You need answers
When problems or questions requiring deep mathematical and computing knowledge arise, they cannot always be solved within your organization. University of Waterloo Mathematics researchers work in partnership with commercial companies, industry research groups and government bodies to find answers. We analyze data, design systems, optimize resources, model processes and facilitate communication methods.
We have an unparalleled breadth of knowledge and practice. Our people are experts in the languages of math and computing. From car air bags to medical imagery, our research teams work on applied and theoretical problems, impacting a wide variety of industries and products that people use every day. The prospect of a new or difficult problem is what stimulates our imagination. We’re driven to find answers - the answers you need to drive innovation.
Partnering with us is win-win. Bring us a challenge and we’ll work with your team to understand what’s important, and together we will find the answers you need.
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To connect with a Faculty of Mathematics researcher, you can search by name or area of expertise.
Areas of applied expertise
Artificial Intelligence and Machine Learning
Artificial intelligence (AI) and machine learning (ML) research in the Faculty of Mathematics has deep roots, dating back to the 1980's. Faculty members have active research interests in diverse subareas including models of intelligent interaction, multi-agent systems, natural language understanding, constraint programming, optimization, computer vision, robotics, machine learning, and reasoning under uncertainty. In addition, researchers are studying how AI algorithms and systems are becoming increasingly integrated with our society, automating tasks and assisting humans with decisions. This deep integration of AI and humans have broad implications for both the well-being of individuals and the health of our society, and requires careful consideration of the ethical and societal implications.
At the University of Waterloo, we have great breadth of research from foundational to applied AI and ML. Many researchers have an interest in applying AI and ML to important commercial and industrial problems. Our researchers are producing end-to-end AI solutions of immediate benefit to all Canadians. Waterloo’s track record of partnership with industry allows us to deliver effective AI innovation for businesses across Canada.
A data-driven revolution is underway in science and society, disrupting every form of enterprise. Data science refers to the data-driven approach to solving problems, and involves analysis of large volumes of varying data, extracting knowledge and insight from it, and using this for improved decision making. Waterloo data science research covers a variety of themes: trust, quality and usability assessing the provenance, trustworthiness, and fitness for use of large data sets as well as scalable data cleaning; management of big data providing simple transactional interfaces that enable users to execute powerful, declarative queries for online exploration and large-scale batch data mining; modelling and analysis enabling insights to be derived from the data using machine learning, statistical learning, and data mining techniques; and dissemination and visualization enabling users to better understand the data and explore it with ease and developing visual-analytics tools for large and complex data.
Recent advances in data science applications have led to groundbreaking benefits – from health sciences, where social network analytics have enabled the tracking of epidemics; to financial systems, where guidance of investment decisions are based on analysis of large volumes of data; to speech recognition applications and more. These achievements only hint at what is possible—the full impact of data science is yet to be realized.
Security and Privacy
Repeatedly news is reported about vulnerabilities and exploits on the Internet, social networks, mobile computing, cyber-physical systems, artificial intelligence and critical infrastructures. The Faculty of Mathematics has a long history of developing technologies, such as elliptic curve cryptography, private messaging, quantum-safe cryptography and hardware random number generators that have made a significant difference in designing computer systems that can withstand these attacks.
In the Faculty of Mathematics, cybersecurity, privacy, cryptography and topics in algorithms, networks and mathematics related to security, have been a high priority for over 25 years. Our research in cryptography, cybersecurity, and privacy is not only foundational. Our researchers have also turned research into innovations that create economic advantage, for example in widely deployed commercial products. This includes commercialization of public key cryptography, resulting in adoption by U.S. National Security Agency for use in government and commercial systems, and technology transfer such as Off-the-Record Messaging, adopted by creators of popular instant messaging applications.
In the heart of Quantum Valley, our quantum computing researchers have access to state-of-the-art facilities on campus that are like no other in the world. At the University of Waterloo, researchers are harnessing the quantum laws of nature to develop powerful new technologies that will drive the 21st century. Quantum computing has the potential to support the simulation and modeling of complex systems in a more powerful way than our current supercomputers. In addition, quantum computers could be used to potentially put today’s systems that secure our information at risk.
In a highly collaborative and interdisciplinary environment, researchers in the Faculty of Mathematics focus on such topics as quantum cryptography, quantum information processing, and quantum software, while others unravel the mathematical models necessary to comprehend the workings of quantum devices.
Biostatistics, Computational Biology and Mathematical Medicine
Technological advances in health research and healthcare have resulted in large and complex data structures on genetic, environmental and behavioral determinants for disease onset and progression, as well as patterns in health service utilization among diseased individuals. Our strengths in mathematical modelling and our innovations in biostatistics, uniquely position us to advance scientific understanding and develop and evaluate predictive models of disease processes. Key goals in computational biology include assessing genetic risks for aggressive forms of disease and work towards the goal of personalized medicine in diverse fields such as cancer, cardiology, and rheumatic disease. Another area of strength in computational biology in the Faculty of Mathematics is the development of bioinformatics software with applications to the prediction of 3D protein structure, protein identification and pathway mining, and efficient organization and extraction of information in DNA databases.
In many settings, medical problems can be characterized in mathematical terms. Our research in mathematical medicine is directed to mathematical modeling, predictions, and the creation of software to guide decision making on shunt placement for hydrocephalus patients, improving diagnostic algorithms and cancer treatment processes, and developing information management systems for health care and hospital performance.
The modern financial industry, comprising the banking and investment sectors, as well as insurance companies and pension funds, relies heavily on modern risk analysis and risk management. As the array of financial products grows in variety and complexity, accurate and reliable risk management has become essential. Researchers in the Faculty of Mathematics are working to develop: frameworks for modelling and analyzing risks in long-term insurance; stochastic mortality models and sustainable hybrid pension scheme solutions; statistical and computational tools for model uncertainty and model risk in financial and insurance risk management; and mathematical and economic theory for the measurement of risk and decisions.
Our researchers in the Department of Statistics and Actuarial Science have a long track record of contributions to the analysis of: the impact of regulation changes on the overall insurance market; surplus, insurance loss and other statistical distributions; and sustainable portfolio management under climate change. This research has applications for insurance companies, banks, governments, and customers in Canada and around the world.
Blockchain is a new and emerging technology positioned on the leading edge of the technology hype curve. It is a distributed ledger technology expected to transform the way transactions happen in the Internet and to impact every segment of the industry and society. In the Faculty of Mathematics, we study the foundations and applications of blockchain technology. Our expertise relevant to blockchain technology spans systems research including networking and distributed systems, distributed systems theory, databases and data mining, and resource management, as well as security research, including cryptography and cryptosystems, data privacy, and information security.
Our researchers are developing new data structures and new protocols for more efficient, more scalable, and more secure blockchains. Our work also explores the application of blockchains to secure communications, the Internet of Things, finance, accounting, health, and energy.
The Faculty of Mathematics at Waterloo is internationally recognized for leading research in financial technology. With researchers studying the core areas of quantitative finance, portfolio valuation and management, high frequency trading, risk management, insurance and financial services. While other institutions focus on the delivery of financial services over computer platforms, we focus on core problems in finance which can be unlocked using mathematics, emerging AI techniques, data science, security and privacy technologies.
Complementary strengths in mathematics, statistics, and computer science, as well as strong relationships with insurance companies and financial institutions through the Department of Statistics and Actuarial Science and the David R. Cheriton School of Computer Science, give us a significant advantage in Fintech research. Recent interdisciplinary research addresses new domains such as smart contracts, corporate finance, regulatory and compliance issues, cryptocurrency impacts on central banking, and monetary policy.