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Math 600 Research Topics
Please contact a faculty member whose course topics is of interest to you before making plans to enroll in a Math 600 course.
| Topic |
Description |
| Stochastic
Optimization
Models by: Ari Ariyawansa |
Development of new generic
classes of stochastic optimization problems useful in stochastic
decision making contexts. |
| Algorithms
for
Stochastic Optimization by: Ari Ariyawansa |
Development and analysis
(convergence and complexity) of algorithms for generic classes of
stochastic optimization problems. |
| Software for
Stochastic Optimization by: Ari Ariyawansa |
Implementation and computational
evaluation of algorithms for generic classes of stochastic optimization
problems. |
| Algorithms
for Direct Search Optimization by: Tom Asaki |
Development, improvement and
analysis of algorithms for nondifferentiable, black-box and
time-sensitive optimization problems. |
| Surrogate-Guided
Optimization by: Tom Asaki |
Development and analysis of
strategies for surrogate models for time sensitive applications. |
| Computational
Problems in Optimization by: Tom Asaki |
Image denoising, data
segmentation, data clustering, variational problems. |
| Controllability
Theory of Parabolic PDE's by Multiplicative Controls by: Alex Khapalov |
The course is based on Part I of
the monograph, "A.Y. Khapalov, Controllability of partial differential
equations governed by multiplicative controls, Springer, Lecture Notes
Series, vol. 1995, 2010." |
| Controllability
Theory of Swimming Phenomenon by: Alex Khapalov |
The course is based on Part III
of the monograph, "A.Y. Khapalov, Controllability of partial
differential equations governed by multiplicative controls, Springer,
Lecture Notes Series, vol. 1995, 2010." |
| Algebra
and
Linear
Algebra by: Judi McDonald |
|
| Theory
and
Applications
of
Nonnegative Matrices by: Michael Tsatsomeros |
Invariant cones and subspaces,
Perron-Frobenius theory, M-matrices, applications in Markov chains,
optimization, control theory, iterative methods for linear systems. |
| Matrices
in
Dynamical
Systems by: Michael Tsatsomeros |
Stability of equilibria, linear
differential systems, linear control theory, controllability,
reachability and observability. |
| Combinatorial
and
Quantitative
Matrix
Analysis by: Michael Tsatsomeros |
Graph theory and matrices, sign
and zero/nonzero patterns, allow and require problems:
sign-solvability, sign nonsingularity, potential stability. |
| Topics
in Analysis by: Kevin Vixie |
|
| Topics
in Harmonic Analysis by: Kevin Vixie |
|
| Topics
in Geometric Measure Theory by: Kevin Vixie |
|
| Properties
of
Recurrence
Sequences by: William Webb |
|
| Public
Key
Cryptography by: William Webb |
|
| Fair
Division by: William Webb |
|
| Fundamental
Theory of Partial Differential Equations by: Hong-Ming Yin |
This topic deals with the
fundamental aspect of partial differential equations. The focus is on
the well-posedness, regularity of solutions and qualitative properties
of the solution for a PDE problem. |
| Inverse
and Ill-posed Problems in Partial Differential Equations by: Hong-Ming Yin |
This topic deals with problems where a coefficient or a source in a partial differential equation is unknown. One needs to find the solution and the coefficient at the same time. This type of problems arises from various applications such as medical imaging, nondestructive detection and discovering material properties. |
| Asset
Pricing in Financial Engineering by: Hong-Ming Yin |
This topic deals with the mathematical modeling for various asset classes such as stocks, real estate and currency. The focus is on how the mathematical model can be formed to predict the future price movement. |
| Electromagnetic
Fields by: Hong-Ming Yin |
The research for this topic is focused on seeking properties of electromagnetic fields. The fundamental theory is based on Maxwell's equations and their generalization. |