Faculty & Staff

My research in applied mathematics is in the field of inverse problems and uncertainty quantification, which involves estimating unknown system parameters using indirect observations and analyzing the changes in predicted outcomes due to changes in the inputs. In particular, I am interested in the design and analysis of efficient and robust nonlinear filtering algorithms for state and parameter estimation within a Bayesian inference framework and the application of such algorithms in analyzing real-world data. Please see my personal website for more information. View Profile

I teach many graduate courses in our Financial Mathematics Professional Master’s Program. I particularly love engaging graduate students in areas of financial mathematics; the material is exciting, cutting edge, and fun to apply and relate to current events and states of financial markets. At the undergraduate level, I teach upper-level optimization electives, as well as calculus courses. I enjoy teaching at this level, showing undergraduate students why the mathematics we study is important and relevant. Currently, I am involved in the study of liquidity modeling in mathematical finance. ... View Profile

Class teaching is not only important for the transmission of knowledge from one generation to another but also an integral and necessary part of academic research. I teach many undergraduate mathematics and statistics courses including calculus, algebra, finite mathematics, data science, introduction to statistics, and applied statistics. My research in statistics is in the field of time series analysis which involves dimension reduction in the uni-variate and multivariate time series datasets. ... View Profile

Education: BS in Geophysics, Moscow Oil and Gas "Gubkin" Institute, 1979   Ph.D. in applied mathematics and geophysics, "Lomonosov" Moscow State University, 1984 SIAM Fellow, Class 2014 I have spent nearly my entire career in industrial research labs, first at the Central Geophysical Expedition (CGE) of the Russian Oil Ministry and then at Schlumberger-Doll Research (SDR) of Schlumberger Technology. ... View Profile

Professor Fehribach has taught and led mathematical research efforts at WPI since 1992. If you are interested in his work, please contact him directly. His research works with Kirchhoff graphs, representing that the null and row spaces of a matrix are orthogonal complements. When the matrix is the stoichiometric matrix for a chemical reaction network, the Kirchhoff graph is effectively a circuit diagram for that reaction network. View Profile

I am a mathematical physicist working on the development and application of mathematical methods to atmospheric research and satellites orbits. As part of this research, I am also developing new methods for the use of symmetry principles to solve differential equations. I have taught a broad spectrum of applied math courses on the undergraduate and graduate levels. View Profile

  My research interest includes stochastic calculus, stochastic differential equations, and related applications in quantitative finance. Specifically, I work in the Malliavin calculus of Brownian motion, fractional Brownian motion, and Lévy processes. We establish new series representations of martingales, which are widely applicable in pricing and hedging problems in finance. I also study stochastic differential equations driven by non-Markovian time-changed Brownian motion and the approximation schemes for their solutions. View Profile

The evolution of defects in materials present particularly interesting mathematical challenges. My research is in applied analysis, and my goals are to improve the mathematical models for these problems, as well as to advance the mathematical methods for studying them.  View Profile

My research is focused on the design and analysis of fast algorithms for machine learning, optimization and data science. I am especially interested in Markov chain and stochastic gradient-based optimization and sampling algorithms.  These algorithms are used to rapidly explore a high-dimensional or non-convex function or probability distribution in applications such as deep learning and Bayesian statistics.  I am also very interested in the application of these algorithms to problems in machine learning, data science, theoretical computer science, and statistics. ... View Profile

Teaching is an art. It is something you develop within yourself. It needs hard work, time, creativity and dedication. Giving clear and understandable lectures, facilitating group activities, and interacting with students are all important parts of my teaching. My objectives as a statistics educator are: (1) to teach students about statistical tools and how to use them correctly, (2) to expose students to the structure of statistical analysis, and (3) to teach students how to communicate statistical results and concepts to a variety of audiences. ... View Profile

