AGT conjecture (String theory related to representation theory and algebraic geometry)

http://arxiv.org/abs/0906.3219

Liouville Correlation Functions from Four-dimensional Gauge Theories

Luis F. Alday, Davide Gaiotto, Yuji Tachikawa

"We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N=2 SCFTs recently defined by one of the authors."

As far as I understand it became big trend in hep-th, cited more than 200 times.

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Nekrasov's paper introducing "Nekrasov partition function" is :

http://arxiv.org/abs/hep-th/0206161

Seiberg-Witten Prepotential From Instanton Counting

It conjectured mathematical formulation for what is known to physicst as "Seiberg-Witten
prepotential" for N=2 supersymmetric Yang-Mills theory. Conjecture has been proved later.