Research

Computational Modeling, Simulation, and Data Analysis (GP1)

This research group specializes in developing advanced computational methods, algorithms, and data-driven models to solve complex problems in science, engineering, and technology. The research includes machine learning, bioinformatics, network analysis, and high-precision simulations, integrating mathematical theory with practical applications.

S. Ravindran >>
Satyaki Roy >>
Dongsheng Wu >>
Mehmet Yalim (CSPAR) >>
Guo-Hui Zhang >>

Research Topics:
Algorithms (Roy, Ravindran, Zhang)
Deep Learning (Ravindran)
Machine & Statistical Learning (Roy)
Bioinformatics (Roy)
Genomics (Roy)
Internet of Things (Roy)
Network Theory (Roy)
Reduced Order Modeling (Ravindran)
High Accuracy Finite Element Analysis (Ravindran, Wu)
Physics Informed Neural Networks (PINNs) (Yalim)
Optimizing Discrete Losses (Yalim)

Algebra, Discrete Mathematics, and Theoretical Computer Science (GP2)

This research group studies the mathematical foundations of discrete structures, computation, and information. Their expertise includes coding theory, combinatorics, cryptography, graph theory, and mathematical logic, with applications in secure communication, optimization, and algorithm design.

Daniel Bossaller >>
S. Ravindran >>
Satyaki Roy >>
Rainer Steinwandt >>
Guo-Hui Zhang >>

Research Topics:
Coding Theory (Bossaller, Zhang)
Combinatorics (Zhang)
Cryptography (Bossaller, Steinwandt, Zhang)
Discrete Math (Zhang)
Graph Theory (Zhang)
Group Theory (Bossaller)
Mathematical Logic (Zhang)
Algorithms (Ravindran, Roy, Zhang)

Analysis, ODEs, PDEs, and Applied Mathematics (GP3)

The main focus of the faculty in this group is to study issues related to mathematical analysis, differential and partial equations, functional analysis, operator theory, applied mathematics, and similar analytical fields. It is organized as follows:

Shangbing Ai
Summer Atkins
Toka Diagana
S. Ravindran
Dongsheng Wu
Mehmet Yalim (CSPAR)

Research Topics:
Differential/Difference Equations (Ai, Atkins, Diagana)
Partial Differential Equations (Diagana, Ravindran, Yalim)
Integrodifferential Equations (Diagana)
Functional Analysis (Diagana)
Operator Theory (Diagana)
Numerical Analysis (Atkins, Ravindran, Yalim)
High Accuracy Finite Element Analysis (Ravindran, Wu)
Fluid Dynamics (Ravindran, Yalim)
Fluid Flow Control (Ravindran)
Control Theory (Atkins, Diagana, Ravindran)

Dynamical Systems, Stochastics, and Mathematical Physics (GP4)

This group studies systems that change over time, including deterministic dynamical models, stochastic processes, and random structures. Research topics cover epidemiology, mathematical biology, random fields, p-adic dynamical systems, and fractals, with applications in the natural and physical sciences.

Shangbing Ai
Summer Atkins
Toka Diagana
Dongsheng Wu

Research Topics:
Dynamical Systems (Ai, Atkins, Diagana).
Stochastic Differential/Partial Differential Equations (Diagana, Wu)
Stochastic Processes and Random Fields (Wu)
Statistical Properties of Gaussian Random Fields (Wu)
Random Fractals (Wu)
P-adic Analysis/Dynamical Systems (Diagana)

Mathematical Modeling in Science and Engineering (GP5)

In this group, our researchers develop and analyze mathematical models that describe, predict, and optimize complex phenomena in biology, engineering, and physical sciences. Their work combines analytical techniques, computational tools, and interdisciplinary collaboration to tackle real-world challenges.

Shangbing Ai
Summer Atkins
Toka Diagana
S. Ravindran
Satyaki Roy
Mehmet Yalim (CSPAR)

Research Topics:

Mathematical Biology (Ai, Atkins, Diagana)
Epidemiology (Ai, Atkins, Roy)
Fluid Flow Control (Ravindran)
Reduced Order Modeling (Ravindran)
Bioinformatics & Genomics (Roy)
Network Theory (Roy)
Computational astrophysics (Yalim)
Solar Atmosphere Modeling (Yalim)
Magnetohydrodynamics (Yalim)
Applications in Engineering and Physical Sciences (Multiple Faculty)