
Algebra, Geometry and Topology:
Algebra and algebraic geometry study operations such as addition and multiplication in an abstract context
and also the geometric shapes that can be expressed using these operations. There are several applications
of our field to industrial mathematics. Two applications that get a lot of attention recently are coding
theory and cryptography. However, there are also applications to computer vision, data mining, quantum
chemistry and several other fields.

Applied and Numerial Analysis:
This group has interest in mathematics commonly used in Engineering problems: analytic and
numerical methods to investigate time series and models involving differential equations. There
are several experts in asymptotic analysis, a technique that can significantly simplify problems
taking advantage of small or large parameters. There are also several experts in scientific computation,
whose research involves developing faster and more accurate techniques for approximating difficult
models. Additional expertise is present in dynamical systems and in optimization.
This group has had successful collaboration with mining and fuel cell companies. A long term
collaboration with Ballard Power Systems has resulted in simulation tools that describe various
aspects of their fuel cell operation. These tools can be used to optimize designs, investigate
failure mechanisms and component tolerances, and to guide experimental design to understand key phenomena.

Complex Fluids:
Our group focuses on applied problems involving fluid dynamics, with a special focus on fluid systems
that are nonNewtonian or otherwise complex. Our research group is focused around the complex fluid
laboratory, which is shared between the members.
As well as mathematical analysis and computation, the group conducts lab/pilot scale experiments as
part of their research, and is well equipped to do so with a large collection of rheometry equipment
and expertise in a range of measurement techniques.
Fluid mechanics problems studied by the group include: drop formation in microfluidic channels, granular
flows, oilfield cementing, roll waves, injection molding, displacement flows, paste extrusion, yield stress
fluid flows, sedimentation in complex fluids, mixing, pattern formation, polymer foaming, convective heat
transfer, wellbore hydraulics, interfacial dynamics, dambreaks, stratified flows, various problems with
hydrodynamic stability, slurry transport, well control, spray forming, self assembly of particles and
droplets. A significant part of this work has been industrially driven and/or pursued collaboratively with
industrial partners. We are always happy to hear from new sponsors and industrial research collaborators.

Discrete Mathematics:
Discrete Mathematics deals with discrete, as opposed to continuous, quantities. This includes areas such as
networks, cryptography, errorcontrol codes, graphs, (discrete) optimization, and analysis and synthesis of
algorithms. Mathematical concepts and constructions in these areas are vitally iimportant to the computer,
communications and data recording industries. The UBC Mathematics Department has experts in all of these areas
and would be happy to discuss related problems of industrial interest.

Mathematical Biology:
Members of the Mathematical Biology group at UBC use computational and analytical techniques
to solve problems arising in biology at all scales, from the subcellular level to the ecosystem
level. We work closely with experimentalists and empirical scientists and we are used to acting
as translators between biological and mathematical languages. We have had considerable success
working with scientists outside academia, for instance at the UBC hospitals and at Merck, Inc.
We are keen to continue working on problems of practical and industrial importance. For more
information, please see our group web pages

Number Theory:
Number theory is the branch of mathematics concerned with the properties of integers, rationals and certain
generalizations, as well as the wider class of problems that arise from their study. Number theory has applications
to fields both numerous and diverse, including coding theory, cryptography, mathematical computation, acoustics,
random number generation, computing Fourier transforms, and Doppler radar.

Partial Differential Equations:
Partial Differential Equations (PDEs) are present in many mathematical models that describe real phenomena in Science,
Engineering and Economics. Some types of PDEs have been so well studied because of their prevalence in applications
that they have become "standard" tools for Applied Mathematicians, Engineers and Economists. However, sometimes changing
a model even slightly to try and get more accurate predictions of the real phenomenon can lead to PDEs with very different
behaviour. Our group studies the analytic and geometric properties of solutions to these less standard PDEs.

Probability:
Probability theory is the study of random phenomena, and has many applications in areas such as insurance, finance,
and risk management.
