The School

«Theory of Multidimensional Approximations
and its Applications»

Modern problems of approximation theory, driven by applications in biology, medicine, and engineering, are formulated in high-dimensional spaces, which leads to new phenomena.

The school aimed to discuss fundamental mathematical problems in multidimensional approximation theory. The primary objective in this field is to obtain results that are independent of the dimension (the number of variables) or, at least, exhibit a weak dependence on it.

There are several fundamentally different approaches to this problem. The modern approach is based on infinite-dimensional models and non-linear sparse approximations with respect to a fixed system (dictionary). Meanwhile, the classical approach, based on the approximation of smooth functions of many variables, remains widely used, in particular for function classes with mixed smoothness.

The school is held with financial support from the Ministry of Science and Higher Education within the program of the Moscow Center for Fundamental and Applied Mathematics under Agreement No. 075-15-2025-345.