor Thesis in Mathematics, 2012

• Carlotta Dainesi, Logica modale della dimostrabilità, UNIBO, Master Thesis in Mathematics, 2012

• Andrea Simonetto, Indagini in Deep Inference, UNIBO, Master Thesis in Computer Science, 2010

• Giacomo Gualandi, L'aritmetica di Peano e i teoremi di incompletezza, UNIBO, Bachelor Thesis in Mathematics, 2010

• Marialisa Sibilano, Numeri ordinali e cardinali, UNIBO, Bachelor Thesis in Mathematics, 2010

• Matteo Capelletti, The non-associative Lambek calculus: logic, linguistic and computational properties, UNIBO, PhD Thesis, 2007

• Romeo Novali: Il Calcolo delle strutture per la logica classica proposizionale (year not specified)