Each summer the IAS/Park City Mathematics Institute Graduate Summer School gathers some of the best researchers and educators in a particular field to present diverse sets of lectures. This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Super symmetry, and Enumerative Geometry, three very active research areas in mathematics and theoretical physics. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics.Two major themes at this institute were super symmetry and algebraic geometry, particularly enumerative geometry. The volume contains two lecture series on methods of enumerative geometry that have their roots in QFT. The first series covers the Schubert calculus and quantum cohomology. The second discusses methods from algebraic geometry for computing Gromov-Witten invariants. There are also three sets of lectures of a more introductory nature: an overview of classical field theory and super symmetry, an introduction to supermanifolds, and an introduction to general relativity. This volume is recommended for independent study and is suitable for graduate students and researchers interested in geometry and physics.
W. Fulton, Enumerative geometry (with notes by Alastair Craw): Enumerative geometry (with notes by Alastair Craw) Bibliography A. Bertram, Computing Gromov-Witten invariants with algebraic geometry: Introduction and motivation Localization $J$-functions An alternative to WDVV Bibliography D. S. Freed, Classical field theory and supersymmetry: Introduction Classical mechanics Lagrangian field theory and symmetries Classical bosonic theories on Minkowski spacetime Fermions and the supersymmetric particle Free theories, quantization, and approximation Supersymmetric field theories Supersymmetric $\sigma$-models Bibliography J. W. Morgan, Introduction to supermanifolds: Introduction to supermanifolds Bibliography C. V. Johnson, Notes on introductory general relativity: Notes on introductory general relativity Bibliography.