Lukas Miaskiwskyi

Lukas Miaskiwskyi

Mathematical Physicist

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Pages

Posts

Future Blog Post

less than 1 minute read

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This post will show up by default. To disable scheduling of future posts, edit config.yml and set future: false.

Blog Post number 4

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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 3

less than 1 minute read

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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 2

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 1

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

publications

talks

Formal Deformation Theory and Invariant Hochschild Cohomology

Published:

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.

teaching