Trends in Set Theory

Trends in Set Theory

8 – 11 July, 2012, Warsaw

Participants of the conference focused on the interactions between set theory and other parts of mathematics, from Banach spaces and C*-algebras to topological groups, sets of the reals, general topological spaces, and others.
This included both the advances concerning appropriate set-theoretic tools from forcing theory, Ramsey theory, descriptive set theory or other branches of set theory as well as concrete applications of these methods in the mathematical practice.

The idea of the conference as focused on applications of set theory in diverse mathematical disciplines was quite original and created a new environment for interactions and the exchange of ideas.

The conference had the official status of a satellite event to the 6th European Congress of Mathematics held in Krakow, Poland in the days 1-7 of July 2012. Its organizers received financial contribution from the European Science Foundation, Institute of Mathematics of the Polish Academy of Sciences and from University of Wroclaw.

Scientific content of the event

  • Set Theory of the Real Line
  • Descriptive Set Theory in Polish Groups
  • Combinatorial Set Theory in Banach Spaces
  • Set-theoretic Topology
  • Algebra an Set Theory
  • Developing Set-theoretic Tools
  • Problem session

Scientific Committee Committee

  • Piotr Koszmider (chair)
  • Grzegorz Plebanek
  • Janusz Pawlikowski
  • Marcin Sabok
  • Slawomir Solecki

List of invited speakers

  1. A. Aviles (Murcia)
  2. J. Brendle (Kobe)
  3. M. Dzamonja (UEA Norwich)
  4. M. Elekes (Renyi Institute)
  5. S. Geschke (Hausdorff Center)
  6. M. Hrusak (UNAM Morelia)
  7. A. Kechris (Caltech)
  8. . W. Kubis (AVCR and UJK Kielce)
  9. J. Lopez-Abad (ICMAT Madrid)
  10. S. Shelah (Jerusalem and Rutgers)
  11. S. Solecki (Urbana-Champaign)
  12. L. Nguyen Van The (Aix-Marseille)
  13. S. Thomas (Rutgers)
  14. S. Todorcevic (CNRS and Toronto)
  15. T. Tsankov (Paris 7)
  16. B. Velckovic (Paris 7)
  17. P. Zakrzewski (Warszawa)
  18. J. Zapletal (AVCR and Gainesville)

