Piotr Koszmider: undergraduate, graduate and postgraduate advising
Students and postdocs
Małgorzata Rojek
Warsaw Doctoral School of Mathematics and Computer Science
Kamil Ryduchowski
Warsaw Doctoral School of Mathematics and Computer Science
Publications:
- P. Koszmider, K. Ryduchowski, Equilateral and separated sets in some Hilbert generated Banach spaces Proc. Am. Math. Soc. 152, No. 3, 1003-1017 (2024)
Zdeněk Silber
Institute of Mathematics of the Polish Academy of Sciences
Joint publications:
- P. Koszmider, Z. Silber, On Subspaces of Indecomposable Banach Spaces; Accepted to Advances in Mathematics.
- Koszmider, Piotr; Silber, Zdeněk Countably tight dual ball with a nonseparable measure. J. Lond. Math. Soc., II. Ser. 110, No. 4, Article ID e12988, 25 p. (2024).
Damian Głodkowski
Warsaw Doctoral School of Mathematics and Computer Science
Doctoral thesis: Some applications of set theory in Banach spaces and operator algebras.
Project publications:
- D. Głodkowski, P. Koszmider, Products of C*-algebras that do not embed into the Calkin algebra. Preprint, arXiv:2412.11191
- D. Głodkowski, A. Widz, Epic math battle of history: Grothendieck vs Nikodym. J. Funct. Anal. 288, No. 4, Article ID 110757, 51 p. (2025).
- D. Głodkowski, A Banach space C(K) reading the dimension of K. J. Funct. Anal. 285, No. 4, Article ID 109986, 32 p. (2023).
- D. Głodkowski, P. Koszmider, On coverings of Banach spaces and their subsets by hyperplanes. Proc. Am. Math. Soc. 150, No. 2, 817-831 (2022).
Kamil Ryduchowski
Licenciate thesis: Antiramsey colorings of pairs with an application to Banach spaces.
Jakub Andruszkiewicz
Master's thesis: ♣ principle - variants and applications.
Arturo Antonio Martínez Celis Rodríguez
Institue of Mathematics of the Polish Academy of Sciences
Joint publications:
- P. Koszmider, A. Martínez-Celis; Rosenthal families, pavings, and generic cardinal invariants. Proc. Amer. Math. Soc. 149 (2021), no. 3, 1289-1303.
Fulgencio Lopez
Institue of Mathematics of the Polish Academy of Sciences
Tristan Bice
Institue of Mathematics of the Polish Academy of Sciences
Joint publications:
- T. Bice, P.Koszmider; C*-algebras with and without <<-increasing approximate units; J. Math. Anal. Appl. 477 (2019), no. 2, 1396--1418.
- T. Bice, P. Koszmider; A note on the Akemann-Doner and Farah-Wofsey constructions. Proc. Amer. Math. Soc. 145 (2017), no. 2, 681--687.
Clayton Suguio Hida
Department of Mathematics of the University of São Paulo
Doctoral thesis: Irredundant sets in in C*-algebras.
Project publications:
- C. Hida, P. Koszmider, Large irredundant sets in operator algebras, Canad. J. Math. 72 (2020), no. 4, 988-1023.
Damian Sobota
Institue of Mathematics of the Polish Academy of Sciences
Doctoral thesis: Cardinal invariants of the continuum and convergence of measures on compact spaces.
Project publications:
- D. Sobota, The Nikodym property and cardinal characteristics of the continuum, Ann. Pure Appl. Logic 170 (2019), no. 1, 1--35.
- D. Sobota, On families of subsets of natural numbers deciding the norm convergence in l1, Proc. Amer. Math. Soc. 146 (2018), no. 4, 1673--1680.
- D. Sobota, Families of sets related to Rosenthal's lemma. Arch. Math. Logic 58 (2019), no. 1-2, 53--69.
Cristobal Rodríguez-Porras
Department of Mathematics of the University Paris 7
Doctoral thesis: A set-theoretic analysis of operators on the Banach space l∞/c0.
Project publications:
- P. Koszmider, C. Rodríguez-Porras, On automorphism of the Banach space l∞/c0, Fund. Math. 235 (2016), no. 1, 49--99.
Saeed Ghasemi
Institue of Mathematics of the Polish Academy of Sciences
Joint publications:
- S. Ghasemi, P. Koszmider, A nonstable C*-algebra with an elementary essential composition series. Proc. Am. Math. Soc. 148, No. 5, 2201-2215 (2020).
