Dr Guo Chuan Thiang

Dr Guo Chuan Thiang
  Org Unit Mathematical Sciences
  Email guochuan.thiang@adelaide.edu.au
  Telephone +61 8 8313 4762
  Location Floor/Room 7 20 ,  Ingkarni Wardli Building ,   North Terrace

I am currently an ARC DECRA Fellow (from 2017) at the Institute for Geometry and its Applications, University of Adelaide, specialising in mathematical physics. 

I was awarded a University of Adelaide Research Fellowship for 2018.

From 2015-2017, I was an ARC Postdoctoral Research Associate at the University of Adelaide.

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.

In 2010, I was a research assistant at the Centre for Quantum Technologies, Singapore.

My research is focussed on the applications of topological K-theory, differential and algebraic topology, 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. Some notes for a lecture series given in Feb-Mar '17 in Leiden are available here.

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 and providing geometric intuition for 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. In particular, there are intriguing links between semimetal topology, and Seiberg-Witten invariants and torsions of manifolds. In the presence of time-reversal symmetry, semimetals realise a new exotic type of monopole.

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. 



In September 2016, I organised a conference on mathematical topics at the interface of string theory, condensed matter physics, K-theory, operator algebras, and geometry. [Website]

In 2017, I am co-organising a workshop on string geometries and dualities [Website], gauge theory and higher geometry [Website], and the Australia-China conference in noncommutative geometry and related areas. [Website]

  • Fu-Kane-Mele monopoles in semimetals (with K. Sato and K. Gomi). Nuclear Physics B 923 107-125 (2017)[1705.06657]
  • Differential topology of semimetals(with V. Mathai). Communications in Mathematical Physics 355(2) 561-602 (2017)[1611.08961]
  • Global topology of Weyl semimetals and Fermi arcs (with V. Mathai). Journal of Physics A: Mathematical and Theoretical (Letter) 50(11) 11LT01 (2017)[1607.02242] publicity at JPhys+
  • T-duality simplifies bulk-boundary correspondence: the parametrised case (with K. Hannabuss and V. Mathai). Advances in Theoretical and Mathematical Physics 20(5) 1193-1226 (2016). [1510.04785]
  • T-duality simplifies bulk-boundary correspondence: some higher dimensional cases (with V. Mathai). Annales Henri Poincaré 17(12) 3399-3424 (2016)[1506.04492]
  • T-duality simplifies bulk-boundary correspondence (with V. Mathai). Communications in Mathematical Physics 345(2) 675-701 (2016). [1505.05250]
  • On the K-theoretic classification of topological phases of matter. Annales Henri Poincaré 17(4) 757-794 (2016)[1406.7366]
  • 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]
  • 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)
  • Conference Proceedings

  • T-duality and K-theory: a view from condensed matter physics. In: Noncommutative Geometry and Physics IV, proceedings for TFC thematic year 2015 on "Fundamental Problems in Quantum Physics: Strings, Black Holes and Quantum Information", pp. 279-314 (2017)
  • On the K-theoretic classification of topological phases of matter (conspectus). In: Proceedings of Frontiers of Fundamental Physics 14 (2014)
  • Preprints
  • T-duality simplifies bulk-boundary correspondence: the general case (with K. Hannabuss and V. Mathai), [1603.00116]
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    Entry last updated: Tuesday, 29 Aug 2017

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