Participants

  1. Alessandro Andretta, Universita di Torino
  2. Antonio Avilés Lopez, Universidad de Murcia
  3. Joan Bagaria, ICREA, Barcelona
  4. Marek Balcerzak, Institute of Mathematics Technical University of Lodz
  5. Taras Banakh, Ivan Franko National University of Lviv and Jan Kochanowski University in Kielce, Poland
  6. Dana Bartosova, Charles University in Prague/University of Toronto
  7. Artur Bartoszewicz, Institute of Mathematics, Technical University of Lodz
  8. Tomek Bartoszynski, National Science Foundation
  9. Wojciech Bielas, Silesian University
  10. Marek Bienias, Technical University of Lodz
  11. Aleksander Blaszczyk, Instytut Matematyki Uniwersytet Slaski w Katowicach
  12. Piotr Borodulin-Nadzieja, University of Wroclaw
  13. Jorg Brendle, Kobe University
  14. Raphael Carroy, University Paris 7/University of Lausanne
  15. David Chodounsky, Institute of Mathematics AS CR
  16. Claudia Correa de Andrade Oliveira, University of Sao Paulo
  17. Marek Cuth, Charles University in Prague
  18. Michal Doucha, Academy of Sciences of the Czech Republic
  19. Mirna Dzamonja, University of East Anglia
  20. M?rton Elekes, Hungarian Academy of Sciences
  21. Ahmad Farhat, University of Wroclaw
  22. Barnabas Farkas, Budapest University of Technology
  23. Jana Flaskova, University of West Bohemia in Pilsen
  24. Kevin Fournier, Université de Lausanne (Suisse), Université Paris 7 (France)
  25. Stefan Geschke, Hausdorff Center
  26. Szymon Glab, Instytut Matematyki Politechniki Lodzkiej
  27. Vassilios Gregoriades, TU Darmstadt
  28. David Guerrero Sanchez, Universidad de Murcia/UNAM
  29. Jacek Hejduk, Wydzia? Matematyki i Informatyki U?
  30. Michael Hrusak, Universidad Nacional Autónoma de México
  31. Istvan Juhasz, Alfred Renyi Institute of Mathematics
  32. Tomasz Kania, Lancaster University
  33. Alexander Kechris, California Institute of Technology
  34. Yurii Khomskii, Kurt Godel Research Center
  35. Michal Korch, Warsaw University
  36. Piotr Koszmider, Polish Academy of Sciences
  37. Adam Krawczyk, University of Warsaw
  38. Mikolaj Krupski, Polish Academy of Sciences
  39. Alicja Krzeszowiec, University of Technology in Lodz
  40. Wieslaw Kubis, AV CR and UJK Kielce
  41. Beata Kubis, Institute of Mathematics Academy of Sciences of the Czech Republic
  42. Adam Kwela, Instytut Matematyczny PAN
  43. Arkady Leiderman, Ben-Gurion University of the Negev, Israel
  44. Jorge Lopez Abad, Instituto de Ciencias Matemáticas-Madrid
  45. Roman Lubczyk, Uniwersytet Opolski
  46. Philipp Lucke, Mathematisches Institut Rheinische Friedrich-Wilhelms-Universitat Bonn
  47. Maciej Malicki, Uczelnia ?azarskiego
  48. Witold Marciszewski, University of Warsaw
  49. Javier Meri, Universidad de Granada
  50. Heike Mildenberger, Universitaet Freiburg
  51. James Donald Monk, University of Colorado at Boulder
  52. Jacek Nikiel, Opole University
  53. Janusz Pawlikowski, University of Wroclaw
  54. Yann Pequignot, Univerist? de Lausanne, Switzerland, Univerist? de Paris VII Denis Diderot, France
  55. Grzegorz Plebanek, University of Wroclaw
  56. Marcin Sabok, Polish Academy of Sciences/University of Wroclaw
  57. Philipp Schlicht, University of Bonn
  58. Jeffrey Serbus, Albert-Ludwigs-Universit?t Freiburg
  59. Saharon Shelah, Hebrew University of Jerusalem/Rutgers University
  60. Slawek Solecki, University of Illinois At Urbana-Champaign
  61. Daniel Tamas Soukup, University of Toronto
  62. Wojciech Stadnicki, University of Wroclaw
  63. Filip Strobin, Technical University of Lodz
  64. Zoltan Szentmiklossy, ELTE TTK, Budapest
  65. Eleftherios Tachtsis, University of the Aegean Department of Statistics & Actuarial-Financial Mathematics
  66. Lionel Nguyen Van Th?, University of Aix-Marseille
  67. Simon Thomas, Rutgers University
  68. Stevo Todorcevic, University of Toronto/CNRS/University of Paris 7
  69. Todor Tsankov, University of Paris 7
  70. Boban Velickovic, University of Paris 7
  71. Zoltan Vidnyanszky, E?tv?s Lor?nd University
  72. Eliza Wajch, University of Natural Sciences and Humanities in Siedlce
  73. Thilo Weinert, Hausdorff Centre for Mathematics
  74. Tomasz Weiss, University of Natural Sciences and Humanities, Siedlce, Poland
  75. Wolfgang Wohofsky, Vienna University of Technology, Institute for Dircrete Mathematics and Geometry
  76. Jerzy Wojciechowski, West Virginia University
  77. Piotr Zakrzewski, University of Warsaw
  78. Jindrich Zapletal, University of Florida, Gainesville\Czech Academy of Sciences
  79. Rafal Zdunczyk, Wydzial Matematyki i Informatyki Uniwersytetu Lodzkiego