- S. Ghasemi, P. Koszmider, An extension of compact operators by compact operators with no nontrivial multipliers; J. Noncommut. Geom. 12 (2018), no. 4, 1503--1529.
- S. Ghasemi, P. Koszmider, Noncommutative Cantor-Bendixson derivatives and scattered C*-algebras Topology Appl. 240 (2018), 183--209.
Héctor Gabriel Salazar Pedroza
Institute of Mathematics of the Polish Academy of Sciences
Marek Cúth
Institue of Mathematics of the Polish Academy of Sciences
Leandro Candido Batista
Institue of Mathematics of the Polish Academy of Sciences
Joint publications:
- L. Candido, P. Koszmider, On complemented copies of c0(ω1) in C(Kn) spaces. Studia Math. 233 (2016), no. 3, 209--226.
Michał Świętek
Institue of Mathematics of the Polish Academy of Sciences
Joint publications:
- P. Koszmider, S. Shelah. M. Świętek; There is no bound on sizes of indecomposable Banach spaces; Adv. Math. 323 (2018), 745--783.
Clayton Suguio Hida
Department of Mathematics of the Polish Academy of Sciences
Project publications:
- C. Hida, Two cardinal inequalities about bidiscrete systems. Topology Appl. 212 (2016), 71--80.
Przemysław Zieliński
Institute of Mathematics of the Technical University of Łódź
Master's thesis: Some applications of infinitary combinatorics in Banach spaces of continuous functions.
Project publications:
- P. Koszmider, P. Zieliński, Complementation and Decompositions in some weakly Lindelof Banach spaces, J. Math. Anal. Appl. 376 (2011) 329-341.
Christina Brech
University of São Paulo and University Paris 7
Doctoral thesis: Generic constructions of Asplund spaces C(K).
Project publications:
- C. Brech, P. Koszmider, Thin-very tall compact scattered spaces which are hereditarily separable, Trans. Amer. Math. Soc. 363 (2011), no. 1, 501-519.
Rogério Augusto dos Santos Fajardo
Department of Mathematics of the University of São Paulo
Doctoral thesis: Consistent constructions of Banach spaces C(K) with few operators..
Project publications:
- R. Fajardo, An indecomposable Banach spaces of continuous functions which has small density, Fund. Math. 202 (2009), no. 1, 43-63.
- R. Fajardo, ; Essentially incomparable Banach spaces of continuous functions. Bull. Pol. Acad. Sci. Math. 58 (2010), no. 3, 247--258.
- R. Fajardo, Quotients of indecomposable Banach spaces of continuous functions. Studia Math. 212 (2012), no. 3, 259--283.
Christina Brech
Department of Mathematics of the University of São Paulo
Master's thesis: Combinatorial aspects of Banach spaces of continuous functions with the Grothendieck property.
Project publications:
- C. Brech; On the density of Banach spaces C(K) with the Grothendieck property, Proc. Amer. Math. Soc. 134 (2006), 3653-3663.
Examples of possible topics of licenciate, master's and doctoral projects
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Set-theoretic methods in C*-algebras
the Calkin algebra as the noncommutative version of the Boolean algebra P(N)/Fin, pure states, separably representable C*-algebras, masas
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Set-theoretic methods in Banach spaces
universal spaces, indecomposable Banach spaces, equilateral sets, separated sets, Auerbach systems, biorthogonal systems, semi-biorthogonal systems
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Set-theoretic methods in algebras of operators on Banach spaces
spaces with few operators, Boolean algebras of projections
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Set theoretic methods in Banach algebras
measure convolution algebras
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Set theoretic methods
forcing, iterated forcing, Ramsey theory, stepping-up, two cardinal combinatorics, sets of reals, trees, almost disjoint families, ultrafilters, independent families, simplified morasses, forcing axioms, gaps in P(N)/Fin
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Boolean algebras
the Boolean algebra P(N)/Fin, measures on Boolean algebras, Nikodym property, Grothendieck property, the Stone duality,
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Set-theoretic topology
βN, N*, Radon-Nikodym compacta, Eberlein and uniformly Eberlein compacta, Efimov problem, Čech-Stone reminders
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Interactions of set theory and physics
Pitowsky's spin models, pure state space of quantum mechanics, quantum physics in nonseparable Hilbert spaces, random ultrafilters as hidden variables