C2

The Czech lands were the most industrial part of the Austrian-Hungarian monarchy, broken up at the end of the WW1. As such, Czechoslovakia inherited developed industry supported by developed system of tertiary education, and Czech and German universities and technical universities, where the first chairs for applied mathematics were set up. The close cooperation with the Skoda company led to the establishment of joint research institutes in applied mathematics and spectroscopy in 1929 (1934 resp.).

The development of industry was followed by a gradual introduction of social insurance, which should have helped to settle social contracts, fight with pauperism and prevent strikes. Social insurance institutions set up mathematical departments responsible for mathematical and statistical modelling of the financial system in order to ensure its sustainability. During the 1920s and 1930s Czechoslovakia brought its system of social insurance up to date. This is connected with Emil Schoenbaum, internationally renowned expert on insurance (actuarial) mathematics, Professor of the Charles University and one of the directors of the General Institute of Pensions in Prague.

After the Nazi occupation in 1939, Czech industry was transformed to serve armament of the Wehrmacht and the social system helped the Nazis to introduce the carrot and stick policy to keep weapons production running up to early 1945. There was also strong personal discontinuity, as the Jews and political opponents either fled to exile or were brutally persecuted.

Roelcke precompact groups are exactly the topological groups that can be realized as automorphism groups of omega-categorical structures (in continuous logic). In this talk, I will discuss a model-theoretic framework for the study of those groups and their dynamical systems as well as two concrete applications. The talk is based on joint work with Itaï Ben Yaacov and Tomás Ibarlucía.

In 1933, lattice theory was a new subject, put forth by Garrett Birkhoff. In contrast, in 1940, it was already a mature subject, worth publishing a book on. Indeed, the first monograph, written by the same G. Birkhoff, was the result of these 7 years of working on a lattice theory. In my talk, I would like to focus on this fast development. I will present the notion of a theory not only as an actors' category but as an historical category. Relying on that definition, I would like to focus on some collaborations around the notion of lattices. In particular, we will study lattice theory as a meeting point between the works of G. Birkhoff and two other mathematicians: John von Neumann and Marshall Stone.

 Anyone who has worked in $\beta $N will not be surprised to learn that some of the algebraically defined subsets of $\beta N$ are not topologically simple, even though their algebraic definition may be very simple.  I shall show that the following subsets of $\beta N$ are not Borel: $N^*+N^*$; the smallest ideal of $\beta N$; the set of idempotents in $\beta N$; any semiprincipal right ideal in $\beta N$; the set of idempotents in any left ideal in $\beta N$.

Abstract:  Anyone who has worked in $\beta $N will not be surprised to learn that some of the algebraically defined subsets of $\beta N$ are not topologically simple, even though their algebraic definition may be very simple.  I shall show that the following subsets of $\beta N$ are not Borel: $N^*+N^*$; the smallest ideal of $\beta N$; the set of idempotents in $\beta N$; any semiprincipal right ideal in $\beta N$; the set of idempotents in any left ideal in $\beta N$.

I will compare features of (classical) cohomology theory of groups to the rather exotic features of bounded (or continuous bounded) cohomology of groups.
Besides giving concrete examples I will state classical cohomological tools/features and see how (if) they survive in the case of bounded cohomology. Such will include the Mayer-Vietoris sequence, the transfer map, resolutions, classifying spaces, the universal coefficient theorem, the cup product, vanishing results, cohomological dimension and relation to extensions. 
Finally I will discuss their connection to each other via the comparison map.

I will report on joint work with Michael Weiss (https://arxiv.org/pdf/1503.00498.pdf):

Let K be a subset of a smooth manifold M. In some cases, functor calculus methods lead to a homotopical formula for M \ K in terms of the spaces M \ S,  where S runs through the finite subsets of K. This is for example the case when K is a smooth compact sub manifold of co-dimension greater or equal to three.