Programme

Saturday, 7th of July 2012
9.00-9.45 S. Shelah; Null ideal (random forcing) for inaccessible exist?
10.00-10.30 J. Zapletal; The free set property for calibrated ideals. (Slides).
11.00-11.30 J. Brendle; Recent results on splitting and disjointness. (Slides).
11.45-12.00 T. Weinert; Idiosynchromatic Poetry. (Slides).
12.05-12.20 W. Wohofsky; Variants of the Borel Conjecture and Sacks dense ideals. (Slides).
12.25-12.40 M. Doucha; Borel equivalence relations and Laver forcing. (Slides).
12.45-13.00 D. Chodounsky; Grigorieff forcing and automorphisms of P(w)/Fin. (Slides).
16.00-16.45 B1 Problem session (weather not permitting version A1)
17.15-17.45 M. Hrusak; Countable Frechet groups. (Slides).
18.15-18.30 Y. Khomskii; Definable Hausdorff Gaps. (Slides).
18.40-18.55 Zoltan Vidnyanszky; Transfinite constructions in V=L. (Slides).
Monday, 9th of July 2012
9.00-9.45 A. Aviles; Multiple gaps.
10.00-10.30 J. Lopez Abad; On the Banach-Saks property and convex hulls. (Slides).
11.00-11.30 W. Kubis; Recent developments in the Fraisse-Jonsson theory. (Slides).
11.45-12.00 M. Cuth; Separable reduction theorems by the method of elementary submodels. (Slides).
12.05-12.20 E. Tachtsis; On a Topological Choice Principle by Murray Bell. (Slides).
12.25-12.40 D. Soukup; Constructing Lindelof, non D-spaces. (Slides).
12.45-13.00 A. Farhat; The basis problem for compacta satisfyinghigh separation axioms. (Slides).
16.00-16.45 S. Thomas; A Descriptive View of Unitary Group Representations. (Slides).
17.15-17.45 B. Velickovic; Towards a structure theory of Maharam algebras. (Slides).
18.00-18.15 P. Luecke; Sigma-1-1-definability at uncountable regular cardinals. (Slides).
18.20-18.35 A. Bartoszewicz; Set theoretical methods in algebraic constructions. (Slides).
18.45-19.00 E. Wajch; An axiomatic theory of classes for physics. (Slides).
Tuesday, 10th of July 2012
9.00-9.45 A. Kechris; Amenability, unique ergodicity and random orderings. (Slides).
10.00-10.30 M. Dzamonja; Embeddings of spaces of the form C(K). (Slides).
11.00-11.30 T. Tsankov; The minimal flows of S_infty. (Slides).
11.45-12.00 D. Bartosova; Universal minimal flow in the language of filters. (Slides).
12.05-12.20 V. Gregoriades; Turning Borel sets into Clopen sets effectively. (Slides).
12.25-12.40 P. Schlicht; Separating the bounding and dominating numbers for classes of uncountable structures. (Slides).
12.45-13.00 A. Kwela; Ranks of F-limits of filter sequences. (Slides).
16.00-16.45 S. Todorcevic; A set-theoretic analysis of the quotient problem and the biorthogonal system problem. (Slides).
17.00-17.30 A short problem session;
17.45-18.00 M. Krupski; Universality properties of l_infty/c_0. (Slides).
18.05-18.20 J. Meri; Spaces with few operators and the lack of complex structure. (Slides).
18.25-18.40 T. Kania; Operator ideal of weakly compactly generated operators. (Slides).
Wednesday, 11th of July 2012
9.00-9.45 S. Solecki; Spatial models of Boolean actions. (Slides).
10.00-10.30 S. Geschke; Definable graphs of low complexity. (Slides).
11.00-11.30 P. Zakrzewski; On Borel sets belonging to every invariant ccc sigma-ideal on 2N. (Slides).
11.45-12.00 M. Balcerzak; Selected results on measure-category products of ideals. (Slides).
12.05-12.20 S. Glab; Covering properties of ideals. (Slides).
12.25-12.40 J. Flaskova; Rapid ultrafilters and summable ideals. (Slides).
12.45-13.00 D. Guerrero Sanchez; Are Eberlein-Grothendieck scattered spaces sigma-discrete?. (Slides).
16.00-16.45 L. Nguyen Van The; Expanding Fraisse classes into Ramsey classes. (Slides).
17.15-17.45 M. Elekes; Set theory and Hausdorff measures. (Slides).
18.00-18.15 T. Banakh; The character of points in the Higson corona of a metric space. (Slides).
18.20-18.35 A. Blaszczyk; Topologies defined on trees. (Slides).