Bryan Wang
Bryan Wang
Associate Professor
HDR Convenor
email bai-ling.wang@anu.edu.au
call +61 2 6125 2905

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Affiliations

  Groups

Research interests

Topology and differential geometry for singular spaces (foliations, stratified orbifolds and moduli spaces from Gromov-Witten theory), including local index theories and higher index theories. Mathematical physics including, topological and differential quantum field theory, gerbes and D-branes.

Projects

Location

Room 2.60, Hanna Neumann Building 145

Publications

  • Higher bundle gerbes and cohomology classes in gauge theories, (with A. Carey, M. Murray), Journal of Geometry and Physics, 21 (1997), no. 2, 183-197.
  • Seiberg-Witten Monopoles in Three Dimensions , (with A. Carey, J. McCarthy, R. Zhang), Letters in Mathematical Physics, 39 (1997), no. 3, 213-228.
  • Notes on Seiberg-Witten-Floer Theory, (with A. Carey), Contemporary Mathematics, Vol. 258, 2000, 71-85. (3) {5}
  • Equivariant Seiberg-Witten-Floer theory, (with M. Marcolli), Communications in Analysis and Geometry, Vol.9 N.3 (2001) 451-640.
  • Featured Review in MathSciNet. Seiberg-Witten invariant and Casson-Walker invariant for rational homology 3-spheres , (with M. Marcolli), Geometriae Dedicata. Vol.91 (1): 45-58, 2002.
  • Weak unique contiuation principal and perturbed monopole equations, (with B. Booss-Bavnbek, M. Marcolli), International Journal of Mathematics, Vol. 13, No. 9 (2002), 987-1008.
  • The geometric triangle for 3-dimensional Seiberg-Witten monopoles, (with A. Carey, M. Marcolli), Communications in Contemporary Mathematics, Vol. 5, no. 2, 2003, 197-250.
  • Seiberg-Witten-Floer homology and gluing formulae, (with A. Carey), Acta Mathematica Sinica, Vol 19, No.2, 245-296, 2003.
  • Variants of Equivariant Seiberg-Witten-Floer Homology, (with M. Marcolli), Contemporary Mathematics, Vol. 366, 225-238, 2005.
  • Seiberg-Witten-Floer homology of a surface times a circle, (with V. Munoz), Mathematische Nachrichten, Vol. 278, No. 7-8, 844-863, 2005.
  • Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories, (with A. Carey, S. Johnson, M. Murray, D. Stevenson), Communications in Mathematical Physics, Vol. 259 No. 3 577-613, 2005.
  • Variants of Equivariant Seiberg-Witten-Floer Homology, (with M. Marcolli), in “Spectral ge- ometry of manifolds with boundary and decomposition of manifolds”, 225–238, Contemporary Mathematics. 366, Amer. Math. Soc., Providence, RI, 2005. {2}
  • On the relationship of gerbes to the odd families index theorem, (with A. Carey), J. Geom. Phys. 57 (2006), no. 1, 23-38.
  • Fusion of Symmetric D-branes and Verlinde ring. (with A. Carey), Communications in Mathematical Physics, Vol. 277, No. 3, February, 2008, 577-625.
  • Thom isomorphism and Push-forward map in twisted K-theory. (with A. Carey), Journal of K-theory, (2008), 1 : 357-393.
  • Geometric cycles, Index theory and twisted K-homology . Journal of Noncommutative Geometry. 2 (2008), no. 4, 497-552.
  • Differential Twisted K-theory and its Applications (with A. Carey and J. Mickelsson), J. Geom. Phys. 59 (2009), no. 5, 632-653.
  • Riemann-Roch and index formulae in twisted K-theory. (with A. Carey), "Topology, C*-algebras, and String Duality", Proceedings of Symposia in Pure Mathematics Vol. 81, 95-131, 2009.
  • Riemann-Roch and index formulae in twisted K-theory, (with A. L. Carey), in “ Superstrings, geometry, topology, and C∗-algebras”, 95–131, Proc. Sympos. Pure Math., 81, Amer. Math. Soc., Providence, RI, 2010. [5](7){8}.
  • Twisted longitudinal index theorem for foliations and wrong way functoriality. (with Paulo Carrillo Rouse). Advances in Mathematics, Vol. 226, No. 6, 4933-4986, 2011.
  • Delocalized Chern character for stringy orbifold K-theory (arχiv:1110.0953). (with Jianxun Hu), Accepted in for publication in Transactions of the American Mathematical Society.
  • Delocalized Chern character for stringy orbifold K-theory, (with J. X. Hu), Trans. Amer. Math. Soc. Vol. 365, no. 12, 6309–6341, 2013.  
  • K-cycles for twisted K-homology, (with A.L. Carey, P. Baum), Journal of K-Theory, Vol. 12 no. 1, 69–98, 2013. 
  • Geometric Baum-Connes assembly map for twisted Differentiable Stacks, (with P. Carrillo Rouse), (with P. Carrillo Rouse), Annales scientifiques de l’ENS Vol. 49, fascicule 2 (2016), 277-323.  
  • Gluing principle for orbifold stratified spaces, (with B. H. Chen, A. M. Li), arXiv:1502.05103, Geometry and Topology of Manifolds, (Editted by A. Futaki et al. ), Springer Proceedings in Mathematics & Statistics Vol. 154, 15-57. [5](6){13}.
  • Localised index theory and L2-Lefchetz fixed formula for orbifolds, (with Hang Wang), Journal of Differential Geometry, Vol. 102 (2016), no. 2, 285-349. 
  • Virtual technique for orbifold Fredholm systems (with B. H. Chen; A.M. Li) Proc. Centre Math. Appl. Austral. Nat. Univ.,Vol. 48 2019, 35 pp. [5](6){13}. 
  • The asymptotic behavior of finite energy symplectic vortices with admissible metrics, (with B. Chen, R. Wang), Scientia Sinica Mathematica 2021, Vol.51(2), pp. 365-392.
  • An equivariant Atiyah-Patodi-Singer index theorem for proper actions II: the K-theoretic in- dex. (with P Hochs; H. Wang) Mathematische Zeitschrift Vol.301 (2022), no.2, 1333-1367.  
  • An equivariant Atiyah-Patodi-Singer index theorem for proper actions I: The index formula (with P Hochs; H. Wang) International Mathematics Research Notices. 2023, no. 4, 3138-3193.  
  • Topological K-theory for discrete groups and index theory. (with P. Carrillo Rouse; H. Wang) Bulletin des Sciences Mathematiques Vol. 185 (2023), Paper No. 103262, 70 pp. 
  • Twisted sectors for Lagrangian Floer theory on symplectic orbifolds. (with B. Chen; K. Ono) Symmetry, Integrability and Geometry: Methods and Applications. Vol. 20 (2024), Paper No. 011, 14 pp.