Abstracts for Seminar on Algebra, Geometry and Physics

In some rather simple cases (like associative algebras case) all necessary structures on the deformation complex (the Hochschild cohomological complex) can be constructed ''by hand''. Here we mean the Gerstenhaber Lie bracket and the cup-product. On the other hand, HH(A)=Ext(A,A) in the category of A-bimodules. The crucial remark is: the category of A-bimodules is monoidal, and A is the unit object in it. It is interesting and instructive for further cases to prove that HH(A) is a 2-algebra only from the above property. We discuss this construction, due to S.Schwede.

The notion of a symmetric operad is a generalisation of that of an associative algebra, just for a monoidal category larger than the tensor category of vector spaces. For a long while, several ingredients that proved to be useful in homological algebra for associative algebras (e.g. Groebner bases, Anick-type resolutions etc.), have been missing in the case of operads, since the monoidal category in question appears to have too rich structure for those approaches to work.

Linear (topological) dynamics studies the orbits of the action of
a semigroup of continuous linear operators on a topological vector space.
We are mostly interested in chaotic-type properties like the existence of a
dense orbit.
The aim of this talk is two-fold: to give an overview of the current state
of (chaotic) linear dynamics and to describe few recent results of the
author. One of the results, we are going to describe boils down to the
construction of a (non-unital) Banach algebra $A$  and  an element $a$  of