Winter School 2011
Andreas Blass, Péter Komjáth, Lionel Nguyen Van Thé, Petr Simon
Program
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.)
Participants
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,Photos
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Photos by A. Pavlović
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The 2011 Wednesday Trip
(by J. Flašková) -
The 2011 Monday walk
(by J. Flašková) -
Photos by D. Soukup
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Photos by P. Simon
Talks, slides, abstracts
| Speaker | Title | Download |
| Jaroslav Šupina | Sequence selection principles for special convergences | slides |
| Marek Balcerzak | Monotone Borel hulls | slides |
| Taras Banakh | Network character and meager convergence in topological spaces | slides |
| Artur Bartoszewicz | Remarks on ideal convergence | slides |
| Tristan Bice | Projections in the Calkin Algebra: Order Structure and Cardinal Invariants | slides |
| Andreas Blass | Ultrafilters on Countable Sets I. | slides |
| Andreas Blass | Ultrafilters on Countable Sets II. | slides |
| Andreas Blass | Ultrafilters on Countable Sets III. | slides |
| Piotr Borodulin-Nadzieja | Sequential properties of space of measures | slides |
| Andrew Brooke-Taylor | Subcompact Cardinals, Squares | slides |
| Barnabás Farkas | Ideals and almost disjoint sets | slides |
| Jana Flašková | Uniformity of the van der Waerden ideal | slides |
| Szymon Glab | Ideals with bases of unbounded Borel hierarchy | slides |
| Rodrigo Hernandez-Gutierrez | Remote Points and Extremal Disconnectedness | slides |
| Radek Honzik | Distributivity of the Cohen forcing in larger universes | slides |
| Archil Kipiani | On Representations of Abstract Groups as Automorphism Groups of Graphs | slides |
| Péter Komjáth | Delta systems, set mappings | |
| Péter Komjáth | Set mappings, con't, polarized partition calculus | |
| Péter Komjáth | Partititon calculus | |
| Andrzej Kucharski | Very I-favorable spaces | slides |
| Hiroaki Minami | Mathias-Prikry forcing and dominating real | slides |
| Lionel Nguyen Van The | Structural Ramsey theory and topological dynamics I. | slides |
| Lionel Nguyen Van The | Structural Ramsey theory and topological dynamics II. | slides |
| Lionel Nguyen Van The | Structural Ramsey theory and topological dynamics III. | slides |
| Alex Primavesi | Embedding structure for LOTSs | slides |
| Karen Raesch | A minimal Prikry-type forcing for singularizing a measurable cardinal | slides |
| Robert Ralowski | Nonmeasurable partitions on the real line | slides |
| Philipp Schlicht | Automatic ordinals and linear orders | slides |
| Petr Simon | Almost Disjoint Refinement by Countable Sets I | slides |
| Petr Simon | Almost Disjoint Refinement by Countable Sets II | slides |
| Petr Simon | Almost Disjoint Refinement by Countable Sets III | slides |
| Daniel Soukup | Guessing clubs for aD, non D-spaces | slides |
| Lajos Soukup | Pcf theory and cardinal invariants of the reals | slides |
| Santi Spadaro | Selection Principles and Dense Sets | slides |
| Jan Spěvák | Mappings between posets of continuous functions | |
| Michal Staš | Perfect set property | slides |
| Andrzej Starosolski | Existence of ordinal ultrafilters and of P-hierarchy | slides |
| Jonathan Verner | Ultrafilters generic over P(N)/I | slides |
| Thilo Weinert | Partition relations and coloured finite digraphs | slides |
| Wolfgang Wohofsky | Borel Conjecture and Dual Borel Conjecture | slides |
| Szymon Zeberski | Nonmeasurability v.s. complete nonmeasurability | slides |
