Mongolia

Research and study of hypergeometric functions began from 17th century. Mathematicians like Gauss, Euler and Kummar are pioneers of the theory. Hypergeometric functions are applied in many areas of mathematics including representation theory, mathematical physics and etc. Beginning of the representation theory goes to the late 1800s. It uses many concepts of many branches of modern mathematics. Relationships between representation theory and hypergeometric functions are very tight, for example, coefficients of the representation matrices are usually described by hypergeometric functions.

The CIMPA research school "Partial Differential Equations in Mechanics" will focus on certain recent progress of mathematical analysis and numerical computations related to the partial differential equations namely to fluid mechanics for engineering science. Lectures aim to introduce advanced techniques for the numerical computation of solutions of several classes of PDEs. In particular finite element, finite difference and spectral methods, definition of numerical simulations for different models, comparison with the predictions of analytic results will be presented.

Stochastic Processes and Applications Mongolia 2015 will be hosted by the School of Mathematics and Computer Science at the National University of Mongolia. Situated in the capital city Ulan Bator, this event takes place at the very heart of Asia and is open to all. The two-week research school will look at classical and contemporary topics from the theory of stochastic analysis with applications.

Research in the solvability of partial differential equations (PDE’s) leads us to a much wider scope. In the realization that alternative methods can be used for proving the existence and uniqueness of solutions of linear and nonlinear PDE’s, a new research area in Applied Mathematics was introduced. The theory of Sobolev spaces was developed, which turned out to be a suitable setting in which to apply ideas of functional analysis to glean information concerning PDE’s.

Optimization problems are encountered in many fields (engineering, finance, economics) an can lead to various mathematical formulations: convex or nonconvex type function, blackbox function, integer or continuous type and with various constraints. In some cases, it is also important to treat the effect of uncertainties and also to handle a large amount of data measurements.