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This volume contains the proceedings of the workshop “Crossing the Boundaries: Gauge Dynamics at Strong Coupling”, hosted by the William I. Fine Theoretical Physics Institute at the University of Minnesota, May 14 - 17, 2009. The workshop honored the 60th birthday of Professor Misha Shifman and his outstanding achievements in the field of gauge dynamics. The meeting attracted a fascinating group of researchers working on the cutting edge of dynamics of gauge theories, including supersymmetric and string theories. Their talks covered a wide area of recent developments in the...

This proceedings volume contains papers presented at the Eight Workshop on Continuous Advances in QCD (quantum chromodynamics), held at the William I Fine Theoretical Physics Institute, USA on May 15-18, 2008.

The authors consider the Hodge Laplacian on the Heisenberg group H n , endowed with a left-invariant and U(n) -invariant Riemannian metric. For 0 k 2n 1 , let k denote the Hodge Laplacian restricted to k -forms. In this paper they address three main, related questions: (1) whether the L 2 and L p -Hodge decompositions, 1 (2) whether the Riesz transforms d 12 k are L p -bounded, for 1<< ; (3) how to prove a sharp Mihilin-Hoermander multiplier theorem for k , 0 k 2n 1 .