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Spring 2016 Lecture Series
Clément Hongler
The second half of the 20th century saw the convergence of Statistical Mechanics and
Quantum Field Theory. In two dimensions, this convergence resulted in the most
beautiful chapters of mathematical physics: Conformal Field Theory (CFT) reveals deep
structures that allow for extremely precise investigations, yielding in particular nonperturbative descriptions with exact formulae.
This series will explain how 2D CFT works, in particular how planar lattice models can
be understood using the Minimal Models of CFT. While this connection remains largely
conjectural, major recent progress in the field of rigorous conformal invariance allows
one to make mathematical sense of much of the story: In particular, for the Ising model
we are close to reaching a complete understanding of how it works. The series will thus
focus on giving an intuitive understanding of the global picture (in a probabilistic
language) together with concrete examples, precise definitions and rigorous statements
whenever they are available.
April 21, 2-3:15pm: General picture: local fields, correlations, partition functions.
Room 102
Examples of models and of exact results coming from CFT.
April 29, 4-6pm:
Fields and geometry: the stress-energy tensor, conformal
symmetry, central charge, Virasoro commutation relations,
unitarity, boundaries.
Room 1302
May 6, 4-6pm:
Room 1302
May 12, 2-4pm:
Room 101
May 18, 4-6pm:
Room 101
Virasoro algebra representation theory: Kac determinant
formula, classification of Virasoro representations, null-field
equations, differential equations.
Minimal models: unitary series, fusion rules, partition
functions, explicit constructions.
Beyond conformal invariance: massive theories, counting
arguments, exact scattering matrices.
251 Mercer St
New York, NY 10012