# Research

Research is an important activity for the faculty of the Department of Mathematics. Professor Roderick Melnik holds a **Tier 1 NSERC Canada Research Chair in Mathematical Modeling**. The Financial Mathematics research group is led by Professor Joe Campolieti, who came to Laurier as **SHARCNET Chair in Financial Mathematics**. Other research groups focus on **dynamical systems** and on **game theory**.

The department has strength in a number of areas of pure and applied mathematics, statistics, financial mathematics, and mathematical modeling and computation. This enables the department to offer strong undergraduate programs and work alongside disciplines using sophisticated mathematical models.

Many of our faculty members are affiliated with nearby PhD-granting institutions, so that the students interested in PhD studies may contact such faculty members directly, depending on their research interests.

## Research Centres and Groups

- Financial Mathematics
- Mathematical Biology
- M2NeT Lab: Modelling and Computational Mathematics
- MS2Discovery Interdisciplinary Institute
- Theoretical Dynamics

## Research Interests

Individual faculty members' specific research interests are listed under their general area of research.

Kathie Cameron – Combinatorial algorithms

- Combinatorial optimization, combinatorial algorithms; graph theory; theory of algorithms; operations research.

Joe Campolieti – Financial mathematics

- High performance computing; mathematical finance; exactly solvable pricing models; path integral and Monte Carlo methods for option pricing; jump diffusion processes in finance.

Yuming Chen – Dynamical systems

- Systems of differential equations with delay; neural networks; numerical simulation; applications to biological systems.

Ross Cressman – Dynamical systems

- Applied mathematics; dynamical systems, mathematical modeling in biology and economics.

Shengda Hu – Algebra

- Symplectic geometry and topology; orbifolds; complex geometry; algebraic geometry; mathematical physics.

Marc Kilgour – Game theory, decision analysis

- Game theory; operational research and mathematical modeling; applications of mathematics.

George Lai – Financial mathematics

- Mathematical finance; Monte Carlo and quasi-Monte Carlo methods and applications; stochastic calculus and applications.

Roman Makarov – Financial mathematics

- Mathematical finance; stochastic analysis; Monte Carlo methods and computational mathematics.

Connell McCluskey – Dynamical systems

- Global stability analysis; dynamical systems; mathematical epidemiology and biology.

Adam Metzler – Financial mathematics, applied probability

- Credit risk, applications to financial regulation, correlation modeling; rare event simulation, hitting times for stochastic processes.

Roderick Melnik – (Tier I Canada Research Chair) Applied and computational mathematics

- Applied and computational mathematics with its enrichments in sciences and technologies; partial differential equations and approximation theory; non-smooth control, mathematical biology and complex dynamic systems.

Mark Reesor – Statistics, financial mathematics

- Quantitative finance, Monte Carlo methods in finance, financial risk management, financial stability, securities law, analytics for business, finance, and insurance.

Manuele Santoprete – Dynamical systems

- Dynamical systems; non-linear differential equations; celestial mechanics and chaos.

Cristina Stoica – Dynamical systems

- Geometric mechanics; symmetry and reduction; applications.

Xu (Sunny) Wang – Statistics

- Statistical learning and data mining in health data; data mining in economics and business; mixture models; applied statistics in health-related research; measurement errors.

Zilin Wang – Statistics

- Survey sampling theory; nonparametric regression techniques and applied statistics

Chester Weatherby – Number theory

- Transcendence and rationality of special values of various functions; gamma values; zeta and multiple zeta values; Baker's theorem on linear forms in logs; math education.

Kaiming Zhao – Algebra

- Lie algebras; associative algebras (quantum algebras); linear algebra; division.