Yang Zhang's Homepage

I am a John Nesbit Fellow in pure mathematics at the School of Mathematics and Physics, University of Queensland. I received my PhD in 2020 from the University of Sydney, under the supervision of Professor Gus Lehrer and Professor Ruibin Zhang.

Currently, I am working with Mark Gould, Artem Pulemotov, and Jorgen Rasmussen.

I am interested in representation theory of Lie (super)algebras, Lie supergroups, quantum (super)groups, hyperplane arrangements, and Milnor fibres.

I organise the Pure Maths Seminar with Ole Warnaar and Ramiro Lafuente. Please contact me if you would like to give a talk or suggest a speaker.

Email: yang.zhang at uq.edu.au

Research

In preparation:

Einstein metrics on homogeneous superspaces, joint with Mark Gould, Artem Pulemotov, and Jorgen Rasmussen. Slides for AustMS 2023.
Classification of unitary highest weight irreducible representations of gl_{m|n}, joint with Mark Gould, Artem Pulemotov

Preprints:

Central elements of the degenerate quantum general linear group, joint with Hengyun Yang. arXiv:2404.19239
Yanmin Dai, and Yang Zhang. Explicit generators and relations for the centre of the quantum group, arXiv:2102.07407
Yang Zhang. Combinatorics of Milnor fibres of reflection arrangements, PhD thesis, 2020.

Publications:

Yang Zhang. On the homology of the noncrossing partition lattice and the Milnor fibre, Advances in Mathematics, 415 (2023), 108897.
Gus Lehrer, and Yang Zhang. Milnor fibre homology complexes, to appear in Pure and Applied Mathematics Quarterly. arXiv:2210.11645.
Yang Zhang. The first and second fundamental theorems of invariant theory for the quantum general linear supergroup, Journal of Pure and Applied Algebra, 224(11) (2020), 106411.
Yang Zhang. On the second fundamental theorem of invariant theory for the orthosymplectic supergroup, Journal of Algebra,501 (2018), no. 1 May 2018, 394–434.
Hengyun Yang, and Yang Zhang. A quantum fermion realisation of the finite dimensional spinor representation of Uq(osp(1|2n)), Journal of Mathematical Physics 58, 071706 (2017) .