Dr. Mihaeila Vajiac is the Director of the Center of Excellence in Complex and Hypercomplex Analysis (CHECHA). She is also the organizer of the Math/Physics/Computatation Seminar at Chapman, and one of the organizers of the Special Session on Geometric Methods in Hypercomplex Analysis at the AMS Fall Western Sectional Meeting in late 2018.
Some of her research interests include:
Complex and Hypercomplex Analysis
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.
Algebraic Computational Methods in Geometric and Physics PDEs
In recent years, techniques from computational algebra have become important to render effective general results in the theory of Partial Differential Equations. My research is following the work of D.C. Struppa, I. Sabadini, F. Colombo, F. Sommen, etc., authors which have shown how these tools can be used to discover and identify important properties of several systems of interest, such as the Cauchy-Fueter, the Mosil-Theodorescu, the Maxwell, the Proca system, as well as the systems which naturally arise from the work of the Belgian school of Brackx, Delanghe and Sommen.
Differential Geometry, Symplectic Geometry, Integrable Sustems
Learn more about each of these on her website.