Bryan Wang
Bryan Wang
Associate Professor / HDR Convenor
email bai-ling.wang@anu.edu.au
call +61 2 6125 2905
link ANU Researcher Portal profile

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Affiliations

  Groups

Research interests

  • Geometric invariants for singular spaces using pseudo-differential operators on Lie groupoids (Baum-Connes conjecture)
  • Gauge theory and low dimensional topology (Yang-Mills and Seiberg-Witten theory)
  • Symplectic topology (Gromov-Witten, Hamiltonian Gromov-Witten theory)
  • Gerbes, D-branes and dualities (Mirror symmetry)

Projects

Teaching information

Regular teaching

1. Semester 2, 2006: MATH3344 Algebraic Topology (Honours). New course & WebCT lecture notes

development. 8 students. (Convenor & lecturer), Weekly load 3 lectures.

2. Semester 1, 2007: MATH1003 Calculus and Matrix Models. Redesigned course & WebCT lecture

notes development. 68 students. (Convenor & lecturer), Weekly load 4 lectures. WebCT lecture notes

were developed and reused by other lecturers for over 10 years.

3. Semester 2, 2007: MATH3344 Algebraic Topology (Honours). 7 students. (Convenor & lecturer),

Weekly load 3 lectures.

4. Semester 1, 2008: MATH1003 Calculus and Matrix Models. 63 students. (Convenor & lecturer),

Weekly load 4 lectures.

5. Semester 1, 2009: MATH1003 Calculus and Matrix Models. 60 students. (Convenor & lecturer),

Weekly load 4 lectures. Change of course contents, WebCT lecture notes redeveloped.

6. Semester 2, 2009: MATH3344 Algebraic Topology (Honours). 16 students. (Convenor &

lecturer), Weekly load 3 lectures.

7. Semester 1, 2010: MATH1003 Algebra and Calculus Methods. 118 students, (Convenor &

lecturer), Weekly load 3 lectures.

8. Semester 2, 2010: MATH3344 Algebraic Topology Honours. 16 students. (Convenor & lecturer),

Weekly load 3 lectures.

9. Semester 1, 2011: MATH1003 Algebra and Calculus Methods. 144 students. (Convenor &

lecturer), Weekly load 4 lectures.

10. Semester 2, 2011: MATH3344 Algebraic Topology (Honours). 14 students. (Convenor & lecturer),

Weekly load 3 lectures.

11. Semester 2, 2012: MATH1113 Mathematical Foundations for Statistics (Linear algebra).

144 students, (Convenor & lecturer), Weekly load 2 lectures. New course & WebCT lecture notes

development.

12. Semester 1, 2013: MATH3320/6212, Advanced Analysis II. 28 students. Weekly load 3 hours per

week.

13. Semester 2, 2013: MATH1113 Mathematical Foundations for Statistics (Linear algebra). 87

students. (Convenor & lecturer), Weekly load 2 lectures.

14. Semester 1, 2014: MATH3320/6212, Advanced Analysis II. 30 students. (Convenor & lecturer),

Weekly load 3 lectures.

15. Semester 2, 2014: MATH1113 Mathematical Foundations for Actuarial Studies (Linear alge-

bra). 80 students. (Convenor & lecturer), Weekly load 2 lectures.

16. Semester 1, 2015: MATH3320/6212, Advanced Analysis II. 36 students. (Convenor & lecturer),

Weekly load 3 lectures.

17. Semester 2, 2015: MATH1113 Mathematical Foundations for Actuarial Studies (Linear alge-

bra). 127 students. (Convenor & lecturer), Weekly load 2 lectures.

18. Semester 1, 2016: MATH3320/6212, Advanced Analysis II. 32 students. (Convenor & lecturer),

Weekly load 3 lectures.

19. Semester 2, 2016: MATH1113 Mathematical Foundations for Actuarial Studies (Linear alge-

bra). 97 students. Weekly load:: (Convenor & lecturer), Weekly load 2 lectures.

20. Semester 1, 2017: MATH3320/6212, Advanced Analysis II. 25 students. (Convenor & lecturer),

Weekly load 3 lectures.

21. Semester 2, 2017: MATH1113 Mathematical Foundations for Actuarial Studies (Linear alge-

bra). 133 students. (Convenor & lecturer), Weekly load 4 lectures.

22. Semester 1, 2018: MATH3320/6212, Advanced Analysis II. 20 students. (Convenor & lecturer),

Weekly load 3 lectures.

23. Semester 2, 2018: MATH1113 Mathematical Foundations for Actuarial Studies (Linear alge-

bra). 110 students. (Convenor & lecturer), Weekly load 2 lectures.

24. Semester 1, 2019: MATH2242/6242 Introduction to Geometry: Curves and Surfaces, 12

students, (Convenor & lecturer), Weekly load 3 lectures.

25. Semester 2, 2019: MATH1113 Mathematical Foundations for Actuarial Studies (Linear alge-

bra). 110 students, (Convenor & lecturer), Weekly load 2 lectures.

26. Semester 1, 2020: MATH3342/6205 Advanced Di erential Geometry, 24 students, (Convenor

& lecturer), Weekly load 3 lectures.

27. Semester 1, 2020: MATH1014 Mathematics and Applications 2, 126 students, (Convenor &

lecturer), Weekly load 2 lectures.

