Publications and talks

PhD thesis

Integration on Surreal Numbers (pdf, abstract) 

Directed by A. Macintyre, at the University of Edinburgh, 

Defended on January 2004 with the jury: A. Macintyre, A. Carbery, A. Maciocia, D. Richardson.

Articles

You can find (partial) lists of my published articles on MathSciNet, Zentrablatt, and Orcid

• The addition theorem for locally monotileable monoid actions (with D. Dikranjan, A. Giordano Bruno, F. Salizzoni) (ArXiv) Journal of Pure and Applied Algebra (2022) doi: 10.1016/j.jpaa.2022.107113

• Generic derivations on o-minimal structures (with E. Kaplan) (ArXiv ); J. of Mathematical Logic 21:2, (2021), doi:10.1142/S0219061321500070 

• Hilbert polynomial of length functions (preprint: ArXiv)

• Algebraic entropy for amenable semigroup actions (with D. Dikranjan and A. Giordano Bruno) (ArXiv); J. Algebra 556:15 (2020) 467--546, doi:10.1016/j.jalgebra.2020.02.033 

• A weak version of the strong exponential closure (with P. D'Aquino and G. Terzo) (ArXiV); Israel Journal of Mathematics 242, (2021)  697–-705, doi:10.1007/s11856-021-2141-1 

• Generic solutions of equations with iterated exponentials (with P. D'Aquino and G. Terzo) (ArXiv);  Transactions AMS 270:2 (2018) 1393--1407, doi:10.1090/tran/7206 

• How to avoid a compact set (with P. Hieronymi and E. Walsberg). Adv. Math. 317 (2017), 758--785. doi: j.aim.2017.07.011

• Two preprints on d-minimality: D-minimal structures and Groups and rings definable on d-minimal structures

• A note on Hieronymi's  theorem: every definably complete structure is definably Baire. In Groups, Modules, and Model Theory - Surveys and Recent Development, M. Droste et al. editors (2017), pp 301-315, doi:10.1007/978-3-319-51718-6 submitted version

• A fundamental dichotomy for definably complete expansions of ordered fields (with  P. Hieronymi) (ArXiv); The Journal of Symbolic Logic 80:04 (2015), pp 1091-1115, doi:10.1017/jsl.2014.10

• A dichotomy for expansions of the real field (with P. Hieronymi and C. Miller) (ArXiv); Proceedings of AMS 141 (2013), 697-698, doi:10.1090/S0002-9939-2012-11369-3.   

• Expansions of the reals which do not define the natural numbers (ArXiv); a version of this article has been submitted.

• Definably connected nonconnected sets (pdf file); Math. Log. Quart. 58, No. 1-2, 125-126 (2012); doi:10.1002/malq.201100062.

• Dimension in topological structures: Topological closure and local properties (with I. Halupczok) (pdf file); in Groups and Model Theory, L. Strüngmann et al. editors, Contemporary Mathematics 576 (2012), 89-94,  doi:10.1090/conm/576

• Lovely pairs for independence relations (pdf file); submitted.

• Hausdorff measure on o-minimal structures (with Elisa Vasquez Rifo) (ArXiv); JSL, 77:2 (2012), 631-648, doi:10.2178/jsl/1333566642.

• Tame structures and open cores (pdf file); some version of this article has been submitted.

Part of this article appeared as:

• • Locally o-minimal structures and structures with locally o-minimal open core; Annals of Pure and Applied LogicVolume 164, Issue 3, March 2013, Pages 211-229;  doi:10.1016/j.apal.2012.10.002

  • Definably complete structures are not pseudo-enumerable; Archive for Mathematical Logic, Volume 50, Issue 5, 2011, Page 603-615; doi:10.1007/s00153-011-0235-x.

• Dimension, matroids, and dense pairs of first-order structures (pdf file); APAL, Volume 162, Issue 7, June-July 2011, pp. 514-543; doi:10.1016/j.apal.2011.01.003.

• Baire's theorem and definably complete structures (with T. Servi) (pdf file); some version of this article has been submitted. The content of this article was published (in revised version) in three parts as:

  • • Definably complete Baire structures, Fundamenta Mathematicae, Volume 209, Number 3 (2010), pp. 215-265; doi:10.4064/fm209-3-2.

    • Relative Pfaffian closure for definably complete Baire structures; Illinois Journal of Mathematics, Volume 55, Number 3 (2011), 1203-1219; link.

    • Theorems of the complement; in: Lecture Notes on O-Minimal Structures and Real Analytic Geometry, (C. Miller, J.-P. Rolin, P. Speissegger Editors), Fields Institute Communications 62 (2012), 219-242; link to Google books.

• O-minimal cohomology: finiteness and invariance results (with A. Berarducci) (pdf file, expanded version); Journal of Mathematical Logic, Volume 9, Issue 2 (2009) pp. 167-182;   doi:10.1142/S0219061309000859.

• Towers of complements to valuation rings and truncation closed embeddings of valued fields (with Franz-Viktor Kuhlmann and Salma Kuhlmann); Journal of Algebra, Volume 323, Issue 3, 1 February 2010, pp. 574-600; doi:10.1016/j.jalgebra.2009.11.023.

• O-minimal spectrum (pdf file), preliminary version.

• Arithmetic of Dedekind cuts of ordered Abelian groups (with M. Mamino) (pdf file); Annals of Pure and Applied Logic, Volume 156, Issues 2-3, December 2008, pages 210-244;  doi:10.1016/j.apal.2008.05.001.

