• Title: Noncommutative atomicity
  Dates: December 2015
  Speaker: Piotr Koszmider
  Institution: IME USP - São Paulo
  

  Program: 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: Non-Commutativity in Topology, Analysis, Algebra and Set Theory
  Dates: November 2015
  Speaker: Tristan Bice (Salvador)
  Institution: IME USP - São Paulo
  

  Program: Distances in C*-algebra: general theory of non-symmetric 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 non-symmetric 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_∞/c₀
  Dates: August 2015
  Speaker: Piotr Koszmider
  Institution: IME USP - São Paulo
  

  Program: The van Mill principle under CH. Decompositions of l_∞/c₀ under CH. The nonexistence of nontrivial traces in B(l_∞/c₀) under CH. Retracts of N* and complemented subspaces of l_∞/c₀ under CH. Universality of l_∞/c₀ under CH. Pathological automorphisms of l_∞/c₀ 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_∞/c₀ under OCA+MA.



• Title: Linear operators on Banach spaces C(K)
  Dates: March 2015
  Speaker: Piotr Koszmider
  Institution: IME USP - São Paulo
  

  Program: Compact spaces: Totally disconnected spaces, dispersed spaces βN, the Stone duality, Mazurkiewicz-Sierpinski theorem, Radon-Nikodym 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, Banach-Stone theorem, Holsztynski's theorem, Cengiz theorem, Plebanek theorem.



• Title: Elements of uncountable combinatorics: applications of the failure of the Ramsey property
  Dates: 4-8 August 2014, 10am
  Speaker: Piotr Koszmider
  Institution: IME USP - São Paulo - Auditório Jacy Monteiro
  

  Program: Countable Ramsey theorem wth applcations; Theorems of Erdos-rado and of Dushnik-Miller; 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 - Shelah-Steprans space with few operators.

Seminars