Fixed-term assistant professor
Department of Mathematical Sciences (DISMA)
Profile
Research interests
Biography
My research lie mainly in geometric group theory, finiteness properties of infinite groups and homological methods in group theory. A particular focus is given to the study of locally compact groups, in particular the construction and development of homological and geometric theories for the groups in this class motivated by analogy with the classical theories for discrete groups. Other areas of interest include accessibility for pro-p groups and the theory of topological and algebraic entropy for locally compact groups. In the recent years I have sometimes engaged in interdisciplinary research, especially with computer science and cryptography, driven by an interest in exploring applications of group theory in other fields.
Scientific branch
(Area 0001 - Mathematical and computer sciences)
Research topics
- Algebraic and topological entropy
- Bass-Serre theory for pro-p groups
- Finiteness properties of locally compact groups
- Geometric group theory for totally disconnected locally compact groups
Skills
ERC sectors
Awards and Honors
- Premio Giovani Talenti dell'Università degli Studi di Milano-Bicocca, con il Patrocinio dell'Accademia Nazionale dei Lincei conferred by Università degli Studi di Milano-Bicocca con il Patrocinio dell'Accademia Nazionale dei Lincei, Italy (2022)
- Qualification Maitre de Conference conferred by Ministère de l’Enseignement Supérieur et de la Recherche - France, Francia (2022)
- Abilitazione Scientifica Nazionale II fascia conferred by MIUR, Italy (2023)
Fellowships
- Fellow - Bielefeld Universitat, Germania (2022-)
Postdoctoral Fellowship - Fellow - Heilbronn Institute for Mathematical research, Regno Unito (2021)
Heilbronn Small Grants Scheme - Fellow - ICTP-INdAM, Italia (2020-2022)
“Research in Pairs” grant - Fellow - London mathematical society, Regno Unito (2020-2022)
LMS “Visits to UK” grant - Fellow - Università degli studi di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Italia (2019-2022)
Assegno di Ricerca - Tipo A2 Junior - Fellow - Università degli Studi di Udine, Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Italia (2018-2019)
Assegno di Ricerca - Fellow - University of Southampton, School of Mathematics, Regno Unito (2016-2018)
Research fellow - Fellow - Universiità degli Studi di Udine, Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Italia (2015-2016)
Assegno di ricerca
Conferences
- Groups & Algebras in Bicocca for Young Algebraists, Program chair
- Topological and Homological Methods in Group Theory 2024, Program chair
- GoTh Workshop: Groups of Thompson and their relatives, Program chair
- Around profinite groups, Program chair
- Groups & Algebras in Bicocca for Young Algebraists, Program chair
- Groups with Geometrical and Topological Flavours, Program chair
- Dynamical Methods in Algebra, Geometry and Topology, Program chair
- Homological algebra and Topological groups, Program chair
Other research or teaching roles outside Politecnico
- Ricercatore, presso Heinrich-Heine-Universität Düsseldorf (1/10/2024-30/9/2026)
- Ricercatore, presso University of Bielefeld (1/10/2022-30/9/2024)
- Assegnista, presso Politecnico di MILANO (13/9/2021-20/2/2022)
- Assegnista, presso Università degli Studi di MILANO-BICOCCA (1/2/2021-31/5/2021)
- Assegnista, presso Politecnico di MILANO (14/9/2020-20/2/2021)
- Assegnista, presso Università degli Studi di MILANO-BICOCCA (1/10/2019-30/9/2022)
- Cultore della materia, presso Università degli Studi di BARI ALDO MORO (1/5/2015-30/7/2015)
- Visiting Researcher, presso The University of Newcastle (1/10/2013-20/12/2014)
- Visiting Researcher, presso Università degli Studi di MILANO-BICOCCA (1/3/2013-5/7/2013)
