A group of mathematicians and physicists from the School of Computational Sciences at Chapman University joined some of their national and international collaborators to form this Center of Excellence. The research conducted under the center's umbrella is mainly motivated by the latest results in Clifford and Hypercomplex Analysis and endeavors to find new ways in which this research can be applied in mathematics and physics. The members of this center of excellence draw on their research experience and use analytical and computational techniques to build sound differential and integral theories in this context, as well as possible applications in Quantum Physics and other interdisciplinary fields.
Complex Analysis is a classical branch of mathematics, having its roots in late 18th and early 19th centuries, which investigates functions of one and several complex variables. It has applications in many branches of mathematics, including Number Theory and Applied Mathematics, as well as in physics, including Hydrodynamics, Thermodynamics, Electrical Engineering, and Quantum Physics.
Clifford Analysis is the study of Dirac and Dirac type operators in Analysis and Geometry, together with their applications. In 3 and 4 dimensions Clifford Analysis is referred to as Quaternionic Analysis. Furthermore, methods and tools of Clifford Analysis are extended to the field of Hypercomplex Analysis.