### 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**