- Cultore della materia, presso Politecnico di BARI (1/3/2013-21/5/2015)
Teaching
Teachings
Bachelor of Science
- Algebra lineare e geometria. A.A. 2025/26, INGEGNERIA AEROSPAZIALE. Collaboratore del corso
- Algebra lineare e geometria. A.A. 2025/26, INGEGNERIA AEROSPAZIALE. Collaboratore del corso
Research
Research fields
Research groups
Publications
Last years publications
Latest publications View all publications in Porto@Iris
- Castellano, Ilaria; Marchionna, Bianca; Weigel, Thomas (2025)
Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one. In: MATHEMATISCHE ANNALEN, vol. 392, pp. 933-964. ISSN 0025-5831
Contributo su Rivista - Castellano, Ilaria; Zalesskii, Pavel A. (2024)
A pro-p version of Sela’s accessibility and Poincaré duality pro-p groups. In: GROUPS, GEOMETRY, AND DYNAMICS, vol. 18, pp. 1349-1368. ISSN 1661-7207
Contributo su Rivista - Arora, S.; Castellano, I.; Cook, G. Corob; Martínez-Pedroza, E. (2023)
Subgroups, hyperbolicity and cohomological dimension for totally disconnected locally compact groups. In: JOURNAL OF TOPOLOGY AND ANALYSIS, vol. 15, pp. 223-249. ISSN 1793-5253
Contributo su Rivista - Castellano, Ilaria (2023)
An Introduction to Totally Disconnected Locally Compact Groups and Their Finiteness Conditions. In: Modern Trends in Algebra and Representation Theory (Series Number 486) / David Jordan, Nadia Mazza, Sibylle Schroll, S.L., Cambridge University Press. ISBN: 9781009093750
Contributo in Volume - Castellano, Ilaria; Giordano Bruno, Anna; Zava, Nicolò (2023)
Weakly weighted generalised quasi-metric spaces and semilattices. In: THEORETICAL COMPUTER SCIENCE, vol. 977, pp. 1-29. ISSN 0304-3975
Contributo su Rivista - Castellano, Ilaria; Dikranjan, Dikran; Freni, Domenico; Bruno, Anna Giordano; Toller, ... (2022)
Intrinsic entropy for generalized quasimetric semilattices. In: JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol. 21. ISSN 0219-4988
Contributo su Rivista - Castellano, I.; Zalesskii, P. (2021)
Subgroups of pro-p PD3-groups. In: MONATSHEFTE FÜR MATHEMATIK, vol. 195, pp. 391-400. ISSN 0026-9255
Contributo su Rivista - Castellano, Ilaria (2020)
The corank of a flow over the category of linearly compact vector spaces. In: JOURNAL OF PURE AND APPLIED ALGEBRA, vol. 224, pp. 1-17. ISSN 0022-4049
Contributo su Rivista - Castellano, Ilaria (2020)
Rational discrete first degree cohomology for totally disconnected locally compact groups. In: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, vol. 168, pp. 361-377. ISSN 0305-0041
Contributo su Rivista - Castellano, I.; Cook, G. Corob; Kropholler, P. H. (2020)
A property of the lamplighter group. In: TOPOLOGICAL ALGEBRA AND ITS APPLICATIONS, vol. 8, pp. 1-4. ISSN 2299-3231
Contributo su Rivista - Castellano, Ilaria (2020)
Topological entropy for locally linearly compact vector spaces and field extensions. In: TOPOLOGICAL ALGEBRA AND ITS APPLICATIONS, vol. 8, pp. 58-66. ISSN 2299-3231
Contributo su Rivista - Castellano, I.; Corob Cook, G. (2020)
Finiteness properties of totally disconnected locally compact groups. In: JOURNAL OF ALGEBRA, vol. 543, pp. 54-97. ISSN 0021-8693
Contributo su Rivista - Castellano, Ilaria; Giordano Bruno, Anna (2019)
Topological entropy for locally linearly compact vector spaces. In: TOPOLOGY AND ITS APPLICATIONS, vol. 252, pp. 112-144. ISSN 0166-8641
Contributo su Rivista - Castellano, Ilaria; Bruno, Anna Giordano (2017)
Algebraic Entropy in Locally Linearly Compact Vector Spaces. In: Rings, Polynomials, and Modules / S.N., S.L., Springer, pp. 103-127. ISBN: 9783319658728
Contributo in Volume - Castellano, I.; Weigel, Th. (2016)
Rational discrete cohomology for totally disconnected locally compact groups. In: JOURNAL OF ALGEBRA, vol. 453, pp. 101-159. ISSN 0021-8693
Contributo su Rivista