Research
SCIENTIFIC PUBLICATIONS:
Published works:
«Massey products in Galois cohomology and Pythagorean fields», Comm. in Algebra, published online. DOI.
«Integrals of groups II», with João Araújo, Peter J. Cameron, Carlo Casolo and Francesco Matucci, Israel J. of Math., published online, publised Open Access. DOI.
«Oriented pro-l RAAGs and maximal pro-l Galois groups», with Simone Blumer and Thomas S. Weigel, Int. Math. Research Notices, 2024 (2024), no. 8, 6790-6819. DOI.
«Chasing maximal pro-p Galois groups via 1-cyclotomicity», Mediterranean J. Math., 21 (2024), no. 56, 34 pp., published Open Access. DOI.
«Massey products in Galois cohomology and the Elementary Type Conjecture», J. of Number Theory 258 (2024), 40-65. DOI.
«Groups of p-absolute Galois type that are not absolute Galois groups», with Alberto Cassella and Simone Blumer, J. of Pure & Applied Algebra, 227 (2023), no. 4, 35 pp. DOI.
«On pro-p groups with quadratic Galois cohomology», with Ilir Snopce and Matteo Vannacci, J. of Algebra 612 (2022), 636-690. DOI.
«Mild pro-p groups and the Koszulity conjectures», with Jan Minac, Federico W. Pasini and Nguyêñ Duy Tân, Expositiones Mathematicæ 40 (2022), no. 3, 432-455. DOI.
«1-smooth pro-p groups and Bloch-Kato pro-p groups», Homology Homotopy & Appl. 24 (2022), no. 2, 53-67. DOI.
«Galois-theoretic features for 1-smooth pro-p groups», Canadian Math. Bull. 65 (2022), no. 2, 525-541, published Open Access. DOI.
«Oriented pro-l groups with the Bogomolov-Positselski property», with Thomas S. Weigel, Research in Number Theory 8 (2022), no. 2, 22 pp., published Open Access. DOI.
«Two families of pro-p groups that are not absolute Galois groups», J. of Group Theory 25 (2022), no. 1, 25-62, published Open Access. DOI.
«One-relator maximal pro-p Galois groups and the Koszulity conjectures», Quarterly J. of Math. 72 (2021), no. 3, 835-854. DOI.
«Pro-p groups with few relations and universal Koszulity», Math. Scandinavica 127 (2021), no. 1, 28-42. DOI.
«Koszul algebras and quadratic duals in Galois cohomology», with Jan Minac, Federico W. Pasini and Nguyêñ Duy Tân, Advances in Math. 380 (2021), 49 pp. DOI.
«Right-angled Artin groups and enhanced Koszul properties», with Alberto Cassella, J. of Group Theory 24 (2021), no. 1, 17-38, published Open Access. DOI.
«Profinite groups with a cyclotomic p-orientation», with Thomas S. Weigel, Documenta Math. 25 (2020), 1881-1916, published Open Access. DOI.
«The Kummerian property and maximal pro-p Galois groups», with Ido Efrat, J. of Algebra 525 (2019), 284-310, published Open Access. DOI.
«Detecting fast solvability of equations via small powerful Galois groups», with Sunil K. Chebolu and Jan Minac, Transactions of AMS 367 (2015), no. 12, 8439-8464, published Open Access. DOI.
«A group-theoretical version of Hilbert's Theorem 90», with Thomas S. Weigel, Bulletin of LMS 47 (2015), no. 4, 704-714. DOI.
«Finite quotients of Galois pro-p groups and rigid fields», Annales Math. Québec 39 (2015), no. 1, 113-120. DOI.
«Bloch-Kato pro-p groups and locally powerful groups», Forum Mathematicum 26 (2014), no. 3, 793-814. DOI.
PhD thesis «Cohomology of absolute Galois groups», University of Western Ontario (Canada), 2015, available here.
All papers are available on arXiv.
Metrics: no. of published articles: 22; (9 open access) no. of citations: 136; h index: 7. (Update: May 2024)
Accepted articles:
...
Preprints:
«Digraphs, pro-p groups, and Massey products in Galois cohomology», submitted to a refereed journal. Avalaible on arXiv.
«Oriented graphs, Frattini-Resistance, and Maximal pro-p Galois groups», submitted to a refereed journal. Available on arXiv.
Work in progress:
«Quotients of Demushkin groups that are not absolute Galois groups».
«Formailizing Hilbert90 for pro-p groups: a survey on 1-cyclotomicity», with Thomas S. Weigel (survey paper for Jahresbericht des DMV).
«Oriented RAAGs», with Alberto Cassella, Simone Blumer, Islam Foniqi and Thomas S. Weigel.
Future projects:
Study Frattini-injectivity and Frattini-resistance for pro-p groups, as defined by Ilir Snopce and Slobodan Tanushevski.
Study quadratically defined graded algebras with Ilir Snopce and Matteo Vannacci, following some recent results by Dessislava Kochloukova and Conchita Martinez-Pérez.
