Research directions for graduate students

For PhD students of  Department of Theorical Mathematics:

1. Differential and integral equations

  • Linear and nonlinear differential equations in Banach spaces;
  • Semi-linear partial differential equation;
  • Optimal control problems for differential equations and partial differential equations;
  • Problems determining coefficients for partial differential equations, inverse problems, etc.

2. Caculus

  • Integral transform;
  • Functional analysis;
  • Complex analysis;
  • Fixed point theory and related issues.

3. Algebra and geometry

For PhD Students of Department of Applied Mathematics:

1. Scientific computation

  • Solve problems of mechanical form, mathematical and applied physics equations,
  • Data mining, machine learning,
  • Image processing,
  • Optimum control, dynamic system,
  • Modeling complex systems.

 2. Optimization methods and applications

  • Multi-objective optimization,
  • Non-convex optimization, DC optimization,
  • Network optimization problems,
  • Methods for solving large-scale optimization problems,
  • Optimization problems applied in financial economics, transportation, telecommunications, agriculture, health…

3. Stochastic process

  • Financial math,
  • Data analysis and experimental design,
  • Simulation of a stochastic process in a complex system,
  • Stochastic processes and applications.

For PhD Students of Department of Informatics and Mathematics

   1. Soft computing and high-performance computing

  • Research on soft computing methods such as Neural networks, computational simulation of natural processes;
  • Research on high-performance computing methods, methods of using multiple concurrent computing resources, parallel computing, multi-threading, hyper-threading and multitasking computing;
  • Quantum computing.

 2. Discrete math, combinatorial theory and graph theory

  • Studying combinatorial structures appearing in algebraic contexts or applying algebraic techniques in combinatorial problems;
  • Research on graph structure, mathematical structure used to describe relationships between objects;
  • Research on optimization problems on graphs, parameterization algorithms, approximation algorithms, structural properties on graphs, parameters of graphs, etc.

3. Code theory, privacy and information security

  • Variable length code theory;
  • Research on cryptographic systems, cryptanalysis and anti-cryptanalysis;
  • Research risks and develop solutions in information safety and security;
  •  Hiding information and applications;

4. Data Science

  • Big data, data warehousing, data mining and knowledge discovery, machine learning;
  • Large and/or complex data structures for which traditional data processing methods have proved unsuitable;
  • Issues related to data mining;
  • Search problems (exact, approximate), information extraction.

5. Mathematical logic and set theory

  • Research on applications of formal logic in mathematics and computer science theory;
  • Research on set theory using the perspectives of mathematical logic;
  • Research on model theory, research theory on mathematical structures such as groups, rings, fields or other algebraic structures, graphs or other discrete structures using tools of mathematical logic;
  • Research on theory of computation using tools of mathematical logic, Turing machines, problems of determinism of algorithms, polynomial derivation and computational complexity.

6. Computer graphics and multimedia