Winter School 2011

Andreas Blass, Péter Komjáth, Lionel Nguyen Van Thé, Petr Simon


This year of the tutorial lectures (each tutorial comprising of several 50 minute lectures) were devoted to advanced topics of Combinatorial and Descriptive Set Theory. They were delivered by leading experts in the respective fields.

Professor Andreas Blass (University of Michigan, Ann Arbor) gave a series of talks introducing recent developements in ultrafilter theory. He had especially emphasized the connections with algebra.

Professor Péter Komjáth (Eötvös Loránd University, Budapest) prepared an introductory course in infinite combinatorics especially concentrating on the results of P. Erdös. He had also mentioned intriguing open questions.

Professor Lionel Nguyen van Thé (Université Paul Cézanne, Marseille) gave an overview of the exciting new connections which were recently discovered between descriptive set theory, topological dynamics and combinatorial set theory. The main topic of his lectures was the relationship of extreme amenability of topological groups and the Ramsey properties of certain Fraïssé classes.

Professor Petr Simon (Charles University, Prague) talked about almost disjoint refinement theorems (a topic one of whose initiators P. Simon is) and the recent results of S. Shelah on completely separable MAD families.

The research presentations were given mainly by younger participants who presented their newest results. The topics included General Topology, Set Theory, Boolean Algebras and Forcing, Descriptive Set Theory, Large Cardinals and the Theory of Ultrafilters.

Each day participants had time to discuss their work with colleagues. The topics of the discussions were diverse and included recent developments in set theory (The exciting new result on the consistency of the Borel and dual Borel conjecture, ultrafilter limits, recent trends in set theoretic topology, automorphisms of ω* etc.)


Paweł Łabędzki, Jaroslav Šupina, Bohuslav Balcar, Marek Balcerzak, Taras Banakh, Artur Bartoszewicz, Tristan Bice, Marek Bienias, Andreas Blass, Piotr Borodulin-Nadzieja, Andrew Brooke-Taylor, David Chodounsky, Michal Doucha, Barnabás Farkas, Jana Flašková, Joanna Garbulińska, Szymon Glab, Magdalena Grzech, Rodrigo Hernandez-Gutierrez, Radek Honzik, Magdalena Kiełek, Archil Kipiani, Péter Komjáth, Marios Koulakis , Andrzej Kucharski, Marcin Kysiak, Anna Lauschmannová, Hiroaki Minami, Lionel Nguyen Van The, Aleksandar Pavlović, Tomáš Pazák, Alex Primavesi, Karen Raesch, Robert Ralowski, Růžena Roháčková, Philipp Schlicht, Robin Scholz, Petr Simon, Daniel Soukup, Lajos Soukup, Santi Spadaro, Jan Spěvák, Michal Staš, Andrzej Starosolski, Jan Stary, Sławomir Szczepaniak, Katie Thompson, Jonathan Verner, Zoltan Vidnyanszky, Martin Weese, Thilo Weinert, Wolfgang Wohofsky, Marek Wyszkowski, Jindrich Zapletal, Szymon Zeberski,


Talks, slides, abstracts

Jaroslav ŠupinaSequence selection principles for special convergences slides
Marek BalcerzakMonotone Borel hulls slides
Taras BanakhNetwork character and meager convergence in topological spaces slides
Artur BartoszewiczRemarks on ideal convergence slides
Tristan BiceProjections in the Calkin Algebra: Order Structure and Cardinal Invariants slides
Andreas BlassUltrafilters on Countable Sets I. slides
Andreas BlassUltrafilters on Countable Sets II. slides
Andreas BlassUltrafilters on Countable Sets III. slides
Piotr Borodulin-NadziejaSequential properties of space of measures slides
Andrew Brooke-TaylorSubcompact Cardinals, Squares slides
Barnabás FarkasIdeals and almost disjoint sets slides
Jana FlaškováUniformity of the van der Waerden ideal slides
Szymon GlabIdeals with bases of unbounded Borel hierarchy slides
Rodrigo Hernandez-GutierrezRemote Points and Extremal Disconnectedness slides
Radek HonzikDistributivity of the Cohen forcing in larger universes slides
Archil KipianiOn Representations of Abstract Groups as Automorphism Groups of Graphs slides
Péter KomjáthDelta systems, set mappings
Péter KomjáthSet mappings, con't, polarized partition calculus
Péter KomjáthPartititon calculus
Andrzej KucharskiVery I-favorable spaces slides
Hiroaki MinamiMathias-Prikry forcing and dominating real slides
Lionel Nguyen Van TheStructural Ramsey theory and topological dynamics I. slides
Lionel Nguyen Van TheStructural Ramsey theory and topological dynamics II. slides
Lionel Nguyen Van TheStructural Ramsey theory and topological dynamics III. slides
Alex PrimavesiEmbedding structure for LOTSs slides
Karen RaeschA minimal Prikry-type forcing for singularizing a measurable cardinal slides
Robert RalowskiNonmeasurable partitions on the real line slides
Philipp SchlichtAutomatic ordinals and linear orders slides
Petr SimonAlmost Disjoint Refinement by Countable Sets I slides
Petr SimonAlmost Disjoint Refinement by Countable Sets II slides
Petr SimonAlmost Disjoint Refinement by Countable Sets III slides
Lajos SoukupPcf theory and cardinal invariants of the reals slides
Daniel SoukupGuessing clubs for aD, non D-spaces slides
Santi SpadaroSelection Principles and Dense Sets slides
Jan SpěvákMappings between posets of continuous functions
Michal StašPerfect set property slides
Andrzej StarosolskiExistence of ordinal ultrafilters and of P-hierarchy slides
Jonathan VernerUltrafilters generic over P(N)/I slides
Thilo WeinertPartition relations and coloured finite digraphs slides
Wolfgang WohofskyBorel Conjecture and Dual Borel Conjecture slides
Szymon ZeberskiNonmeasurability v.s. complete nonmeasurability slides
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