Co-authors (so far): João J. Araújo (Lisbon, POR), Simone Blumer (Milan, ITA), Peter Cameron (St. Andrews, GBR), Carlo Casolo + (Florence, ITA), Alberto Cassella (Zaragoza, SPA), Sunil K. Chebolu (Normal-IL, USA), Ido Efrat (Be'er Sheva, ISR) Francesco Matucci (Milan, ITA), Jan Minač (London-ON, CAN), Federico W. Pasini (London-ON, CAN), Ilir Snopce (Brasilia, BRA), Nguyêñ Duy Tân (Hanoi, VTN), Matteo Vannacci (Bilbao, SPA), Thomas S. Weigel (Milan, ITA).
REVIEW ACTIVITY:
I've peer-reviewed articles as a referee for the following journals: Bulletin LMS, Canadian J. Math., Compositio Math., Czechoslovak Math. J., J. Algebra, J. Group Theory, J. Inst. Math. Jussieu, J. Pure Applied Algebra, New York J. Math.
SEMINARS:
Here is a list of selected seminars I've delivered as an invited speaker.
Webinar «Nets for fishing absolute Galois pro-p groups», seminar AGAG, 16/05/2022, video.
Webinar «The Bogomolov-Positselski Conjecture for maximal pro-p Galois groups», seminar QFLAG, 30/03/2022, video.
Talk «Who wants to be an absolute Galois group?», conference New trends around profinite groups, hosted by CIRM, Levico Terme (Italy), 14/09/2021.
Webinar «1-cyclotomic pro-p groups», seminar Bilbao Algebra Seminar, 21/04/2021.
Web-lecture «Mathematics and mathematicians in the Italian Reinassance», for the course History of Mathematics (course teacher: Prof. Sunil K. Chebolu), Illinois State University (USA), 15/10/2020.
Talk «Pro-p groups with quadratic cohomology and generalised pro-p RAAGs», conference Group Theory Days in Düsseldorf, University of Düsseldorf (Germany), 21/01/2020.
Lecture «Maximal pro-p quotients of absolute Galois groups: Questions and Answers», at the Advanced School on representations of pro-p groups, hosted by ICMAT, Madrid (Spain), 11/07/2019.
Talk «The Bloch-Kato conjecture and maximal pro-p Galois groups», University of Strasbourg (France), 20/03/2018, and University of Düsseldorf (Germany), 16/04/2018.
Talk «The Kummerian property for pro-p groups», conference Topics in Group Theory and representations, Gargnano (Italy), 10/10/2017.
Talk «Absolute Galois groups of fields and the cyclotomic character», conference Nilpotent fundamental groups, hosted by BIRS, Banff AB (Canada), 23/06/2017.
Talk «Koszul pro-p groups», conference 1st Joint Meeting Brazil-Italy in Mathematics (Group Theory session), hosted by IMPA, Rio de Janeiro (Brazil), 30/08/2016.
Talk «Good (and bad) candidates for maximal pro-p Galois groups», seminar Field Arithmetic seminars, Tel-Aviv University (Israel) 13/01/2016.
Communications at the UMI (Italian Mathematical Union) congresses: «A group theoretic version of Hilbert 90» (Algebra session), XX Congresso UMI, Siena (Italy), 11/09/2015; and «The Bloch-Kato conjecture without motives» (Algebra session), XXI Congresso UMI, Pavia (Italy), 4/09/2019.
PROBLEMS:
Smaller problems:
Show that the Minač-Tân pro-p group
G = < x, y, z, t, w | [[x, y], z][t, w] = 1 >
is not a Bloch-Kato pro-p group (cf. Remark 3.7 in «Profinite groups with a cyclotomic p-orientation», Doc. Math. 2020), if you do this you win a bottle of Franciacorta wine (cf. Example 3.2 in «Groups of p-absolute Galois type that are not absolute Galois groups», J. Pure Appl. Algebra, in press).
Show that the pro-p group
G = < x, y, z, t, w | [x, w] = [x, y][z, t] = 1 >
(which is a free amalgamated pro-p product, with pro-p-cyclic amalgam, between a 4-generated Demushkin group with q=0 and a 2-generated free abelian pro-p group) is not absolutely torsion-free (and thus it cannot be completed into a 1-cyclotomic oriented pro-p group, and thus it does not occur as an absolute Galois group).
Cartoon: "Educazione subatomica" by Zerocalcare.
Big questions:
Show that every pro-p group which may be completed into a 1-cyclotomic oriented pro-p group satisfies the (strong?) n-Massey vanishing property for every n > 2.
Show that every pro-p group G which may be completed into a 1-cyclotomic oriented pro-p group satisfies a Tits' alternative: namely, either G is p-adic analytic (or locally uniform, or solvable... these properties are equivalent in this case!), or it contains a free non-abelian subgroup (cf. Question 4.7 in «Galois-theoretic features for 1-smooth pro-p groups», Canad. Math. Bull. 2021 - in fact it is equivalent to consider the same question for an absolutely torsion-free pro-p group).