Ideals and exceptional sets in Polish spaces  04 - 08 June 2018

Room : BI A0 448

Organisers

Márton Elekes, Alfréd Rényi Institute of Mathematics

Slawomir Solecki, Cornell University

Exceptional sets play an important role in numerous branches of mathematics, for instance in measure theory, topology, harmonic and complex analysis, Banach space theory, algebraic geometry, combinatorics, probability and ergodic theory, set theory and descriptive set theory, just to mention a few. Exceptional sets describe notions of smallness from various points of view, some notable examples are the countable sets, null sets of a measure, meager sets, sets of zero analytic capacity in complex analysis, non-stationary sets in set theory, Gaussian or Aronszajn or cube null sets in Banach spaces, Haar null sets in the sense of Christensen in Polish groups, as well as various ideals on the natural numbers, for example the sets of zero asymptotic density.

These notions have numerous applications to all the areas mentioned above, as well as to the structure of Polish groups and to the theory of Polish group actions.

The analysis of exceptional sets naturally leads to problems of descriptive set theoretic nature. On the one hand, regularity properties of the exceptional sets are often handled by methods of descriptive complexity, and on the other hand, in the investigation of ideals on the natural numbers the descriptive complexity of the ideal itself plays a central role.

The goal of this workshop is to bring together experts from various fields related to exceptional sets and discuss the recent developments.
Name University Dates of visit
Dana Bartosova Carnegie Mellon University 01/06/2018 - 30/06/2018
Gianluca Basso Université de Lausanne, Università di Torino 04/06/2018 - 08/06/2018
Piotr Borodulin-Nadzieja University of Wroclaw 02/06/2018 - 09/06/2018
Jörg Brendle Kobe University 03/06/2018 - 09/06/2018
Pierre-Emmanuel Caprace Université Catholique de Louvain 28/05/2018 - 24/06/2018
Dario Darji University of Louisville 03/06/2018 - 09/06/2018
Pierre De La Harpe Université de Genève 04/06/2018 - 08/06/2018
Gabriel Debs Institut de Mathématiques de Jussieu, Paris Rive Gauche 03/06/2018 - 08/06/2018
Longyun Ding Nankai University 04/06/2018 - 08/06/2018
Márton Elekes Alfréd Rényi Institute of Mathematics 03/06/2018 - 29/06/2018
Barnabas Farkas TU Wien 04/06/2018 - 08/06/2018
Jan Grebik Charles University 04/06/2018 - 08/06/2018
Michael Hrusak Unviersidad Nacional Autónoma de México 02/06/2018 - 14/06/2018
Viktor Kiss MTA Rényi Institute 02/06/2018 - 09/06/2018
Michał Korch University of Warsaw 02/06/2018 - 08/06/2018
Wieslaw Kubis Institute of Mathematics, Czech Academy of Sciences 03/06/2018 - 09/06/2018
Etienne Matheron Université d'Artois 03/06/2018 - 09/06/2018
Heike Mildenberger Albert-Ludwigs-Universitaet Freiburg im Breisgau 04/06/2018 - 08/06/2018
Donát Nagy Eötvös Loránd University 03/06/2018 - 09/06/2018
Márk Poór Eötvös Loránd University 04/06/2018 - 08/06/2018
Vibeke Quorning University of Copenhagen 03/06/2018 - 30/06/2018
Dilip Raghavan National University of Singapore 04/06/2018 - 09/06/2018
Marcin Sabok McGill University 05/06/2018 - 22/06/2018
Maya Saran Ashoka University 03/06/2018 - 09/06/2018
Jonathan Schilhan University of Vienna 03/06/2018 - 08/06/2018
Slawomir Solecki Cornell University 01/06/2018 - 29/06/2018
Juris Steprans York University 03/06/2018 - 09/06/2018
Stevo Todorcevic University of Toronto, CNRS, Institut de Mathématiques de Jussieu-PRG 03/06/2018 - 08/06/2018
Todor Tsankov Université Paris Diderot 03/06/2018 - 24/06/2018
Anush Tserunyan University of Illinois 02/06/2018 - 30/06/2018
Asger Törnquist University of Copenhagen 03/06/2018 - 14/06/2018
Zoltan Vidnyánszky Universität Wien 03/06/2018 - 09/06/2018
Piotr Zakrzewski Warsaw University 03/06/2018 - 09/06/2018
Jindrich Zapletal University of Florida 03/06/2018 - 23/06/2018
Miroslav Zeleny Charles University 03/06/2018 - 09/06/2018
Total Guests : 35
Name University Dates of visit
Jörg Brendle Kobe University 03/06/2018 - 09/06/2018
Dario Darji University of Louisville 03/06/2018 - 09/06/2018
Michael Hrusak Unviersidad Nacional Autónoma de México 02/06/2018 - 14/06/2018
Viktor Kiss MTA Rényi Institute 02/06/2018 - 09/06/2018
Wieslaw Kubis Institute of Mathematics, Czech Academy of Sciences 03/06/2018 - 09/06/2018
Etienne Matheron Université d'Artois 03/06/2018 - 09/06/2018
Dilip Raghavan National University of Singapore 04/06/2018 - 09/06/2018
Marcin Sabok McGill University 05/06/2018 - 22/06/2018
Maya Saran Ashoka University 03/06/2018 - 09/06/2018
Juris Steprans York University 03/06/2018 - 09/06/2018
Stevo Todorcevic University of Toronto, CNRS, Institut de Mathématiques de Jussieu-PRG 03/06/2018 - 08/06/2018
Asger Törnquist University of Copenhagen 03/06/2018 - 14/06/2018
Zoltan Vidnyánszky Universität Wien 03/06/2018 - 09/06/2018
Piotr Zakrzewski Warsaw University 03/06/2018 - 09/06/2018
Jindrich Zapletal University of Florida 03/06/2018 - 23/06/2018
Miroslav Zeleny Charles University 03/06/2018 - 09/06/2018
Total Guests : 16

