PhD in Applied Mathematics - Mathematical Physics in Waterloo Canada | University of Waterloo

Contemporary civilization has been profoundly influenced by the enduring interplay between Mathematics and the Sciences. Within this framework, the Department of Applied Mathematics provides graduate students with specialized study options in Control Theory and Dynamical Systems, Fluid Mechanics, Mathematical Medicine and Biology, Mathematical Physics, and Scientific Computation. Student research initiatives employ advanced mathematical applications across diverse scientific disciplines, spanning from optimizing cancer treatments and manipulating shape memory alloys to processing fractal images, advancing quantum computing, and investigating climate patterns, cosmic inflation, and nanoscale technologies. As part of the University of Waterloo's Faculty of Mathematics – ranked 20th globally in the 2015 QS Mathematics Rankings – our department maintains strong collaborations with Science and Engineering faculties, along with premier research centers including those focused on Mathematical Medicine, Theoretical Neuroscience, Quantum Computing, Theoretical Physics, Nanotechnology, Water Research, and Industrial Mathematics. We provide both Master's and doctoral programs, with our thesis-based MMath typically requiring two years. Graduates often progress to PhD studies or secure prominent roles in industry and government sectors. The PhD program, generally completed in four years, primarily leads to academic research positions, though some graduates enter industrial, governmental, or commercial R&D roles.

Our Mathematical Physics research explores quantum information theory, nanotechnology, and quantum gravity/cosmology. Quantum information theory investigates how quantum phenomena can revolutionize information transmission and processing, contributing to global efforts in molecular, atomic, and photonic control. A key objective involves harnessing quantum entanglement to enable parallel computational processes, potentially yielding exponential performance gains for specific calculations. These quantum principles also facilitate secure communication channels, with existing applications in cryptography. Several faculty members actively collaborate with Waterloo's Institute for Quantum Computing (IQC), advancing these cutting-edge developments.