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
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K. Krupiński, L. Newelski, On bounded type definable equivalence relations
ps,
Notre Dame Journal of Formal Logic (43), 231-242, 2002.
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K. Krupiński, Products of finite abelian groups as profinite groups
ps, Journal of Algebra (288), 556-582, 2005.
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K. Krupiński, Abelian profinite groups
ps, Fundamenta Mathematicae (185), 41-59, 2005.
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T. Blossier, K. Krupiński, A special thin type
ps, Illinois Journal of Mathematics (49), 281-290, 2005.
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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 (20), 2050018 (48 pages), 2020.
- 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.
- J. Gismatullin, G. Jagiella, K. Krupiński, Bohr compactifications of groups and rings
pdf, submitted.
- K. Krupiński, T. Rzepecki, Generating ideals by additive subgroups of rings
pdf, preprint.
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).
Detailed CV
Algebra I R
Kolokwium nr 2 odbedzie sie zdalnie w poniedzialek 14 grudnia w godzinach 12.10-13.15.
Obowiazuje material z wykladow 5-8.
Sposób przeprowadzenia kolokwium opisany jest tutaj: pdf
Konsultacje: sroda, 14.00-15.30, zdalnie (prosze o informacje e-mailowa w srody do godziny 14.00, czy w danym dniu ktos chce wziac udzial w konsultacjach;
jesli beda chetni, o 14.00 rozpoczne spotkanie, do którego zainteresowani studenci beda mogli się dolaczac; jesli nie bedzie nikogo chetnego, nie bede rozpoczynac spotkania).
Program i zmodyfikowane zasady zaliczania ćwiczeń pdf
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Teoria stabilnosci I
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Stable groups
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Theories with NIP
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