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:

PhD students:

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