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Mathematical Physics
Introduction:
The Mathematical Physics group of LPTHE is a central actor in the study of fundamental structures of physical theories, especially quantum and classical integrability, Conformal Field Theory, random matrix theory and non-perturbative aspects of Quantum Field Theory. Our work tends to focus on these mathematical aspects, with connections to several areas in Mathematics: symplectic geometry, quantum algebra, representation theory, combinatorics, algebraic geometry, probability theory, etc. It also leads to concrete applications to physical problems, such as critical exponents and correlations for critical phenomena, quantum entanglement, quantum disordered systems, or dynamical systems.
Staff members:
M. Bellon
Y. Ikhlef
S. Lacroix
F. Smirnov
C. Viallet
P. Zinn-Justin (on leave)
J.-B. Zuber
PhD students:
A. Rossboth
Recent PhDs: A. Rotaru, E. Russo, C. Babenko, T. Dupic, A. Garbali, P. Clavier, S. Negro
Research themes:
Combinatorics & Representation Theory:
Littlewood-Richardson coefficients
Horn´s problem
Higher-genus partitions
1d Quantum Systems:
Exact correlations
Entanglement entropy
Statistical Mechanics:
Random geometries
Critical interfaces
Dynamical systems:
Discrete Painlevé
"Algebraic entropy"
Discrete integrable systems
Solitons
Fundamental QFT:
Form factors
Perturbed CFT
Quantum Toda chain
Alien calculus
Schwinger-Dyson equations
Interactions with Mathematics:
Combinatorics:
Enumeration of partitions
Higher-genus partitions
Algebraic Geometry:
Quantum Riemann bilinear id
Homology of dynamical systems
Complex analysis:
Resummation theory
Mould calculus
Probability Theory:
Proofs of conformal invariance
Dimers
Rigorous Liouville QFT
Representation Theory:
Lie algebras/groups
Quantum groups
Cellular algebras
Horn´s problem
Number Theory:
Algebraic dynamical systems
Complexity