28. Semester 1, 2021: MATH3342/6205 Advanced Di erential Geometry, 31 students, (Convenor

& lecturer), Weekly load 3 lectures.

29. Semester 1, 2021: MATH1014 Mathematics and Applications 2: 119 students, (Convenor &

lecturer), Weekly load 2 lectures.

30. Semester 1, 2022: MATH3320/6212, Advanced Analysis II. 35 students, (Convenor & lecturer),

Weekly load3 lectures.

31. Semester 2, 2022: MATH1014 Mathematics and Applications 2: 130 students, (Convenor &

lecturer), Weekly load 2 lectures.

32. Semester 1, 2023: MATH3320/6212, Advanced Analysis II. 34 students, (Convenor & lecturer),

Weekly load 3 lectures.

33. Semester 1, 2023: MATH1014 Mathematics and Applications 2. 105 students, (Convenor &

lecturer), Weekly load 2 lectures.

34. Semester 1, 2024: MATH3320/6212, Advanced Analysis II. 52 student, (Convenor & lecturer),

Weekly load 3 lectures.

35. Semester 1, 2024: MATH2320, Advanced Analysis I. SDU Weihai, 80 students, (Convenor &

lecturer). 11 hours Zoom lectures and 4 hours in-person.

 

Research-led special topic courses (voluntary teaching)

1. Semester 1, 2006: MATH3349 Special Topics course on K-theory and index theory. Weekly load 2

lectures.

2. Semester 1, 2008: MATH3349 Special Topics Course on Algebraic Cobordism Theory. Weekly load

2 lectures. Weekly load 3 lectures.

3. Semester 1, 2009: MATH3349 Special Topics Course on Advanced Algebraic Topology. Weekly load

3 lectures.

4. Semester 2, 2010: MATH3349 Special Topics Course on Spin geometry. Weekly load 3 lectures and 1

tutorial.

5. Semester 1, 2011: MATH3349 Special Topics Course on K-theory and Index theory. Weekly load 3

lectures.

6. Semester 2, 2011: MATH3349 Special Topics Course on Characteristic classes and spectral se-

quences. Weekly load 3 lectures and 1 tutorial.

7. Semester 2, 2012: MATH3349 Special topics course on Dirac operators and index theory. Weekly

load 3 lectures and 1 tutorial.

8. Semester 2, 2013: MATH3349 Special Topics Course on Symplectic Geometry. Weekly load 3 lectures

and 1 tutorial.

9. Semester 1, 2014: MATH3349 Special Topics course on Dirac operator and Index theory. Weekly

load 3 lectures and 1 tutorial.

10. Semester 2, 2014: MATH3349 Special Topics Course on Symplectic Geometry and Gromov-Witten

theory. Weekly load 3 lectures and 1 tutorial.

11. Semester 1, 2015: MATH3349 Special Topics course on Dirac operator and Index theory. Weekly

load 3 lectures and 1 tutorial.

12. Semester 1, 2015: MATH3349 Special Topics course on Symplectic Geometry. Weekly load 3 lectures

and 1 tutorial.

13. Semester 2, 2015: MATH3349 Special Topics Course on Geometry of gauge theory. Weekly load 3

lectures and 1 tutorial.

14. Semester 1, 2016 : MATH3349 Special Topics Course on Donaldson-Floer theory, Weekly load 3

lectures and 1 tutorial.

15. Semester 2 2018 MATH3349 Special topics on Dirac operators and Index theory. Weekly load 3

lectures and 1 tutorial.

16. Semester 2 2018 MATH3349 Special Topics on Gauge theory. Weekly load 3 lectures and 1 tutorial.

17. Semester 1 2019 MATH3349 Special topic seminars on Equivariant de Rham cohomology. Weekly

load 3 lectures and 1 tutorial.

18. Semester 2 2019 MATH3349 Special topic seminars on Symplectic Geometry. Weekly load 3 lectures

and 1 tutorial.

19. Semester 1 2020 MATH3349: Special topics on Introduction to gauge theory. Weekly load 3 lectures

and 1 tutorial.

20. Semester 1 2020 MATH3349: Special topics on Introduction to Fukaya category and Mirror

symmetry. Weekly load 3 lectures and 1 tutorial.

21. Semester 2 2020 MATH3349: Special topics on Introduction to symplectic geometry and gauge

theory. Weekly load 3 lectures and 1 tutorial.

22. Semester 2 2020 MATH3349: Special topics on Gauge theory and Mirror symmetry. Weekly load

3 lectures and 1 tutorial.

23. Semester 2 2021 MATH3349: Special topics on Introduction to symplectic geometry and gauge

theory. Weekly load 3 lectures and 1 tutorial.

24. Semester 2 2022 MATH3349 Special Topics on Introduction to gauge theory. Weekly load 3 lectures

and 1 tutorial.

25. Semester 2 2023 MATH3349 Special Topics on K-theory and index theory. Weekly load 3 lectures

and 1 tutorial.

26. Semester 1 2024 MATH3349 Special Topics on Symplectic reductions and applications. Weekly

load 3 lectures and 1 tutorial.

27. Semester 2 2024 MATH3349 Special Topics on Mirror Symmetry. Weekly load 3 lectures and 1

tutorial.

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.