Continuous Lie Algebra Homology of Gauge Algebras
Talk, Finite-infinite workshop, Vienna, Austria
This talk was held online during the Covid-19 pandemic, slides and a recording are available here: Click!
Talks and presentations
Various Talks on Quantization, Localization & Cohomology of Gauge Algebras
Talk, Julius Maximilian University of Würzburg, Germany
These were various introductory talks about my research, in the yearly “Math at the Mill” conference, together with current and former members of Chair X in Würzburg.
Formal Deformation Theory and Invariant Hochschild Cohomology
Talk, University of Technology Delft, the Netherlands
Abstract: We give a short introduction to the algebraic problem of formal deformation theory as originally considered by Gerstenhaber, where one takes an associative algebra and considers “small” perturbations of the given multiplication, effectively testing the rigidity of the algebra structure. Deformation Quantization, a discipline of mathematical physics, builds on this idea, and gives a motivation to consider the formal deformation theory of the algebra of smooth functions on a manifold, which we will elaborate on. Furthermore, we explain Hochschild cohomology and its significance in this context as an obstruction space. Again motivated by physics, given a (Lie) group action on the algebra, we restrict to the theory of invariant deformations. This straightforward specification leads to interesting questions of the interplay of the action with the deformation theory, which we will describe and answer in some physically interesting cases.