Working groups

Christina Brech, Piotr Koszmider:
Settheoretic aspects of the isomorphic theory of Banach spaces. 
Cristóbal RodríguezPorras, Piotr Koszmider:
Linear operators on the Banach space l_{∞}/c_{0}. 
Christina Brech, Piotr Koszmider, Omar Selim:
Forcing nonseparable Banach spaces with small duals. 
Christina Brech, Thiago Rodrigo Alves
On Gowers' dichotomies. 
Christina Brech, Clayton Suguio Hida, Piotr Koszmider:
Set theoretic methods in Asplund Banach spaces. 
Tristan Bice, Piotr Koszmider:
Almost disjoint families and C*algebras. 
Leandro Candido Batista, Piotr Koszmider:
Tensor products of Banach spaces with few complemented subspaces. 
Piotr Koszmider, Rogério Augusto dos Santos Fajardo:
Banach spaces of continuous functions with few operators. 
Piotr Koszmider, Saeed Ghasemi:
Settheoretic constructions of C*algebras. 
Piotr Koszmider, Michal Swietek:
Indecomposable Banach spaces of big sizes.
Minicourses

Title: Noncommutative atomicity
Dates: December 2015
Speaker: Piotr Koszmider
Institution: IME USP  São PauloProgram: Basic properties of the algebra of compact operators. The subalgebra generated by the minimal projections. Irreducible representations. Reduced universal representation. Characterizations of the algebra of compact operators. Some nonseparable constructions. Scattered C*algebras.

Title: NonCommutativity in
Topology, Analysis, Algebra and Set Theory
Dates: November 2015
Speaker: Tristan Bice (Salvador)
Institution: IME USP  São PauloProgram: Distances in C*algebra: general theory of nonsymmetric distances, examples and applications in algebra and functional analysis. Filters in C*Algebras: examinning filters in the positive unit ball of general C*algebras and investigating their relationship to semigroup and distance structure. Projections in the Calkin algebra: special nonsymmetric distance structure in the Calkin algebra, focusing on filters in the Calkin algebra coming from P(N)/Fin. Cardinal Invariants of the Calkin algebra: combinatorial objects like gaps and towers, some relations between these new cardinal invariants.

Title: Linear operators on Banach spaces C(K) II  The Banach space l_{∞}/c_{0}
Dates: August 2015
Speaker: Piotr Koszmider
Institution: IME USP  São PauloProgram: The van Mill principle under CH. Decompositions of l_{∞}/c_{0} under CH. The nonexistence of nontrivial traces in B(l_{∞}/c_{0}) under CH. Retracts of N* and complemented subspaces of l_{∞}/c_{0} under CH. Universality of l_{∞}/c_{0} under CH. Pathological automorphisms of l_{∞}/c_{0} under CH. The Farah principle under OCA+MA. The nonexistence of nontrivial homeomorphisms of N* and noninner automorphisms of the Calkin algebra under OCA+MA. Canonizations of some operators on l_{∞}/c_{0} under OCA+MA.

Title: Linear operators on Banach spaces C(K)
Dates: March 2015
Speaker: Piotr Koszmider
Institution: IME USP  São PauloProgram: Compact spaces: Totally disconnected spaces, dispersed spaces βN, the Stone duality, MazurkiewiczSierpinski theorem, RadonNikodym compacta, ; Riesz representation theorem; Topological representation of linear operators on C(K)s with applications  Projections in l_{∞}, projections in the C(K) for K ladder system space; Weakly compact operatorson C(K)s; Gantmacher's Theorem, The Grothendieck property; Canonization of operators on C(KS)s, BanachStone theorem, Holsztynski's theorem, Cengiz theorem, Plebanek theorem.

Title: Elements of uncountable combinatorics: applications of the failure of the Ramsey property
Dates: 48 August 2014, 10am
Speaker: Piotr Koszmider
Institution: IME USP  São Paulo  Auditório Jacy MonteiroProgram: Countable Ramsey theorem wth applcations; Theorems of Erdosrado and of DushnikMiller; Club and stationary sets; Ulam's matrix; Failure of the Ramsey property in the first uncountable cardinal  Todorcevic's coloring; Applications of Todorcevic's coloring of squares to Banach space theory  ShelahSteprans space with few operators.
Seminars
 C*algebras Fridays, 2pm, B01 (OctoberNovember 2014)
Scientific exchange
 Piotr Koszmider
Planned Period: JanuaryMarch 2017
Host institution: IME USP  São Paulo  Clayton Suguio Hida
Period: April  December 2016
Host institution: IM PAN Varsóvia  Cristóbal RodriguezPorras
Period: JuneJuly 2016
Host institution: IM PAN Varsóvia  Leandro C. Batista
Period: July 2016
Host institution: IM PAN Varsóvia  Piotr Koszmider
Period: 16th February to 16th March 2016
Host institution: IME USP  São Paulo  Piotr Koszmider
Period: 21st November to 21st December 2015
Host institution: IME USP  São Paulo  Tristan Bice
Period: 22th November to 28th November 2016
Host institution: IME USP  São Paulo  Piotr Koszmider
Period: 25th July to 26th August 2015
Host institution: IME USP  São Paulo  Piotr Koszmider
Period: 01st February to 31th March 2015
Host institution: IME USP  São Paulo  Omar Selim
Period: 25th January to 31th January 2015
Host institution: IM PAN  Warsaw  Leandro C. Batista
Period: February 2014 to January 2015
Host institution: IM PAN  Warsaw
Financial support: FAPESP  Piotr Koszmider
Period: 22nd July to 30th August 2014
Host institution: IME USP  São Paulo