Spaces of quasi-maps into the flag varieties and their applications

Alexander Braverman

Research output: Contribution to conferencePaperpeer-review

14 Citations (Scopus)


Given a projective variety X and a smooth projective curve C one may consider the moduli space of maps C → X. This space admits certain compactification whose points are called quasi-maps. In the last decade it has been discovered that in the case when X is a (partial) flag variety of a semi-simple algebraic group G (or, more generally, of any symmetrizable Kac- Moody Lie algebra) these compactifications play an important role in such fields as geometric representation theory, geometric Langlands correspondence, geometry and topology of moduli spaces of G-bundles on algebraic surfaces, 4-dimensional super-symmetric gauge theory (and probably many others). This paper is a survey of the recent results about quasi-maps as well as their applications in different branches of representation theory and algebraic geometry.

Original languageEnglish
Number of pages26
Publication statusPublished - 2006
Externally publishedYes
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: 22 Aug 200630 Aug 2006


Conference25th International Congress of Mathematicians, ICM 2006


  • Geometric Langlands duality
  • Quasi-maps
  • Schubert varieties
  • Supersymmetric gauge theory


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