Lothar GOETTSCHE
(International Center for Theoretical Physics, Trieste)

Instanton counting and Donaldson invariants

This is joint work with Nakajima and Yoshioka. Nekrasovs partition function can be viewed as the generating function for the Donaldson invariants of the affine plane A2. Our aim is to determine the Donaldson invariants of a compact smooth toric surface in terms of the Nekrasov partition function. We have carried this out in the case of rank 2. Using the Nekrasov conjecture, proven by Nekrasov-Okounkov and Nakajima-Yoshioka, this determines the Donaldson invariants of toric surfaces completely for rank 2. I will try to also mention work in progress on higher rank as well as on generalizations of Donaldson invariants.

Further References:

  1. Hiraku Nakajima, Kota Yoshioka, Instanton counting on blowup, math.AG/0306198.
  2. Hiraku Nakajima, Kota Yoshioka, Lectures on Instanton Counting, math.AG/0311058.
  3. Nikita Nekrasov, Andrei Okounkov, Seiberg-Witten Theory and Random Partitions, hep-th/0306238.
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