Concordia University

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Areas of study

  • Actuarial Mathematics & Mathematical Finance 
    This group is active in commodity market models, credibility theory, forward-backward stochastic differential equations, insurance statistics, risk management, risk theory, stochastic analysis and valuation of financial guarantees embedded in life insurance contracts. The group is recognized by the Society of Actuaries as a Center of Actuarial Excellence. (CRM Lab associated with this area: Actuarial and Financial Mathematics Laboratory Quantact).
  • Analysis, Partial Differential Equations & Applied Mathematics 
    Research topics include harmonic analysis on Euclidean space, in particular the theory of singular integral operators, Hardy spaces, and other function spaces, applications of harmonic analysis to partial differential equations, applications of PDE's and curvature flows to convex geometry, and the study of geometric properties of solutions of PDE's, including evolution equations of curves and surfaces by curvature driven speed, fluid dynamics and turbulence, mathematical neuroscience. (CRM Lab associated with this area: Mathematical Analysis Laboratory)
  • Dynamical Systems
    Current research topics include ergodic theory and absolutely continuous invariant measures, the interplay between ergodic theory and topological analysis, computer modeling, small stochastic perturbations, random maps theory with applications to modelling financial markets, scientific computing and linear algebraic methods, nonsmooth analysis and control theory, bifurcation theory and chaos.
  • Mathematics Education
    Research and study interests focus on problems of teaching and learning mathematics at mainly the secondary and post-secondary levels. These problems are studied using qualitative research methods and approached from a range of theoretical perspectives, including history, philosophy and epistemology of mathematics, foundations of mathematics, theories of understanding mathematics, theories of institutionalized mathematics education, and specialized theories of teaching and learning particular mathematical content in areas such as algebra, geometry or calculus.
  • Mathematical Physics & Differential Geometry
    Present research deals with quantum and classical integrable systems, inverse spectral and inverse monodromy methods, moduli spaces of Riemann surfaces, relativistic field theory, spectral theory of random matrices and random processes, quajtization techniques, square integrable group representations, wavelets and signal analysis, symmetry reduction techniques and spectral analysis in quantum physics.   (CRM Labs associated with this area: Mathematical Physics Laboratory and CIRGET)
  • Number Theory & Computational Algebra
    Current work is centered around the algebraic, analytic and p-adic theory arising from the arithmetic of cyclotomic fields, elliptic and modular curves and higher dimensional algebro-geometric objects, their associated L-functions, Galois representations, Iwasawa theory, modular functions and forms and their group theoretic connections (for example, "Moonshine").   (CRM Lab associated with the Number Theory area: CICMA).
  • Statistics & Probability 
    Areas of concentration are curve estimation, distribution theory, estimation of variance components, inference, linear models, modeling data, non-parametric methods, survey sampling, survival analysis, stochastic processes and applicaitons, stochastic analysis and non-linear filtering.   (CRM Lab associated with the Statistics area: Statistics Laboratory)
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