Academic Profile

Academic Profile

Assoc Prof Andrew James Kricker

Associate Professor, School of Physical & Mathematical Sciences

Phone: +65 65137458
Office: SPMS-MAS 04 18
Assoc Prof Andrew James Kricker

Prof. Kricker obtained his Ph.D. in Mathematics from the University of Melbourne in 1998. Since then he has served Postdoctoral Fellowships at the Tokyo Institute of Technology, the Hebrew University of Jerusalem, and the University of Toronto, before joining NTU's School of Physical and Mathematical Sciences for its inaugural semester in 2005.
Research Interests
Prof. Kricker's most significant research interest lies in the mathematical ramifications of current developments in mathematical and theoretical physics. To be precise, he is interested in the ramifications of certain developments in quantum field theory and quantum gravity in the fields of topology, algebra, and combinatorics. Prof. Kricker's particular speciality is in so-called "quantum topological invariants". These are invariants of knots, 3-manifolds, and various other low-dimensional topological structures, that arise from Topological Quantum Field Theories. More generally, he has a considerable general interest in the fields that surround this topic: knot theory, the theory of low-dimensional manifolds, Lie algebras, Hopf algebras, representation theory, homological algebra, algebraic combinatorics, and so on.
Current Projects
  • Higher Algebraic Structures Emerging in the Study of Topological Quantum Field Theories
  • Investigating the Finite Approximation of L2-Topological Invariants via Computational and Theoretical Approaches in the Setting of Arithmetic Hyperbolic 3-Manifolds
  • Topological, Algebraic and Combinatorial Ramifications of Topological Quantum Field Theories
Selected Publications
  • Andrew Kricker. (2011). Differential operators and the wheels power series. Algebraic and Geometric Topology, 11(2), 1107-1162.
  • Andrew Kricker. (2011). Non-commutative Chern-Weil Theory and the Combinatorics of Wheeling. Duke Mathematical Journal, 157(2), 223-281.
  • A. Kricker, D. Moskovich. (2009). Surgery presentations of coloured knots and of their covering links. Algebraic and Geometric Topology, 9(3), 1341-1398.
  • S. Garoufalidis, A. Kricker. (2004). Finite type invariants of cyclic branched covers. Topology, 43, 1247-1283.
  • S. Garoufalidis, A. Kricker. (2004). A rational non-commutative invariant of boundary links. Geometry and Topology, 8, 115-204.

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