My research is broadly speaking in the area of Nonlinear Partial Differential Equations with applications to physics and materials science. Specifically, I am interested in applying comprehensive techniques from nonlinear partial differential equations, calculus of variations and geometric measure theory to understand complex singularity structures in certain physical systems, including superconductors, liquid crystals, thin film blisters, convection pattern formations and some systems described by hyperbolic conservation laws. The studies of these systems are highly interdisciplinary. ... View Profile

What is a better way of learning, soaking knowledge up like a sponge or like a sieve? A sponge may be saturated quickly, while an appropriate sieve retains the valuable and discards the superfluous.  The essence of teaching is to enable the student to recognize the jewels in a subject, unearth them, and create a valuable collection.   View Profile

Qingshuo Song's research interests include stochastic control theory, and its applications to mathematical finance and various engineering problems. Qingshuo received his BSc from Nankai University, MA and PhD from Wayne State University. Prior to joining Worcester Polytechnic Institute, he had been working with City University of Hong Kong (Associate Professor 2010-2018), University of Michigan (PostDoc 2009) and University of Southern California (PostDoc 2006-2009). View Profile

I have been teaching and conducting research at WPI since 1988. Teaching is a lot of fun since it involves interactions with students, and we can pass our knowledge and experiences to students for their better future. I have been conducting research for cardiovascular modeling in the past 30 years and has made various contributions, especially in using image-based modeling for vulnerable plaque progression and rupture investigations. I collaborate with faculty from many universities, including Harvard, MIT, University of Washington (Seattle), Washington University (St. ... View Profile

My main research area of interest is mathematical modeling of problems in scientific and engineering applications. Recent examples include heat transfer properties in patterned liquid-cooled electronics, heat transfer in geothermal energy harnessing applications, and inter-facial pattern formation on thin fluid films and sheets. The mathematical content of these problems focus on, but are not limited to, continuum mechanics, free-boundary problems, nonlinear partial differential equations, and nonlinear differential equations. ... View Profile

Professor Volkov's research is on Partial Differential Equations theory, Integral Equations theory, and asymptotic and numerical methods. He is interested in abstract existence and uniqueness questions as well as inverse problems and their numerical solutions. He has collaborated with geophysicists and engineers to work on problems related to electromagnetic theory, or seismology. He has published over 30 research papers in prestigious scientific journals. He has taught all levels of math classes, such as Linear Algebra II, Introduction to Analysis, and Graduate Analysis. ... View Profile

I use physical principles at the molecular scale to solve macroscopic problems in biology, e.g. How do a molecule's mechanical properties influence the behavior of a cell?  How do single molecule measurements relate to muscle function?  To answer such questions, I use a combination of computer simulations and mathematical analysis.  This theoretical work is complemented by experiments performed by my collaborators.  In my teaching, I enjoy emphasizing connections between math and other disciplines. View Profile

My research is in the field of Mathematical Finance, which aims at building probabilistic models that provide insights into the behavior of financial market participants, and developing the underlying mathematical theories. My work focuses on the optimal investment and consumption policies in various market settings. I received my Ph.D. in Mathematics from Boston University in 2013, and spend the next two years in the University of Michigan at Ann Arbor as a Postdoctoral Assistant Professor, before joining WPI as a tenure track Assistant Professor. ... View Profile

My research involves analysing size and shape development in biological processes. The form of living systems can be affected by growth and internal force, so it is important to know how they are patterned spatial-temporally. To do this, I develop deterministic approximate inference schemes using static and live imaging data; and develop mathematical models and numerical methods to describe tissue growth and morphogenesis. My research at WPI has attracted interest from all levels of students, and they have become enthusiastic and creative contributors. View Profile

My professional interests include electromagnetic and multiphysics modeling, scientific computations, and optimization in various interdisciplinary areas involving high frequency electromagnetics. I am particularly interested in applications of microwave power engineering as well as microwave imaging (i.e., non-destructive evaluation and testing of materials from the characteristics of the electromagnetic field). I run the Industrial Microwave Modeling Group (IMMG), which I established in 1999 as a division of WPI’s Center for Industrial Mathematics and Statistics (CIMS). ... View Profile