BIREP – Representations of finite dimensional algebras at Bielefeld

Wissenschaftlicher Assistent

Faculty of Mathematics

Bielefeld University

PO Box 100 131

D-33501 Bielefeld

Office: V5-218

Phone: +49 521 106 5019

Email: hubery

I am currently a member of the BIREP Representation Theory group at Bielefeld University. My position is supported by the Alexander von Humbolt Stiftung/Foundation in the framework of an Alexander von Humbolt Professorship endowed by the Federal Ministry of Education and Research.

Previously I was supported by the Collaborative Research Center CRC701 Spectral Structures and Topological Methods in Mathematics.

Before that I was a lecturer in the School of Mathematics at the University of Leeds.

## WS 2016/17 |
## Non-commutative Algebra 1 |
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## SS 2017 |
## Non-commutative Algebra 2 |
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## WS 2017/18 |
## Non-commutative Algebra 3 |
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## SS 2018 |
## Representations of tame hereditary algebras |
Course Notes |

My research centres around the representation theory of finite-dimensional algebras, together with their connections to various other fields such as algebraic geometry, Lie theory and quantum groups, and combinatorics and cluster algebras.

I have also supervised two Ph.D. students

Stefan Wolf, Thesis
The Hall algebra and the composition monoid

Julia Sauter, Thesis Springer theory and the geometry of quiver flag varieties

Ringel-Hall algebras These are unfinished notes from a graduate course on Ringel-Hall algebras. We start with hereditary algebras, cover the basic theory of Ringel-Hall algebras and Green's Formula, prove necessary results about generalised Kac-Moody Lie algebras and their quantised enveloping algebras, and finally prove Kac's Theorem on the dimension vectors of indecomposable modules using character formulae.