Previous talks this semester:
21.01.2016, 11^{15} room 105
Speaker: Damian Sobota (IM PAN)
Title: The Nikodym property of von Neumann algebras
Abstract: "The Nikodym property of C*algebras comes from the theory of
Boolean algebras and is closely related to the classical BanachSteinhaus theorem for Banach spaces
(also called the Uniform Boundedness Principle).
A Boolean algebra A has the Nikodym property if every elementwise bounded sequence of
finitely additive measures on A is uniformly bounded.
Classical examples of algebras with the Nikodym property contain σcomplete algebras,
algebras with Haydon's Subsequential Completeness Property and the
algebra of Jordanmeasurable subsets of the unit interval [0,1].
The Nikodym property for C*algebras is defined similarly.
A C*algebra A has the Nikodym property if every
sequence of linear functionals on A which is bounded on each projection in A is
bounded on each element of A (and consequently normbounded).
In the first part of the talk, we shall prove the Nikodym theorem stating
that all σcomplete Boolean algebras have the Nikodym property and provide several
basic facts concerning the property for C*algebras.
After this, using the representation of commutative von Neumann algebras in terms of L_{∞}(μ)spaces
and the Nikodym theorem, we shall obtain the similar result of Darst for von Neumann algebras.
The second part will be devoted to the proof of the abovementioned representation theorem of commutative von Neumann algebras."
14.01.2016, 11^{15} room 105
Speaker: Maciej Malicki (SGH)
Title: Amenable groups
Abstract: "The talk will present an overview of some aspects of classical and contemporary studies of amenable groups.
I will start with basic definitions, and say a little bit about the BanachTarski paradox.
Then, using a characterization of the notion of amenability that can be applied to all
topological groups (the existence of invariant measures on flows), I will formulate
certain variants of it, such as extreme amenability, and unique ergodicity.
I will also briefly discuss recent research in this area, in connection with
Fraissé limits, Ramsey theory, and StoneÈech compactifications."
19.11.2015, 11^{15} room 105
Speaker: Tomasz Kochanek (IMPAN)
Title: A nonseparable reflexive Banach space without the EltonOdell property
Abstract: "We shall discuss a construction of a nonseparable, reflexive Banach space X for which there is no
e > 0 and an uncountable subset A of the unit ball of X so that x  y > 1 + e for all distinct x,y from A.
In other words, X fails the "uncountable" version of the EltonOdell property;
recall that a nonreflexive example, namely c_{0}(ω_{1}), was given by Elton and Odell themselves.
The space in question can be described as a "quasisymmetric version of a long Tsirelon space with weights".
A crucial role in the construction is played by certain Todorcevic's pseudometric on ω_{1} which we shall also discuss.
The construction moreover shows that the two theorems obtained jointly with T. Kania
(discussed during this seminar on October 1) are, in a sense, sharp.
05.11.2015, 11^{15} room 105
Speaker: Eva Pernecka (IMPAN)
Title: Uniformly differentiable mappings from l_{∞}
Abstract: "We will discuss the rigidity of l_{∞} and l_{∞}^{n} with respect
to uniformly differentiable mappings. Our main result is a nonlinear analogy of the result on rigidity of l_{∞} with
respect to nonweakly compact linear operators by Rosenthal, and it generalises
the theorem on noncomplementability of c_{0} in l_{∞} due to Phillips."
29.10.2015, 11^{15} room 105
Speaker: Saeed Ghasemi (IMPAN)
Title: The rigidity of isomorphisms between some corona algebras  continuation
15.10.2015, 11^{15} room 105
Speaker: Saeed Ghasemi (IMPAN)
Title: The rigidity of isomorphisms between some corona algebras  continuation
08.10.2015, 11^{15} room 105
Speaker: Saeed Ghasemi (IMPAN)
Title: The rigidity of isomorphisms between some corona algebras
Abstract: "The rigidity question was first studied for the automorphisms of Boolean algebras.
A groundbreaking result of Shelah shows that it is consistent with the usual axioms of mathematics (ZFC) that all
automorphisms of the Boolean algebra P(N)/Fin are trivial, in the sense that they are implemented by almost permutations
of the natural numbers N. While assuming the Continuum Hypothesis, a transfinite induction due to Rudin shows that
there are many nontrivial automorphisms of P(N)/Fin. Using the Stone duality, the results of this kind can be
translated in the category of (zerodimensional locally compact and Hausdorff) topological spaces.
Motivated by a question of BrownDouglasFillmore, the rigidity question was studied in the noncommutative
settings for the corona of C*algebras. It is proved by PhilipsWeaver that assuming the Continuum Hypothesis
the Calkin algebra has outer automorphisms. On the other hand Farah showed that
the Open Coloring Axiom implies that all the automorphisms of the Calkin algebras are inner (implemented by almost unitary elements of B(H)).
In my talks we will take a closer look at Farah's result and study the rigidity question for
the isomophisms between the corona of FiniteDimensional Decomposition algebras (reduced products of matrices)
and its relevance to Farah's result. We will also look at the later question in more general setting,
motivated by the more recent results of FarahShelah about the Boolean algebra counterparts."
01.10.2015, 11^{15} room 105
Speaker: Tomasz Kochanek (IMPAN/UW)
Title: Uncountable sets of unit vectors that are separated by more than 1
Abstract: "Kottman proved that in the unit ball of any infinitedimensional
Banach space one can find an infinite subset such that the distance between any two distinct elements
is larger than 1. Elton and Odell, employing Ramsey theory, strengthened this result by showing that
it is possible to have all distances at least equal to 1+c for some c>0 depending only on the given space.
Both these results are farreaching generalizations of the Riesz lemma. We will investigate their
nonseparable versions focusing on two results: (1) the analogue of Kottman's theorem is valid for every nonseparable reflexive Banach space
(the set from the assertion is then uncountable); (2) the analogue of the EltonOdell theorem
is valid for every nonseparable superreflexive Banach space."
24.09.2015, 11^{15} room 105
Speaker: Antonio Aviles (Universidad de Murcia)
Title: Compact subsets of the first Baire class.
Abstract: "Compact spaces consisting of Baire first class functions in the pointwise
topology have been extensively studied with a number of remarkable results by Rosenthal,
Bourgain, Fremlin, Talagrand, Todorcevic and others. They play a role in the category of
compact spaces that is analogous to that of Borel
sets in the class of all subsets of the real line.
We shall discuss some history and some recent results about them in collaboration with Stevo Todorcevic."
Talks in the second semester of 201415.
Talks in the first semester of 201415.
Talks in the second semester of 201314.
Talks in the first semester of 201314.
Talks in the second semester of 201213.
Talks in the first semester of 201213.
Talks in the second semester of 201112.
Talks in the first semester of 201112.
