AGT conjecture (String theory related to representation theory and algebraic geometry)
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.
Nekrasov's paper introducing "Nekrasov partition function" is :
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.