ICME Students Research Profiles
|Andrew Bradley||My principal research interest is developing mathematical software in support of science and engineering.||View »|
|Cris Cecka||Research primarily in Fast Multipole Methods and High Performance Computing with GPUs.||View »|
|Young Soo Choi||PDE-constrained Optimization
Numerical Partial Differential Equation(Heat, Fluid and Solid)
Numerical Linear Algebra.
|Huang-Wei Chang||My current research is about analyzing large datasets from the geometry and topology prespectives. That is, we consider the data to be point cloud data and they form a finite metric space. Then we try to understand the data by analyzing the geometry and topology of the space. To be specific, the development of modern computation techniques has made simulating huge datasets of protein folding possible. I'm working on analyzing the folding trajectories to obtain hints about the underlying dynamics.||View »|
|David Fong||An iterative algorithm for least-squares problems
An iterative method is presented for solving linear systems and linear
least-squares systems. The method is based on the Golub-Kahan
bidiagonalization process. It is analytically equivalent to the
standard method of MINRES applied to the normal equation. Compared to
LSQR, it is safer to terminate LSMR early.
|Chen Gu||Discrete Mathematics and Algorithms.
|My research explores the use of algorithms inspired by gradient flow for
constrained numerical optimization. The goal is to develop a natural way to
use second derivatives. Existing schemes like curvilinear search are plagued
with scaling issues. Trust-region algorithms lose desirable convergence
properties when presented with linear constraints. The gradient flow algorithm
avoids these problems by defining a search arc as the solution to an ODE. When
the second derivative is indefinite, directions of negative curvature are used
and scaled naturally. When the second derivative is positive definite, the arc
terminates at the Newton step. Constraints are handled in an active set
|Xiaoye Jiang||The main theme of my thesis is learning on domains which have non-trivial algebraic structure. Learning on ranking, matching and multi-object tracking are classical examples of this situation, and there has recently been a surge of research work in these areas via algebraic approaches.||View »|
|Inina Kalashnikova||My area of application is fluid mechanics, more specifically, high Reynolds number flows. The methods I am involved in developing are aimed to reduce the computational cost of simulating complex physical flows that are of interest in today's world, e.g., air flow over the wing of a jet. My Ph.D. adviser is Dr. Charbel Farhat and I am a member of the Farhat Research Group (FRG) . My current work involves extending the recently proposed discontinuous enrichment method (DEM) in finite elements to the advection-diffusion equation. Ultimately I hope to extend the method to the Navier Stokes Equations, the key equations in fluid mechanics.||View »|
|Mikhail Kapralov||Research interests: combinatorial optimization, graph algorithms, streaming, machine learning.||View »|
|Jason Lee||Research interests: Machine Learning, Optimization, Statistics
Multiscale Analysis, Signal Processing
|Eleanor Lin||My research is on modeling human behaviour during during Closely-Spaced-Parallel-Approaches (CSPA). We use a game theoretic model to predict the probabilistic actions of the pilots and ground control during close encounters in these landing situations. Once we are able to predict their behaviours, better warning algorithms that take their probabilistic baviours into account can be developed to improve safety in CSPAs.||View »|
|Pierre-David Letourneau||Research projects include the development and implementation of an algorithm capable of performing matrix-vector products in O(N) complexity for matrices arising from translation-invariant analytic kernels (black-box FMM). I am also developping C++ code for solving the wave equation in homogeneous medium in the presence of a large number of homogeneous scatterers with size on the order of the wavelength.||View »|
|Maks Ovsjanikovs||Animation Reconstruction
Shape Analysis and Symmetry Detection
Robust Unique Localization.
With populations across the entire world benefiting from ever increasing access to mobile phones, cellular providers are amassing incredibly extensive data sets about their subscribers.
My aim is to use these data sets to research human group behavior. Providers not only have information about who calls whom, but also about the location (to the nearest cellular tower) of the mobile phone as it communicates with the network. Considered on the whole, this location data provides a geographic distribution of the population using mobile phones. When considered as part of a multi-year study, access to such data allows us to create and refine models about agents in a country-wide social network.
|Arvind Saibaba||Developing efficient computational methods to solve large-scale inverse problems that arise in subsurface imaging and uncertainty quantification.||View »|
Deformation of fluid-filled vesicles in mixed shear and extensional flows.
Giant unilamellar vesicles are membrane-bound capsules with applications as drug delivery agents. Vesicle research is related to drop dynamics, with the complexity added by the elasticity of the membrane. My research seeks to use computational modeling to understand how vesicles deform when placed in complex flows that have both extensional and shear components. The simulations employ boundary integral methods with adaptive meshing. Future work will incorporate Brownian motion effects.
|Nicole Taheri||My doctoral research focuses on a wide variety of optimization problems, from electric transportation networks to metabolic biology systems to wireless sensor networks.||View »|
|Andrew Tausz||My main research is in computational algebraic topology, more specifically topological data analysis.||View »|
|Guanyuan Wang||Computational methods for Fluid-Structure Interaction problems, Embedded Boundary Methods, and Computational Fluid Dynamics.||View »|
|Nick West||My research focuses on the development of practical numerical algorithms and simulation techniques for analyzing complex stochastic systems. I am also interested in problems from financial mathematics and atmospheric modeling.||View »|
|Reza Zadeh||I work on Machine Learning Theory and Applications, Discrete Optimization, and Scientific Collaboration.||View »|