Previous talks this semester:
05.09., 12.09 2019; 10.15, room 105,
Marek Miarka (doctoral student MIMUW),
Title: Stability of the Fredholm index
Abstract: "We will present the proof of a classical result which says that the index of a Fredholm operator between Banach spaces does not change if we perturbate the operator by a strictly singular operator. No previous knowledge of the above notions is needed to follow the talk"
22.08.2019; 10.15, room 105,
Eva Pernecká (Czech Technical University in Prague),
Title: A notion of support in Lipschitz-free spaces
Abstract: "We will show that the class of free spaces over closed subspaces of a complete metric space is closed under arbitrary intersections and that this leads to a natural definition of support applicable to all elements of free spaces. Although this property does not seem surprising, the proof is rather nontrivial. It follows from the particular algebraic structure of the spaces of Lipschitz functions (the isometric dual of the free space) described by Weaver. We will discuss some characterizations and properties of supports. We will present their application to the study of extreme points of free spaces. And finally, we will have a look at the elements of free spaces induced by Radon measures. This is a joint work with Ramón J. Aliaga."
20.08.2019; 14.00, room 403,
Saeed Ghasemi (Czech Academy of Sciences),
Title: Universal AF-algebras
Abstract: "We study the approximately finite-dimensional (AF) C*-algebras that appear as inductive limits of sequences of finite-dimensional C*-algebras and left-invertible embeddings. We show that there is such a separable AF-algebra that satisfies similar homogeneity and universality properties as the Cantor set. Joint work with Wiesław Kubiś, see: arxiv.org/pdf/1903.10392.pdf"
23.05., 30.05., 06.06., 13.06. 2019; 10.15, room 105,
Piotr Koszmider (IMPAN),
Title: Lifting uncountable combinatorics to the Banach space level:
Banach spaces C(K) with few operators. Part 1-4.
Abstract: "This series of 4 talks will be a minicourse on Banach spaces of continuous functions which have few operators, projections, injections etc. In particular they can be indecomposable and nonisomorphic with their hyperplanes.
To obtain this linear operator level rigidity one needs to construct compact Ks which are not only rigid in the usual sense, i.e., in terms of continuous mappings on K. One needs to deal with weak* continuous functions from K into the space M(K)
of Radon measures on K, so the combinatorics of the constructions needs stronger conditions then for
endo-rigid Boolean algebras or strongly rigid compact spaces. We will present main arguments leading to C(K)s with the required properties but the proofs of many lemmas will be omitted. The talks should be accessible to everyone with general analytic and topological background."
09.05.2019 , 10.15, room 105,
Arturo Martínez-Celis (IMPAN),
Title: Choice vs Determinacy
Abstract: "We will discuss the concept of infinite game and winning strategies and we will present some examples, theorems and applications to topology. In particular we will prove that every uncountable Borel set has a homeomorphic copy of the Cantor set.
The axiom of determinacy (AD) states that for certain kind of games, the Gale-Stewart games, one player has always a winning strategy. The aim of this talk is to present the differences between the universes satisfying AD and the universes satisfying the axiom of choice."
26.04.2019 (Friday), 10.15, room 106,
Fulgencio Lopez (IMPAN),
Title: Compact extensions of first order logic, continuation from 16.04
Abstract: We aim to provide an exhaustive proof of the results of Keisler and Magidor and Malitz about the compactness of certain extensions of first order logic. Keisler's Theorem refers to the extension L(Q) where Q is the quantifier "There is an uncountable subset with a one dimensional property", similarly we can define Qn to be "There is an uncountable subset with an n-dimensional property". We will show that L(Q) is compact (Keisler's Theorem) and, assuming diamond, so
is L(Qn:n∈ N) (Magidor and Malitz). We will also discuss why this framework can
sometimes be useful for constructions of set theoretical structures.
16.04.2019 (Tuesday), 10.15, room 106,
Fulgencio Lopez (IMPAN),
Title: Compact extensions of first order logic
Abstract: We aim to provide an exhaustive proof of the results of Keisler and Magidor and Malitz about the compactness of certain extensions of first order logic. Keisler's Theorem refers to the extension L(Q) where Q is the quantifier "There is an uncountable subset with a one dimensional property", similarly we can define Qn to be "There is an uncountable subset with an n-dimensional property". We will show that L(Q) is compact (Keisler's Theorem) and, assuming diamond, so
is L(Qn:n∈ N) (Magidor and Malitz). We will also discuss why this framework can
sometimes be useful for constructions of set theoretical structures.
Talks in the first semester of 2018-19.
Talks in the second semester of 2017-18.
Talks in the first semester of 2017-18.
Talks in the second semester of 2016-17.
Talks in the first semester of 2016-17.
Talks in the second semester of 2015-16.
Talks in the first semester of 2015-16.
Talks in the second semester of 2014-15.
Talks in the first semester of 2014-15.
Talks in the second semester of 2013-14.
Talks in the first semester of 2013-14.
Talks in the second semester of 2012-13.
Talks in the first semester of 2012-13.
Talks in the second semester of 2011-12.
Talks in the first semester of 2011-12.
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