• Embedding Henselian fields into power series (pdf file); Journal of Algebra, Volume 304, Issue 1, October 2006, pages 112-156; doi:10.1016/j.jalgebra.2006.06.037.

• Initial embeddings in No of models of Tan(exp) (pdf file), unpublished.

• Recursive definitions on surreal numbers (pdf file), unpublished.

Slides and notes

• Three talks on the Kolchin polynomial of commuting (quasi)-endomorphisms of a matroid: Pisa '22, Cetraro '22, Udine '23 (joint work with E. Kaplan)

• O-minimal structures with several dense  independent subfields: Online seminar: Topological and Differential Expansions of O-minimal Structures '21

• From algebraic entropy to Hilbert polynomials: Lodz '21: the topic is my article Hilbert polynomial of length functions

• A two cardinal theorem for small sets: Konstanz '18: how to make small sets countable.

• Several talks on (algebraic) entropy of actions of amenable semigroups (joint work with D. Dikranjan and A. Giordano Bruno, article in preparation): AILA '17,   Udine '18, Wroclaw '18, Pisa '19.

• Several talks on "restrained" structures: Logic Colloquium '09, two, three, Bologna '11, Paris '11, Ravello '13, Lisbon '13, ?'16 (see my articles: with P. Hieronymi A fundamental dichotomy for definably complete expansions of ordered fields,  with P. Hieronymi and C. Miller A dichotomy for expansions of the real field, and the preprint Tame structures and open cores)

• Exponential Fields (Camerino '13). The topic is my work with P. D'Aquino and G. Terzo.

• Groups definable in d-minimal structures (Poster and Talk).    We generalize to such objects some known results from o-minimality. In particular, we can endow a definable group with a definable topology making it a topological group. Moreover, a definable ring of dimension at least 1 and without zero-divisors is a skew field

• Definable compactness (Bilbao '14 and Mülheim '16).  A general definition of definable compactness (for definable sets with a definable topology), focusing on locally definably compact fields.

• Cohomology of o-minimal expansions of groups (pdf). The topic is my article with Berarducci "O-minimal cohomology: finiteness and invariance results".

• Lovely pairs for independence relations (pdf): commented slides of the talk given at the British Postgraduate Model Theory Conference, Leeds, January 2011.  Expanded and updated version (pdf): talk given at the Lancashire Yorkshire Model Theory Seminar, Leeds, June 2016.   The topic is my preprint by the same name.

• Notes on Hrushovski's article "Stable group theory and approximate subgroups" (pdf ): notes for our seminar in Münster, WS2010-11.  They supplement van den Dries' notes on the same article.

• Dimension, matroids, and dense pairs of structures (pdf): notes of the talk given at the workshop Model theory: around valued fields and dependent theories, Oberwolfach, January 2010.  The topic is my article by the same name.

• Snow White and the omega dwarves (pdf): notes of the seminar given at Freiburg, February 2008.  Some (surprising) variants of the Hat puzzle (thanks to all the guys in Pisa for the discussions on this puzzle).

• Pairs of fields (pdf file): notes of the seminar given at Freiburg, June 2008. Exposition of some theorems on (dense) pairs of structures.

• Truncation-closed embeddings of Henselian fields into power series (gzipped postscript file). The topic is my article Embedding Henselian fields into generalised power series fields.

• O-minimal spectrum (pdf): slides of the talk given at Regensburg, June 2007.  The topic is my article O-minimal spectrum.

• Tagli di Dedekind di gruppi Abeliani ordinati (pdf, in Italian): commented slides of the talk given at the Incontro Italiano Insiemi e Modelli, Torino, April 2007.  Dedekind cuts of ordered Abelian groups (pdf): slides of a talk given at Freiburg, 22 Oct 2007.  The topic is my article with M. Manino Arithmetic of Dedekind cuts of ordered Abelian groups.

• Hausdorff measure on o-minimal structures (pdf): commented slides of the talk given at the Colloque autour de l'o-minimalité, Paris, September 2006. Let K be an o-minimal structure expanding an ordered field. Expanding the work of Berarducci and Otero, we define the d-dimensional Hausdorff measure of definable subset of Kn​​, where d<n are natural numbers. We prove some of the properties for this measure, analogue of the ones for the Hausdorff measure on the reals.

• Initial Embeddings in the Surreal Numbers of Models of Tan(exp)​​ (pdf): commented slides on the talk given at the Oxford Workshop in Model Theory, September 2006. Every model of  Tan or of Tan(exp)​​ admits an initial embedding in the field of surreal numbers No.

• Čech cohomology of definable sets in o-minimal structures (with A. Berarducci) (pdf): commented slides of the talk given at the International Congress NonStandard Methods and Applications in Mathematics, Pisa, May 2006. Let A be a semi-algebraic set, definable without using parameters in some real closed field M. Let à be its real spectrum, and A(R) be the realization of A on the reals. We will give a simple proof, based on the trasfer principle, of the fact that the Čech cohomology of à is isomorphic to the one of A(R) in a natural way. With a similar proof, we show an analogous result also for other o-minimal structures M.

• O-minimality of the standard part (pdf). Let M be an o-minimal structure expanding a field. Let R be the residue field of M, with the structure generated by the images of definable subsets of M under the residue map. Using a theorem by Baisalov and Poizat, we prove that R is weakly o-minimal.