Monday 4 June
10:00-11:00 CIB front desk registration
11:00-12:00 Stevo Todorcevic Tukey theory of topological directed orders Slides
12:00-13:30 Lunch break
13:30-14:30 Michael Hrusak Cardinal invariants related to some uniform properties of metric spaces Slides
14:30-15:00 Coffee break
15:00-16:00 Asger Törnquist Un-definability of mad families relative to a class of Borel ideals

Tuesday 5 June
09:30-10:30 Piotr Zakrzewski On Borel maps, calibrated σ-ideals and homogeneity.
10:30-11:00 Coffee break
11:00-12:00 Wieslaw Kubis Small Borel sets in the plane
12:00-13:30 Lunch break
13:30-14:30 Zoltan Vidnyánszky
Borel chromatic numbers: basis and antibasis results
14:30-15:00 Coffee break
15:00-16:00 Udayan Darji Nonsingular odometers



Wednesday 6 June
09:30-10:30 Jörg Brendle Definability of maximal independent families Slides
10:30-11:00 Coffee break
11:00-12:00 Maya Saran Gδ sets in σ-ideals generated by compact sets Slides


Thursday 7 June
09:30-10:30 Viktor Kiss Random elements of non-locally compact Polish groups Slides
10:30-11:00 Coffee break
11:00-12:00 Marcin Sabok The Hrushovski property for hypertournaments and profinite topologies
12:00-13:30 Lunch break
13:30-14:30 Dilip Raghavan Proof of a conjecture of Galvin
14:30-15:00 Coffee break
15:00-16:00 Etienne Matheron Small subsets of the circle and ergodicity properties of linear operators

Friday 8 June
09:30-10:30 Jindrich Zapletal
Hypergraphs and proper forcing
10:30-11:00 Coffee break
11:00-12:00 Juris Steprans Actions of Groups with Polynomial Growth in the Cohen Model (with Damjan Kalajdzievski)
12:00-13:30 Lunch break
13:30-14:30 Miroslav Zeleny Infinite games and sigma-ideals of sigma-porous type
14:30-15:00 Coffee break