Previous talks this semester:
June 16, 2016, 11^{15}13, room 105, Tomasz Kochanek (IM PAN/UW)
Title: Structural properties of Banach spaces in terms of certain classes od Baire1 functions"
Abstract:
"We will discuss some connections between structural properties of separable Banach spaces and certain classes of
functions acting on the unit dual ball with the weak* topology. One of the most classical results in this spirit,
due to Odell and Rosenthal, says that a separable Banach space X contains an isomorphic copy of l_{1} if and only if
the unit ball of X** contains a nonBaire1 element. We will describe another class of functions which is responsible
for containing a copy of c_{0} (via Rosenthal's c_{0}theorem) and leads quite naturally to other more exotic
classes which are responsible for producing spreading models equivalent to the canonical bases of l_{1} or c_{0}.
The talk will be largely based on the paper by R. Haydon, E. Odell and H. Rosenthal,
"On certain classes of Baire1 functions with applications to Banach space theory", Lecture Notes in Math. 1470 (1991), 135."
June 9, 2016, 11^{15}13, room 105, Marcin Sabok (McGill/IM PAN)
Title: Classification of operator systems
Abstract:
I will discuss the problem of classification of separable operator systems up to complete order isomorphism.
While the relation for arbitrary separable operator systems is a complete orbit equivalence relation,
the restriction to the class of finitedimensional ones gives a smooth equivalence relation.
This is joint work with M. Argerami, S. Coskey, M. Kennedy, M. Kalantar and M. Lupini."
June 2, 2016, 11^{15}13, room 321, Damian Sobota (Ph.D. student IM PAN)
NOTE THE UNUSUAL ROOM!
Title: Phillips's lemma, Schur's theorem and cardinal invariants of the continuum.
Abstract:
Phillips's lemma asserts that for every sequence of measures (μ_{n}) on P(N) satisfying lim_{n} μ_{n}(A)=0 for
every subset A of N, we have: lim_{n} Σ_{j} μ_{n}({j})=0.
The lemma has many consequences in vector measure theory and Banach space theory.
E.g. Schur's theorem stating that every weakly convergent sequence in l_{1} is norm convergent is an
easy application of Phillips's lemma. During my talk I will show in ZFC that there exists a family F of subsets
of N such that F=cof(N) (the cofinality of the Lebesgue measure zero ideal) and satisfying the following Phillipslike condition:
for every sequence of measures (μ_{n}) on P(N) satisfying lim_{n} μ_{n}(A)=0 for every A in F, we have:
lim_{n} Σ_{j} μ_{n}({j})=0.
On the other hand, I will also show that no family F of subsets of N such that F<p (the pseudointersection number) can be used."
May 19, 2016, 11^{15}13, room 105, Maciej Malicki (The Warsaw School of Economics)
Title: Amenable groups.
Abstract:
I will continue an overview of some aspects of classical and contemporary studies of amenable groups.
This time I will focus on properties of universal minimal flows of nonarchimedean groups
(i.e. automorphism groups of countable models), and the notion of extreme amenability.
Recall that a flow is a continuous action of a topological group on a compact space.
A flow is called minimal if all its orbits are dense. For every topological group there
exists a universal such flow, and, it turns out that there exist
many "large" groups  called extremely amenable  for which it is trivial.
I will explain how to construct the universal minimal flow for a
nonarchimedean group of the form Aut(M) using StoneČech compactifications,
and how to relate extreme amenability to certain properties of ultrafilters
naturally associated with the model M. This connection is based on Ramsey theory."
May 12, 2016, 11^{15}13, room 105, Gonzalo Martínez Cervantes (Ph. D, student, Murcia)
Title: Weakly RadonNikodým compact spaces.
Abstract:
A compact space is said to be weakly RadonNikodým if it is
homeomorphic to a weak*compact subset of the dual of a Banach space not containing an isomorphic copy of l_{1}.
In this talk I will show some topological properties of this class of compact spaces and
its relation with other classes of compact spaces such as RadonNikodým or Corson compacta.
Most of the results of this talk are contained in the paper 'On weakly RadonNikodým spaces' which is available on arxiv.org.
May 5, 2016, 11^{15}13, room 105, Przemysław Ohrysko (Ph. D. student, IM PAN)
Title: The Gelfand space of the measure algebra.
Abstract:
In this talk I would like to present some recent results concerning the
Banach algebra M(T) of Borel regular measures on the circle group with the
convolution product. Since it is wellknown that the spectrum of a measure
can be much bigger then the closure of the values of its FourierStieltjes
transform (the WienerPitt phenomenon) it is natural to ask what kind of
topological properties of the Gelfand space Ge(M(T)) are responsible for this
unusual spectral behaviour. It follows immediately from the existence of
the WienerPitt phenomenon that the set Z identified with FourierStieltjes
coefficients is not dense in Ge(M(T)). However, it is not clear if any other
countable dense subset of this space exists. During my talk, I will disprove
this fact  i.e. I will show the nonseparability of the Gelfand space of the
measure algebra on the circle group. This result is contained in a paper 'On
topological properties of the measure algebra on the circle group' written in
a collaboration with Michał Wojciechowski which has not been published yet
but is available on arxiv.org with identifier: 1603.05864.
April 28, 2016, 11^{15}13, room 105, Tomasz Kochanek (IMPAN/UW)
Title: The Szlenk power type of injective tensor products of Banach spaces.
Abstract:
We shall discuss the notion of the Szlenk power type (strictly related to the Szlenk index) and its
relationships with asymptotic geometry of Banach spaces. In particular,
we will describe how the socalled tree maps and subsequential tree estimates
can be used as tools to understand the dynamics of the Szlenk derivations. Next,
we will prove a formula for the Szlenk power type of the injective tensor product of
Banach spaces with the Szlenk index at most ω (a joint result with S. Draga).
This allows us, for example, to determine the moduli of asymptotic smoothness
of the spaces of compact operators between l_{p}spaces.
April 21, 2016, 11^{15}13, room 105, Gonzalo Martínez Cervantes (Ph. D, student, Murcia)
Title: Riemann integrability versus weak continuity.
Abstract:
We introduce some properties of Banach spaces related with Riemann integrability
and we study the relation between weakcontinuity and Riemann integrability.
In particular, a Banach space is said to have the weak Lebesgue property if every Riemann integrable
function from the unit interval into it is weakly continuous almost everywhere.
We present several results concerning the weak Lebesgue property.
April 7, 2016, 11^{15}13, room 105, Tomasz Żuchowski (Ph. D. student, UWr)
Title: Nonseparable growth of N supporting a strictly positive
measure.
Abstract:
We will construct in ZFC a compactification γN of N such
that its remainder γN\N is not separable and carries a strictly
positive measure, i.e. measure positive on all nonempty open subsets.
Moreover, the measure on our space is defined by the asymptotic density of
subsets of N. Our remainder is the Stone space of some Boolean subalgebra of
the algebra Bor(2^{N}) of all Borel subsets of 2^{N} containing all clopen sets.
This line of research is motivated by the problem
of characterizing the Banach spaces c_{0}⊆ X⊆ l_{∞} such that the space c_{0} is complemented in X.
Talks in the first semester of 201516.
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.
