# Research

Research in the Department of Mathematics and Statistics occurs in a number of disciplines.

In commutative algebra and model theory, there is active research in valuation theory and ordered fields, real algebraic geometry, quadratic forms, positivstellensätze and moment problems, and resolution of singularities.

In non-associative algebra the research focus is on polynomial identities for nonassociative structures, and the closely related topic of free algebras, with an emphasis on computational methods. Traditionally research in Topology has been conducted in such areas of General and Geometric Topology as absolute extensors, classical dimension, continua, fixed point sets, selections.

Work in statistical physics involves lattice models of polymers, and the study of self-avoiding polygons using Markov-Chain Monte-Carlo methods. In applied probability there is work on queuing networks and performance models of communications systems.

Research in statistics includes adaptive decisions procedures, asymptotic distribution theory, randomization, aspects of causal inference, and applications of hidden Markov models.

Research directions in applied mathematics and mathematical physics currently include: nonlinear partial differential equations, applied analysis; Hamiltonian systems with symmetry, differential geometry and classical mechanics, discrete analogues of structured systems; foundations of quantum theory, including quantum measurement, relativistic quantum mechanics, quantum mechanics on phase space, group representations, coherent states, and squeezed states; integrable systems, analysis and partial differential equations, inverse problems, and applications of Lie theory; mathematical modelling; theory of symmetries and conservation laws of differential equations; exact and approximate solution of nonlinear differential equations, symbolic and numerical scientific computation.

For specific research interests of faculty members, see our Faculty Research page