Apr. 20    DIFFERENTIAL GEOMETRY SEMINAR  [A.Liu, H.Wu and S.Kobayashi]
           Tamas Hausel, UCB
           L^2 cohomology and Schwarzschild instantons
           3 Evans,  4:15-5:10pm
   The emphasis in this talk is the analogy between problems of L^2
   cohomology on non-compact, complete hyperkahler manifolds and Yang-Mills
   instantons on gravitational instantons. We will survey the motivations
   from physics, most notably from S-duality in string theory, which give
   predictions on the L^2 cohomology (the space of L^2 harmonic forms) on
   certain non-compact, complete hyperkahler manifolds like the moduli space
   of SU(2) magnetic monopoles (Sen's S-duality testing conjecture) and
   moduli space of instantons on ALE spaces - or more generally Nakajima's
   quiver varieties (Vafa-Witten's strong S-duality test). We will talk about
   classical and recent theories which could attack these problems. We will
   finish by mentioning some recent results with Gabor Etesi on
   SU(2)-instantons on the Euclidean Schwarzschild manifold and if time
   permits instantons on Taub-NUT space.