The goal of this meeting was to offer background on Set Theory, especially large cardinals, and discuss a number of situations in Abelian Group Theory, Category Theory and Algebraic Topology where set-theoretical methods play a crucial role for the solution of certain open problems. The courses were aimed at a mixed audience of graduate students, recent doctors, and also specialists in some focus area of the meeting who wanted to know more about the other areas.

Lectures started on Thursday, September 1, at 15.30. The afternoon of September 2 was devoted to Algebraic Topology and the afternoon of September 3 focused on Category Theory. Problem sessions were organized on Monday afternoon and Tuesday afternoon. A two-day workshop followed, ending September 8 in the evening.

The course was promoted and sponsored by the Spanish Topology Network as a part of its annual program. The event was also supported by Ingenio Mathematica (i-MATH) and by the Mathematical Institute of the University of Barcelona.

 

COURSE LECTURES

Joan Bagaria, Universitat de Barcelona
A gentle introduction to the theory of large cardinals
Abstract      Slides      Lecture notes

Andreas Blass, University of Michigan
Set-theoretic aspects of abelian groups
Abstract      Lecture notes

Rüdiger Göbel, Universität Duisburg-Essen
How to construct large wild algebraic structures
Abstract
Slides of Lecture 1      Transparencies of Lecture 1
Slides of Lecture 2      Transparencies of Lecture 2
Slides of Lecture 3      Transparencies of Lecture 3

Menachem Magidor, Hebrew University of Jerusalem
Set-theoretical methods used in abelian group theory:
A potential for generalization

Slides of Lecture 1
Slides of Lecture 2
Slides of Lecture 3

 

HOMOTOPY AFTERNOON

Carles Casacuberta, Universitat de Barcelona
Combinatorial models for unstable and stable homotopy
Abstract      Slides

Luke Wolcott, University of Washington
Set theory questions in homotopy theory
Abstract      Lecture notes

 

CATEGORY AFTERNOON

Jiří Rosický, Masarykova univerzita
Accessible categories and inaccessible cardinals
Abstract      Lecture notes

Jan Šťovíček, Univerzita Karlova
Infinite combinatorics in homological algebra
Abstract      Slides

 

PROBLEM SESSION

Discussion guidelines

 

WORKSHOP TALKS

Andrew Brooke-Taylor, University of Bristol
Large cardinals and colimits
Abstract      Slides

Wojciech Chachólski, KTH, Stockholm
Three stories about complexity of fibrations
Abstract

Boris Chorny, University of Haifa
Enriched Brown representability for the dual
Abstract

Sakaé Fuchino, Kobe University
Reflection of some properties of uncountable structures
Abstract      Slides      Printable slides      Link to preprints

Misha Gavrilovich, Kurt Gödel Research Center
A homotopy viewpoint on PCF
Abstract

Rüdiger Göbel, Universität Duisburg-Essen
Absolute E-rings
Article

Javier J. Gutiérrez, Universitat de Barcelona
Coreflective semilocalizing subcategories in triangulated categories with models
Abstract      Slides

Dolors Herbera, Universitat Autònoma de Barcelona
Almost free modules and Mittag-Leffler conditions
Abstract      Slides

Patrick Keef, Whitman College
Mahlo cardinals and the torsion product
Abstract      Slides

Menachem Magidor, Hebrew University of Jerusalem
Reflecting group radicals and other cardinal sins
Slides

Adam Przeździecki, Warsaw University of Life Sciences
How comprehensive is the category of abelian groups?
Abstract      Slides