Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T18:28:11.117Z Has data issue: false hasContentIssue false
  • English
  • Français

On Some Recent Interactions Between Mathematics and Physics

Published online by Cambridge University Press:  20 November 2018

Raoul Bott
Raoul Bott*
Affiliation:
Department of mathematics and Statistics, Queen's University Kingston, Ontario Canada k7l 3n6
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It gives me quite extraordinary pleasure to have been asked to deliver the Jeffrey-Williams lecture of the Canadian Mathematical Society. The reasons are manifold. First of all Canada was my home for the most formative years of my life — from 16 to 23 — and was in fact the first country willing to take me on as an adopted son. I was of course born in Budapest, but in Europe the geographical accidents of birth are not taken seriously, rather I inherited my father's status and so managed to become stateless "by induction" so to speak.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 2 , 01 June 1985 , pp. 129 - 164
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Atiyah, M.F. and Bott, R., The Yang-Mills equations over Riemann surfaces. Phil. Trans. Roy. Soc. Lond. A308 (1982), pp. 523–615.Google Scholar
2. Donaldson, S.K., An application of gauge theory to four dimensional topology, J. Diffl. Geom. 18, No. 2(1983), pp. 279–315.Google Scholar
3. Fried, D., Gauge theories and four manifolds, Math. Sci. Research Inst., Berkeley, (1983).Google Scholar
4. Freedman, M.H., The topology of four dimensional manifolds, J. Diffl. Geom. 17 (1982), pp. 357–453.Google Scholar
5. Harder, G., Eine Bemerkung zu einer Arbeit von P. E. Newstead, J. Math. 242 (1970), pp. 16—25.Google Scholar
6. Harder, G. and Narasimhan, M.S., On the cohomology groups of moduli spaces of vector bundles over curves, Math. Ann. 212 (1975), pp. 215–248.Google Scholar
7. Jaffe, A. and Glimm, G., Quantum physics, New York: Springer Verlag, (1981).Google Scholar
8. Kirwin, F.C., The cohomology of quotient spaces in algebraic and symplectic geometry I, Thesis, Oxford (1982), to appear in Math. Notes, Princeton Univ. and Press Yellow Series.Google Scholar
9. Mitter, P.K. and Viallet, C.M., On the bundle of connections And the gauge orbit manifold in Yang-Mills theory, Commun. Math. Phys. 79 (1981), pp. 457–472.Google Scholar
10. Mumford, D., Geometric invariant theory, Berlin: Springer-Verlag, (1965).Google Scholar
11. Narasimhan, M.S. and Ramadas, T.R., Geometry of SU(2) gauge fields, Commun. Math. Phys. 67 (1979), pp. 121–136.Google Scholar
12. Narasimhan, M.S. and Seshadri, C.S., Stable and unitary vector bundles on a compact Riemann surface, Ann. Math. 82 (1965), pp. 540–567.Google Scholar
13. Newstead, P.E., Characteristics classes of stable bundles over an algebraic curve, Trans. Am. Math. Soc. 169 (1972), pp. 337–345.Google Scholar
14. Palais, R.S., The geometrization of physics, Lecture notes in Math. Inst, of Math. National Tsing Hua Univ. 1981.Google Scholar
15. Seshadri, C.S., Space of unitary vector bundles on a compact Riemann surface, Ann. Math. 85 (1967), pp. 303–336.Google Scholar
16. Snatycki, J., Geometric quantization and quantum mechanics, Appl. Math. Sci. 30, Berlin: Springer-Verlag, (1980).Google Scholar
17. Taubes, C.H., Self-dual connections on non-self-dual 4-manifolds, J. Diffl. Geom. 17 (1982), pp. 139–170.Google Scholar
18. Uhlenbeck, K., Connections with Lp bounds on curvature, Commun. Math. Phys. 83 (1982), pp. 31–42.Google Scholar