Guo Chuan Thiang

Contact
E-mail: guo.thiang@adelaide.edu.au
Phone: +61 8 8313 4762
Address: School of Mathematical Sciences, University of Adelaide


About
I completed a DPhil in mathematics at the University of Oxford in December 2014 (conferred March 2016). Prior to this, I studied physics and mathematics at the National University of Singapore and the University of Cambridge.
I am currently a post-doc at the Institute for Geometry and its Applications, University of Adelaide, specialising in mathematical physics.
In 2018, I will begin a University of Adelaide Research Fellowship.


Research
My research is focussed on the applications of topological K-theory, operator algebras, and noncommutative geometry to the phenomena of topological phases of matter in condensed matter physics. My contributions include the rigorous analysis and clarification of the general classification problem for topological insulating phases, and more recently, the classification of topological semimetal phases.

I am also interested in the mathematical structures underlying T-duality and the analysis of D-branes in string theory, and finding their analogues in the condensed matter setting. For instance, I introduced the notion of T-duality of topological insulators in a paper with V. Mathai. Together with K. Hannabuss, we demonstrated the conceptual and computational utility of T-duality in simplifying the analysis of the bulk-boundary correspondence for topological insulators.

I am currently investigating the global topology of semimetallic band structures through techniques in generalised degree theory. These have the potential to realise exotic topologically stable fermions which are characterised by subtle topological invariants. I am also interested in the possibility of using K-theoretic and T-duality techniques to study bosonic analogues of topological insulators, and its string theory implications.

Previously, I dabbled in algebraic quantum field theory, and was a researcher in quantum information theory at the Centre for Quantum Technologies, National University of Singapore.


Publications

T-duality trivializes bulk-boundary correspondence: the parametrised case (with K. Hannabuss and V. Mathai). To appear in Advances in Theoretical and Mathematical Physics. [1510.04785]

T-duality simplifies bulk-boundary correspondence: some higher dimensional cases (with V. Mathai). Annales Henri Poincaré. (Published online). [1506.04492]

T-duality simplifies bulk-boundary correspondence (with V. Mathai). Communications in Mathematical Physics, 305(2) 675-701 (2016) [1505.05250]

T-duality of topological insulators (with V. Mathai). Journal of Physics A: Mathematical and Theoretical (Fast Track Communication), 48 42FT02 (2015), [1503.01206] 
publicity at IOPSCIENCE

Topological phases: isomorphism, homotopy and K-theory. International Journal of Geometric Methods in Modern Physics. 12, 1550098 (2015), [1412.4191]

On the K-theoretic classification of topological phases of matter. Annales Henri Poincaré 17(4) 757-794 (2016). [1406.7366]

Degree of Separability of Bipartite Quantum States. Physical Review A 82(1) 012332 (2010)

Optimal Lewenstein-Sanpera Decomposition for two-qubit states using Semidefinite Programming (with B.-G. Englert and P. Raynal). Physical Review A 80(5) 052313 (2009)

Preprints

Global topology of Weyl semimetals and Fermi arcs (with V. Mathai), [1607.02242]

T-duality simplifies bulk-boundary correspondence: the general case (with K. Hannabuss and V. Mathai), [1603.00116]

Other writings

Bell Correlations in Quantum Field Theory, [philsci-archive.8689]

Some attempts at proving the non-existence of a full set of mutually unbiased bases in dimension 6, [1012.3147]

Webpage under construction, more details to come soon.