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Previous talks this semester:
Postponed:
Kamil Ryduchowski (UW): Antiramsey coloring of pairs
Abstract: "We present a fundamental theorem by Todorcevic, stating that there exists a coloring of the complete graph of the first uncountable cardinality in uncountably many colors without an uncountable monochromatic clique. We also discuss other results of Todorcevic of similar nature, which are in some sense multidimensional variants of that coloring."
Literature:
- Todorcevic, Stevo, Partitioning pairs of countable ordinals. Acta Math. 159 (1987), no. 3-4, 261--294.
- Velleman, Dan, Partitioning pairs of countable sets of ordinals. J. Symbolic Logic 55 (1990), no. 3, 1019--1021.
29.10.2020, Thursday 15.15, room 106
Piotr Koszmider (IMPAN): An application of Schreier's family
Abstract: "This is an introduction to basic facts on the isomorphic classification of
separable Banach spaces C(K). As an example we show an ingenious argument by Józef Schreier
which uses the combinatorial structure of the ordinal ωω to understand some Banach spaces
and to resolve a question of S. Banach."
Literature:
- On the classification of spaces C[0,α] see Chapter 2.6 of Hajek, Petr; Montesinos Santalucia, Vicente; Vanderwerff, Jon; Zizler, Vaclav Biorthogonal systems in Banach spaces. CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 26. Springer, New York, 2008.
- A deep modern versions of Milutin's theorem can be found in: Argyros, Spiros A.; Arvanitakis, Alexander D. A characterization of regular averaging operators and its consequences. Studia Math. 151 (2002), no. 3, 207–226.
- Schreier's argument is Exercise 19.3.9 (F) in Semadeni, Zbigniew Banach spaces of continuous functions. Vol. I. Monografie Matematyczne, Tom 55. PWN—Polish Scientific Publishers, Warsaw, 1971.
22.10.2020, Thursday 15.15, room 106
Piotr Koszmider (IMPAN): Eberlein compact spaces, WCG Banach spaces and ladder systems.
Abstract: "This is an introduction to basic facts and examples concerning Eberlein compact spaces (compact subspaces of Banach spaces with the weak topology) and WCG Banach spaces which are associated with each other. As the main set-theoretic example we will consider ladder system spaces on
ω1 and spaces induced by almost disjoint families."
Literature:
- On the weak and weak* topologies see Chapter 3 of Fabian, Marian; Habala, Petr; Hajek, Petr; Montesinos Santalucia, Vicente; Pelant, Jan; Zizler, Vaclav Functional analysis and infinite-dimensional geometry. CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 8. Springer-Verlag, New York, 2001.
- On EC and WCG spaces see Chapters 11 and 12 of Fabian, Marian; Habala, Petr; Hajek, Petr; Montesinos Santalucía, Vicente; Pelant, Jan; Zizler, Václav Functional analysis and infinite-dimensional geometry. CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 8. Springer-Verlag, New York, 2001.
- The proof that C(K) is Lindelof in the weak topology, where K is the ladder system space is here:
Pol, Roman A function space C(X) which is weakly Lindelof but not weakly compactly generated. Studia Math. 64 (1979), no. 3, 279–285.
- A survey of results on the spaces KA, where A is an almost disjoint family of
subsets of N: Hrusak, Michael Almost disjoint families and topology. Recent progress in general topology. III, 601–638, Atlantis Press, Paris, 2014.
- A survey of results on the spaces KA, where A is an almost disjoint family of
subsets of N: Hernandez-Hernandez, F.; Hrusak, M. Topology of Mrowka-Isbell spaces. Pseudocompact topological spaces, 253–289, Dev. Math., 55, Springer, Cham, 2018.
- Some results on the spaces KA, where A is an almost disjoint family of
subsets of uncountable sets: Ferrer, Jesus; Koszmider, Piotr; Kubis, Wieslaw Almost disjoint families of countable sets and separable complementation properties. J. Math. Anal. Appl. 401 (2013), no. 2, 939–949.
Talks in the second semester of 2019-20.
Talks in the first semester of 2019-20.
Talks in the second semester of 2018-19.
Talks in the first semester of 2018-19.
Talks in the second semester of 2017-18.
Talks in the first semester of 2017-18.
Talks in the second semester of 2016-17.
Talks in the first semester of 2016-17.
Talks in the second semester of 2015-16.
Talks in the first semester of 2015-16.
Talks in the second semester of 2014-15.
Talks in the first semester of 2014-15.
Talks in the second semester of 2013-14.
Talks in the first semester of 2013-14.
Talks in the second semester of 2012-13.
Talks in the first semester of 2012-13.
Talks in the second semester of 2011-12.
Talks in the first semester of 2011-12.
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