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Instytut Matematyczny Uniwersytetu Wrocławskiego Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland e-mail: kkrup@math.uni.wroc.pl |
A Ph.D. scholarship in model theory is available. The deadline for applications is 15 May 2020. For details see pdf.
Interests
I am interested in pure model theory and its connections with algebra and topology, particularly in:- topological dynamics methods in model theory
- Lascar strong types, Galois groups, and spaces of strong types,
- profinite structures, profinite groups and rings regarded as profinite structures,
- Polish structures, Polish [compact] $G$-groups,
- stable, simple, rosy and NIP theories, groups and fields,
- $\omega$-categorical groups and rings,
- minimal and quasi-minimal structures.
Publications
- K. Krupiński, L. Newelski, On bounded type definable equivalence relations ps, Notre Dame Journal of Formal Logic (43), 231-242, 2002.
- K. Krupiński, Products of finite abelian groups as profinite groups ps, Journal of Algebra (288), 556-582, 2005.
- K. Krupiński, Abelian profinite groups ps, Fundamenta Mathematicae (185), 41-59, 2005.
- T. Blossier, K. Krupiński, A special thin type ps, Illinois Journal of Mathematics (49), 281-290, 2005.
- K. Krupiński, Profinite structures interpretable in fields ps, Annals of Pure and Applied Logic 142, 19-54, 2006.
- K. Krupiński, F. Wagner, Small profinite groups and rings ps, Journal of Algebra (306), 494-506, 2006.
- C. Ealy, K. Krupiński, A. Pillay, Superrosy dependent groups having finitely satisfiable generics pdf, Annals of Pure and Applied Logic (151), 1-21, 2008.
- K. Krupiński, Fields interpretable in rosy theories ps, Israel Journal of Mathematics (175), 421-444, 2010.
- K. Krupiński, Fields interpretable in superrosy groups with NIP (the non-solvable case) ps, Journal of Symbolic Logic (75), 372-386, 2010.
- K. Krupiński, Some model theory of Polish structures ps, Transactions of the American Mathematical Society (362), 3499-3533, 2010.
- K. Krupiński, Generalizations of small profinite structures pdf, Journal of Symbolic Logic (75), 1147-1175, 2010.
- K. Krupiński, A. Pillay, On stable fields and weight pdf, Journal of the Institute of Mathematics of Jussieu (10), 349-358, 2011.
- K. Krupiński, On relationships between algebraic properties of groups and rings in some model-theoretic contexts pdf, Journal of Symbolic Logic (76), 1403-1417, 2011.
- K. Krupiński, On $\omega$-categorical groups and rings with NIP pdf, Proceedings of the American Mathematical Society (140), 2501-2512, 2012.
- J. Dobrowolski, K. Krupiński, On $\omega$-categorical, generically stable groups pdf, Journal of Symbolic Logic (77), 1047-1056, 2012.
- J. Dobrowolski, K. Krupiński, On $\omega$-categorical, generically stable groups and rings pdf, Annals of Pure and Applied Logic (164), 802-812, 2013.
- K. Krupiński, F. Wagner, Small, nm-stable compact G-groups pdf, Israel Journal of Mathematics (194), 907-933, 2013.
- K. Krupiński, P. Tanović, F. Wagner, Around Podewski's conjecture pdf, Fundamenta Mathematicae (222), 175-193, 2013.
- K. Krupiński, A. Pillay, S. Solecki, Borel equivalence relations and Lascar strong types pdf, Journal of Mathematical Logic (13), 1350008 (37 pages), 2013.
- J. Dobrowolski, K. Krupiński, Locally finite profinite rings pdf, Journal of Algebra (401), 161-178, 2014.
- T. Gogacz, K. Krupiński, On regular groups and fields pdf, Journal of Symbolic Logic (79), 826-844, 2014.
- K. Krupiński, Superrosy fields and valuations pdf, Annals of Pure and Applied Logic (166), 342-357, 2015.
- J. Gismatullin, K. Krupiński, On model-theoretic connected components in some group extensions pdf, Journal of Mathematical Logic (15), 1550009 (51 pages), 2015.
- K. Krupiński, T. Rzepecki, Smoothness of bounded invariant equivalence relations pdf, Journal of Symbolic Logic (81), 326-356, 2016.
- K. Krupiński, A. Pillay, Generalized Bohr compactification and model-theoretic connected components pdf, Mathematical Proceedings of the Cambridge Philosophical Society (163), 219-249, 2017.
- K. Krupiński, Definable topological dynamics pdf, Journal of Symbolic Logic (82), 1080-1105, 2017.
- K. Krupiński, A. Pillay, T. Rzepecki, Topological dynamics and the complexity of strong types pdf, Israel Journal of Mathematics (228), 863-932, 2018.
- K. Krupiński, A. Pillay, Amenability, definable groups, and automorphism groups pdf, Advances in Mathematics (345), 1253-1299, 2019.
- K. Krupiński, L. Newelski, P. Simon, Boundedness and absoluteness of some dynamical invariants in model theory pdf, Journal of Mathematical Logic (19), 1950012 (55 pages), 2019.
- K. Krupiński, T. Rzepecki, Galois groups as quotients of Polish groups pdf, Journal of Mathematical Logic, accepted.
- E. Hrushovski, K. Krupiński, A Pillay, Amenability and definability pdf. This preprint is not meant to be published, as it has been divided (with some changes) into the next two papers.
- E. Hrushovski, K. Krupiński, A Pillay, Amenability, connected components, and definable actions pdf, submitted.
- E. Hrushovski, K. Krupiński, A Pillay, On first order amenability pdf, submitted.
- K. Krupiński, A. Pillay, On the topological dynamics of automorphism groups; a model-theoretic perspective pdf, submitted.
- K. Krupiński, J. Lee, S. Moconja, Ramsey theory and topological dynamics for first order theories pdf, submitted.
Work in progress
- Borel complexity of the relation of being in the same Lascar strong type, model theoretic connected components (collaboration with I. Kaplan and T. Rzepecki).
- Topological dynamics and measure in model theory (collaborations with: A. Chernikov, J. Lee, S. Moconja, A. Onshuus, A. Pillay, P. Simon).
- Ramsey properties for first order theories (collaboration with: J. Lee, S. Moconja).
- Model-theoretic connected components (collaboration with J. Gismatullin and G. Jagiella).
- $\omega$-categorical groups (collaboration with D. Macpherson).
- Quasi-minimal structures (collaboration with S. Moconja).