# Experts in: Mathematical methods in physics

### MACKENZIE, Richard

Professeur titulaire

- Physics of elementary particles and fields
- Mathematical methods in physics
- Fractional statistics sytems (anyons, etc.)
- Theory of quantized fields
- Quantum mechanics
- Solitons
- Symmetry and conservation laws
- Spontaneous breaking of gauge symmetries
- Classical and semiclassical techniques in gauge field theories
- Extended classical solutions, cosmic strings, domains walls, textures
- Semiclassical theories and applications of quantum mechanics
- Decoherence, open systems, quantum statistical methods

Theoretical particle physics; quantum field theory and applications in particle physics, cosmology, condensed matter physics, etc. Semiclassical methods, topology in field theory, solitons, instantons. Quantum information.

### PARANJAPE, Manu

Professeur titulaire

- Mathematical methods in physics
- Physics of elementary particles and fields
- Fractional statistics sytems (anyons, etc.)
- General relativity and gravitation
- Functional analytical methods
- Field theory
- Quantum tunneling
- Solitons
- Classical general relativity
- Self-gravitating systems
- Continuous media and classical fields in curved spacetime
- General theory and models of magnetic ordering
- Crystal-field theory and spin Hamiltonians
- Classical spin models
- Quantized spin models
- Quantum spin frustration

I am interested in almost everything, but more specifically, Quantum Field Theory. Including gravitation, tunnelling, spin systems, solitons, non-commutative geometry. Here is a link to my last NSERC application.

### VINET, Luc

Directeur, Professeur titulaire

- Mathematical methods in physics
- Algebraic structures
- Theory of quantized fields
- Quantum information
- Quantum mechanics
- Symmetry and conservation laws
- Integrable systems
- Random process

My research focuses on finding precise solutions to physics models. I work on designing systems for the perfect transfer of quantum information. I study the (random) quantum walks used in the development of quantum calculation algorithms. I examine the asymmetrical exclusion processes that apply in a large number of fields like biopolymerization and traffic-flow problems. My research also deals with stochastic processes used in genetic modelling. A large proportion of my work is devoted to integrable or superintegrable systems, so called because they have many conservation laws. They are important in theoretical terms and have many applications. The methodology underlying my research is based in part on the study of symmetries. I am also working to develop their mathematical description in terms of algebraic structures and orthogonal polynomials and special functions.