Some model-theoretical and geometric properties of fields with jet
operators, PhD thesis,
Wrocław University, April 2001, dvi
Stable Groups and Algebraic Groups, J. London Math. Soc. (1) 61 (2000), 51-57,
- (with Anand Pillay) Proalgebraic and differential algebraic group structures on affine spaces, Amer.
J. Math. 122 (2000), 213-221,
- (with Marcin Chałupnik) Lazard's Theorem for differential algebraic and proalgebraic groups, Pacific
J. Math. (2) 202 (2002), 305-312,
- (with Anand Pillay) A Note on Groups Definable in Difference Fields, Proc. of AMS (1) 130 (2002), 205-212,
- Derivations of the Frobenius map, Journal of Symbolic Logic, (1) 70 (2005), 99-110,
- Geometric axioms for existentially closed Hasse fields, Annals of Pure and Applied Logic, 135 (2005), 286-302,
- Jet operators on fields, Journal of Algebra, 289 (2005), 312-319,
- (with Anand Pillay) Quantifier elimination for algebraic D-groups, Transactions AMS, 358 (2006) 167-181,
- (with Anand Pillay) On algebraic sigma-groups, Transactions AMS, 359 (2007) 1325-1337,
- (with Assaf Hasson) Strongly minimal expansions of (C,+) definable in o-minimal fields,
Proc. London Math. Soc., (1) 97 (2008), 117-154,
- A note on a theorem of Ax, Annals of Pure and Applied Logic, 156 (2008), 96-109,
- Schanuel property for additive power series, Israel Journal of Mathematics, (1) 190 (2012), 349-363,
- (with Anand Pillay) On the isotriviality of projective iterative delta-varieties,
Journal of Pure and Applied Algebra, (1) 216 (2012), 20-27,
- (with Daniel Hoffmann) Integrating Hasse-Schmidt derivations, Journal of Pure and Applied Algebra (4) 219 (2015),
- (with Daniel Hoffmann) A note on extending actions of infinitesimal group schemes, Journal of Algebra, 446 (2016),
- (with Daniel Hoffmann) Existentially closed fields with G-derivations, J. London Math. Soc. (3) 93 (2016), 590-618,
doi: 10.1112/jlms/jdw009, pdf
- (with Serge Randriambololona) Strongly minimal reducts of valued fields, Journal of Symbolic Logic, (2) 81 (2016),
doi: 10.1017/jsl.2015.61, pdf
- Ax-Schanuel condition in arbitrary characteristic, to appear in Journal of the Institute of Mathematics of Jussieu,
doi: 10.1017/S1474748017000378, pdf
- (with Daniel Hoffmann) Existentially closed fields with finite group actions, accepted to Journal of Mathematical Logic,
- (with Marcin Chałupnik) Difference modules and difference cohomology, submitted,
- (with Özlem Beyarslan) Model Theory of Fields with Virtually Free Group Actions, submitted, pdf
Preprints and Notes not intended for formal publication
- (with Anand Pillay) Subvarieties of commutative meromorphic groups,
Homological algebra (mini-lecture notes), pdf
Algebraic curves (lecture notes), pdf
Model theory (Şirince summer school mini-lecture notes), pdf
Slides from talks
Strongly minimal sets definable in expansions of RCF
(joint work with A. Hasson),
o-minimal conference, Leeds, March 2006; seminar talk, Regensburg, June 2006.
Definability in Differential Fields, Logic Colloquium 2007, Wrocław, 14-19 July.
Iterative D-varieties via group scheme actions (joint work with A. Pillay),
Atelier MODNET de Théorie des Modèles des corps,
Luminy (France), 12-16 November 2007.
Independence in positive characteristic,
Geometric Model Theory, a conference in honour of Boris Zilber,
in celebration of his 60th birthday; Oxford, March 2010.
Transcendence in positive characteristic,
Model Theory Conference in Seoul, May 2010.
Unlikely formal intersections,
Workshop Interactions of model theory with number theory and algebraic geometry, MPIM Bonn (Germany), June 2012.
Model Theory of Fields with Operators, Tutorial at PhD's in Logic VIII, Darmstadt (Germany), 9-11 May 2016.
Difference algebra and generic rational cohomology (joint work with M.
Chałupnik), Workshop on Interactions between Model Theory and Arithmetic Dynamics, The Fields Institute,
Toronto (Canada), 25-29 July 2016.
Model theory of Galois actions (joint work with Ö.
Beyarslan) Differential Galois Theory and Differential Algebraic Groups, The Fields Institute, Toronto (Canada), 24-28 July 2017.