Previous talks this semester:
10.03.2020, Tuesday 10.15, room 105
Fulgencio Lopez (IMPAN): Uncountable equilateral sets and antiRamsey families of functions.
Abstract: "The study of equilateral and separated sets in Banach spaces has been an active area of interest since Petty considered this question in non euclidean spaces in 1971. We will give some background results in the area and then focus on the case of spaces of continuous functions. In particular we will show that having an antiRamsey family of functions implies there is a compact connected K, such that its space of continuous functions has no uncountable equilateral sets. A known result says that the existence of uncountable equilateral sets in all nonseparable C(K) spaces is undecidable." (joint work with P. Koszmider)
3.03.2020, Tuesday 10.15, room 105
T. Kochanek (IMPAN/MIM UW): On representations of the Calkin algebra  the noncommutative
analogue of P(N)/Fin or l_{∞}/c_{0}
Abstract: Continuing our study of the poset of projections of the Calkin algebra Q(H), we will first show that below any strictly decreasing sequence of projections of Q(H) there is some nonzero projection. This fact gives rise to considering a `quantized` analogue of the pseudointersection number. Next, we will prove a general result saying that the poset of projections of Q(A) does not form a lattice, whenever Q(A) is the corona algebra of any stabilization A of some unital C*algebra. In particular, this implies that the Calkin algebra is not an AW*algebra. Then, we will proceed to the problem of representation of Q(H), focusing on two papers. First, Anderson and Bunce (Amer. J. Math. 1977) showed that under Martin's axiom (as well as under the Continuum Hypothesis), there exists a faithful *representation of Q(H) such that the WOTclosure of its range
is a II_{∞} type factor. Later, Anderson (J. Funct. Anal. 1979) showed that such a result holds true in ZFC. We shall discuss both of those (quite similar) constructions.
25.02.2020, Tuesday 10.15, room 105
T. Kochanek (IMPAN/MIM UW): On representations of the Calkin algebra  the noncommutative
analogue of P(N)/Fin or l_{∞}/c_{0}
Abstract: The first part will be a mild introduction to the Calkin algebra Q(H) which was first investigated thoroughly by J.W. Calkin in his paper published in Annals Math. in 1941. We shall present some basic facts on Q(H), explaining what it has to do with essential spectra, Fredholm operators, the BDF theory of extensions, and a few other things. With the aid of Banach limit, we will construct a `concrete' representation ρ of Q(H) on a Hilbert space of density continuum. Also, we will show that the range of ρ is not closed in the weak operator topology, which should provoke considering the problem of finding some `special' representations of Q(H), as well as the problem of extending *homomorphisms into Q(H). This will be the topic of the second part.
Talks in the first semester of 201920.
Talks in the second semester of 201819.
Talks in the first semester of 201819.
Talks in the second semester of 201718.
Talks in the first semester of 201718.
Talks in the second semester of 201617.
Talks in the first semester of 201617.
Talks in the second semester of 201516.
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.
