Faculty members involved
Kirill Kopotun
(link)
has particular interest in various topics in nonlinear approximation, constrained approximation, measures of smoothness, weighted approximation, adaptive algorithms, and other related areas.
One of the central tasks in Approximation Theory is to determine a connection between approximation and smoothness properties of what's been approximated (functions, surfaces, etc.),
and the main goal of the research program is further investigation of the exact connection between smoothness of (classes of) functions (surfaces, bodies, etc.) and their approximation orders.
In general, nonlinear approximation methods perform much better than linear ones, and the order of approximation from nonlinear manifolds is much better than the order of approximation by the elements of linear spaces,
which is the main reason for investigating nonlinear approximation techniques.
Andriy Prymak
(link) focuses on rather theoretical aspects of approximation theory, particularly on shapepreserving approximation,
and on relations of measures of smoothness and approximation. Problems in shapepreserving approximation demand the approximating tool (often a polynomial or a spline) to possess the same geometric property (monotonicity, convexity) as the original function does. In many cases one can achieve the same order of approximation as in the unconstrained case, but this may require very different methods, especially in the multivariable settings.
Rate of approximation can be related to certain measures of smoothness of a function (more sensitive analogs of derivatives). His work in this direction includes generalizations of various classical inequalities, connections of approximation theory to geometry of Banach spaces, and studies of "boundary effects" in approximation on convex domains.
His other interests include various properties of convex functions and bodies, relations of approximation theory to other areas of analysis (harmonic analysis and Fourier analysis) and mathematics (graph theory),
computational and numerical methods.
Current students and postdoctoral fellows
 Isiaka Akinsanya (M.Sc.)  K. Kopotun
 Farzaneh Jannat (M.Sc.)  K. Kopotun
 Kyrylo Muliarchyk (M.Sc.)  K. Kopotun
 Sahar Rahimzad Lamey (M.Sc.)  K. Kopotun
 Olena Usoltseva (Ph.D.)  A. Prymak
Representative recent publications

A. Bondarenko, A. Prymak, D. Radchenko, On concentrators and related approximation constants, J. Math. Anal. Appl., 402 (2013) 234241

K. A. Kopotun, D. Leviatan, A. Prymak, I. A. Shevchuk, Uniform and pointwise shape preserving approximation by algebraic polynomials, Surv. Approx. Theory, 6 (2011), 2474

Z. Ditzian, A. Prymak, Convexity, moduli of smoothness and a Jacksontype inequality, Acta Math. Hung., 130 (2011), no. 3, 254285

Z. Ditzian, A. Prymak, Approximation by dilated averages and Kfunctionals, Canadian Journal of Mathematics, 62 (2010), no. 4, 737757