I algebraic geometry

Major research achievements:

Members of the group have been invited to deliver lectures at the International Congresses of Mathematicians, ICM (A. Pełczyński, plenary 1983) and four sectional (Latala, Figiel, Tomczak-Jaegerman, Szarek). Out of 40 articles in the "Handbook of the Geometry of Banach Spaces" (North Holland, 2001) 4 have been authored by members of the group (~ 10%).

E.g. MathSciNet Math.Rev shows P. Wojtaszczyk 68 papers and two books cited 520 times by 461 authors and T. Figiel 50/443/385. Famous and extremaly useful are two books by Wojtaszczyk:

[Woj1] Banach spaces for analysts. Cambridge University Press, Cambridge, 1991. xiv+382 pp,

[Woj2] A mathematical introduction to wavelets. Cambridge University Press, Cambridge, 1997. xii+261 having 194 and 96 citations (not counting Polish translations).

Prof. Wojtaszczyk is interested in mathematical problems of sparse representation. In recent years the idea of sparsity is getting more and more important in various areas. Essentially it is a belief that many natural phenomena which seem to depend on many factors can be represented as dependent on a much smaller number of judiciously chosen parameters. This general philosophy

give rise to  a variety of different mathematical questions. There exists an extensive mathematical literature devoted to mathematical aspect of this general philosophy. As of now his research deals with three mathematical manifestation of this philosophy:

1. 
   Compressed sensing and its generalisations e.g. sparse functions. Mathematically it uses tools and ideas from probability theory (Latala, Adamczak), geometry of Banach spaces (Mankiewicz), theoretical computer science, combinatorics, approximation theory (A. Kamont, Z. Ciesielski), information based complexity, etc.  Its results and ideas are used in signal processing, machine learning, electronic microscopes, astronomy, etc.
   
2. 
   Greedy algorithms. Mathematically it uses tools and ideas from functional analysis, geometry of Banach and Hilbert spaces,  theory of n-widths, convexity theory, probability theory. It finds applications in mathematical statistics, numerical solutions of PDE's with parameters, machine learning, etc.
   

1. 
   P. Bechler, R. DeVore, A. Kamont, G. Petrova, P. Wojtaszczyk, Greedy wavelet projections are bounded on BV, Trans. Amer. Math. Soc. 359(2007)619-635, IF=1,094; citations
    WoS=4, MSN=3
   
2. 
   F. Albiac, P. Wojtaszczyk, Characterization of 1-greedy bases, J.Approx. Theory 138 (2006)65-86, IF=1,040; cytowania WoS=2, MSN=0
   
3. 
   P.Wojtaszczyk, Greediness of the Haar system in rearrangement invariant spaces, w Banach Center Publications 72, Approximation and Probability, Warszawa 2006, WoS does not record this paper citations MSN=5
   
4. 
   R. DeVore, G. Petrova, P. Wojtaszczyk, Anisotropic smoothness spaces via level sets, Commumications in Pure and Appl. Math, 61:9(2008) 1264-97 IF=3,873; citations WoS=1, MSN=0
   
5. 
   P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing, Foundations of Computational Mathematics, 10(2010) 1-13, IF=2,745; citations
   WoS=4, MSN=5
   
6. 
   R. DeVore, G. Petrova, P. Wojtaszczyk, Instance optimality in probability with an $\ell_1$-minimization decoder, Applied and Computational Harmonic Analysis, 27 (2009) 275-288, IF=3,176; citations WoS=5, MSN=2
   
7. 
   R. DeVore, G. Petrova, P. Wojtaszczyk, Approximation of functions of few variables in high dimensions, Constructive Approximation 33:1(2011) 125-143, IF=1,743; citations
   WoS=1 MSN=1
   
8. 
   P. Bechler, P. Wojtaszczyk, Error estimates for orthogonal matching pursuit and random dictionaries, Constructive Approximation 33:2(2011) 273-288, IF=1,743, citations
   WoS=0, MSN=1
   
9. 
   P.Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods, SIAM J. Math. Anal. 43:3(2011) 1457-72, IF=1,744; citations WoS=1, MSN=0
   
10. 
    P. Wojtaszczyk, Complexity of approximation of functions of few variables in high dimensions, Journal of Complexity, 27:2(2011) 141-150, IF=0,986; citations WoS=0, MSN=0
    

Global citations  WoS=392 (without autocitations 248) MSN=605 index h=12.
Remark 1.  IF means 5-year impact factor of the journal, WoS Web of Science, MSN MathSciNet.
Remark 2. Web of Science does not count citations of books. According to MathSciNet may books had 213 and 100 citations.

Prof. Yu Tomilov got in 2009 Sioerpinski prize for mathematicians below 40 of the Polish Academy of Sciences.

Mankiewicz run Warsaw IMPAN node of the FP6 RTN network PhD (Phenomena in High Dimension).

Zemanek and Tomilov run at IMPAN the FP6 ToK programme TODEQ 2006-2010.