Applied Mathematics and Statistics Research at Mines

Advanced Mathematics and Statistics for the Modern World

Applied Mathematics and Wave Phenomena focuses on solving problems that are inherently interdisciplinary with direct physical applications to fields that span the sciences and engineering.

Such research invariably leads to studying complex behavior that requires tools from mathematical modelling, analysis, and numerical simulation to gain a better understanding of the underlying physical phenomena. Application areas include fluid dynamics, plasma physics, fracture mechanics, hydrological chemical reaction networks, transport phenomena, inverse problems, geophysics, and signal processing. Topics of interest include numerical methods for solving partial differential equations, approximation theory, machine learning, wave motion, nonlinear dynamics, qualitative structure and bifurcation theory, complex networks, and optimization, among others.

Affiliated Faculty

Cecilia Diniz Behn

email: cdinizbe@mines.edu

• Multiple time scales in the interactions between sleep and circadian rhythms
• Glucose-insulin dynamics and quantifying tissue-specific insulin resistance
• Orexin/hypocretin neurons and their role in stabilizing sleep-wake behavior
• Stochastic and deterministic contributions to the fine architecture of sleep-wake behavior

Ebru Bozdağ

Email: bozdag@mines.edu
Website: https://ebrucsm.wordpress.com/
Research Group: Computational and Global Seismology Group

• Global & Computational Seismology 
• Linearized and non-linear inverse theory 
• 3D (numerical) wave propagation 
• Deep Earth and planetary sciences 
• Seismic hazard 

Greg Fasshauer

Email: fasshauer@mines.edu

• Kernel-based Methods
• Applications of Kernel-based Methods
• Numerical Analysis
• Functional Analysis
• Approximation Theory
• Statistics and Stochastics
• Machine Learning
• Computer-Aided Geometric Design
• Multivariate Splines

Mahadevan Ganesh

Email: mganesh@mines.edu

• Forward and inverse acoustic and electromagnetic scattering in 3-D.
• Efficient algorithms for the Stokes and Navier-Stokes equations on rotating surfaces.
• Quadrature finite element methods for elliptic, parabolic and hyperbolic problems.
• Free surface nonlinear evolutionary systems with applications.

John Griesmer

Email: griesmer@mines.edu

• Ergodic theory
• Additive combinatorics
• Harmonic analysis

Willy Hereman

Email: whereman@mines.edu

• Applied Mathematics, Mathematical Modeling, Differential Equations, Theoretical Mechanics, Symbolic Computing
• Nonlinear Wave Phenomena, Soliton Theory, Symmetry Analysis, Integrability, Software Development in Mathematica, Wavelets

Eileen Martin

Email: eileenrmartin@mines.edu

• Near-surface, engineering, environmental and urban geophysics
• Analysis of large sensor networks
• Fiber-optic sensing, including distributed acoustic sensing
• Signal processing, imaging, and inverse problems
• Data-intensive high performance computing
• Passive seismic methods

Paul Martin

Email: pamartin@mines.edu

• Scattering, diffraction and propagation of waves
• Waves in anisotropic and inhomogeneous media
• Fracture mechanics; diffraction by cracks
• Integral equations, especially hypersingular equations

Steve Pankavich

Email: pankavic@mines.edu

• Analysis of Partial Differential Equations
• Kinetic Theory
• Chemical Reactions Dynamics
• Lagrangian Numerical Methods for transport phenomena

Brennan Sprinkle

email: bsprinkl@mines.edu

• Brownian dynamics, Numerical methods for SDEs, Colloidal suspensions
• Computational fluid dynamics, Immersed boundary methods
• Simulating actin suspensions/fiber networks