Privatdozent Dr. Michael Gnewuch

Institut für Informatik
Christian-Albrechts-Universität zu Kiel
Christian-Albrechts-Platz 4
Room 919
D-24098 Kiel
Tel. ++49-(0)431-880-7465
E-mail: mig(at)informatik.uni-kiel.de

News

From beginning of April 2013 my new (main) affiliation is the Computational Stochastics Group at the Felix Klein Center for Mathematics, Technical University of Kaiserslautern, Germany. For contact details please see my website at the TU Kaiserslautern.
Prize for Achievement in Information-Based Complexity (IBC Prize) 2012.
Our proposal for an Oberwolfach Workshop on Uniform Distribution Theory and Applications has been accepted and the workshop (ID: 1340) will take place from Sept. 29 to Oct. 5, 2013.

Further interesting workshops on discrepancy theory in 2013:

A Workshop on Discrepancy, Numerical Integration, and Hyperbolic Cross Approximation, organized by V.N. Temlyakov (South Carolina) and T. Ullrich (Bonn), will take place at HCM Uni Bonn September 2013.
A Workshop on Uniform Distribution Theory and Quasi-Monte Carlo Methods, organized by F. Pillichshammer, P. Kritzer, H. Niederreiter, and A. Winterhof, will take place at the RICAM in Linz from October 14-18.

Recent Preprints

J. Baldeaux, M. Gnewuch. Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition, arXiv:1209.0882v1 [math.NA], Preprint 2012.
J. Dick, M. Gnewuch. Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence, arXiv:1210.4223 [math.NA], Preprint 2012.
C. Doerr, M. Gnewuch, M. Wahlström. Calculation of Discrepancy Measures and Applications, Preprint 2012. To appear in: W.W.L. Chen, A. Srivastav, G. Travaglini (Eds.), Panorama of Discrepancy Theory, Springer-Verlag.
M. Gnewuch. Lower error bounds for randomized multilevel and changing dimension algorithms, arXiv:1209.1808 [math.NA], Preprint 2012. To appear in: J. Dick, F. Y. Kuo, G. Peters, I. H. Sloan (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer-Verlag.
M. Gnewuch, S. Mayer, K. Ritter. On weighted Hilbert spaces and integration of functions of infinitely many variables, Preprintreihe DFG-Schwerpunktprogramm 1324, Preprint 133, 2012.

Teaching (Lehre)

Ab Sommersemester 2013

Lehre an der TU Kaiserslautern.

Sommersemester 2012/Wintersemester 2012/13

Research Fellow an der University of New South Wales in Sydney.

Wintersemester 2011/12

Vorlesung Die probabilistische Methode und ihre Anwendung
Übungen zu die probabilistische Methode und ihre Anwendung

Sommersemester 2011

Seminar Quasi-Monte-Carlo-Simulation und Anwendungen in der Finanzmathematik in Theorie und Praxis (Zeit: Freitag 12:30 -- 14:00. Raum: Mathematisches Seminar Raum 124 (Zeichensaal).

Wintersemester 2010/11

Wintersemester 2009/10, Sommersemester 2010

Research Fellow an der Columbia University in the City of New York.

Wintersemester 2008/9

Sommersemester 2008

Wintersemester 2007/8

Sommersemester 2007

Seminar Graphentheorie

Wintersemester 2006/7

Sommersemester 2006

Wintersemester 2005/6

Übung zu Numerik partieller Differentialgleichungen (Finite Elemente)

Publications

Articles

M. Gnewuch. Lower error bounds for randomized multilevel and changing dimension algorithms, arXiv:1209.1808 [math.NA], Preprint 2012. To appear in: J. Dick, F. Y. Kuo, G. Peters, I. H. Sloan (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer-Verlag.
M. Gnewuch. Infinite-Dimensional Integration on Weighted Hilbert Spaces, Mathematics of Computation 81, 2175-2205, 2012.
M. Gnewuch, M. Wahlström, C. Winzen. A new randomized algorithm to approximate the star discrepancy based on threshold accepting., SIAM Journal of Numerical Analysis 50, 781-807, 2012.
M. Gnewuch. Weighted Geometric Discrepancies and Numerical Integration on Reproducing Kernel Hilbert Spaces, Journal of Complexity, Vol. 28, 2-17, 2012.
M. Gnewuch. Entropy, Randomization, Derandomization, and Discrepancy., in: L. Plaskota, H. Wozniakowski (Eds.),Monte Carlo and Quasi-Monte Carlo Methods 2010, 43-78, Springer-Verlag, 2012.
M. Gnewuch, H. Wozniakowski. Quasi-Polynomial Tractability, Journal of Complexity, Vol. 27, 312-330, 2011.
B. Doerr, M. Gnewuch, M. Wahlström. Algorithmic construction of low-discrepancy point sets via dependent randomized rounding, Journal of Complexity, Vol. 26, 490-507, 2010.
B. Doerr, M. Gnewuch, M. Wahlström. Implementation of a component-by-component algorithm to generate small low-discrepancy samples, in: P. L'Ecuyer, A. B. Owen (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2008, 323-338, Springer, Berlin Heidelberg, 2009.
M. Gnewuch, H. Wozniakowski. Generalized Tractability for Multivariate Problems, Part II: Linear Tensor Product Problems, Linear Information, and Unrestricted Tractability, Foundations of Computational Mathematics, Vol. 9, 431-460, 2009.
M. Gnewuch. On Probabilistic Results for the Discrepancy of a Hybrid-Monte Carlo Sequence, Journal of Complexity, Vol. 25, 312-317, 2009.
G. Ökten, M. Gnewuch. Correction of a proof in A probabilistic result on the discrepancy of a hybrid-Monte Carlo sequence and applications, Monte Carlo Methods and Applications, Vol. 15, 169-172, 2009.
M. Gnewuch, A. V. Rosca. On G-discrepancy and mixed Monte Carlo and quasi-Monte Carlo sequences, Acta Universitatis Apulensis, Vol. 18, 97-110, 2009.
M. Gnewuch, A. Srivastav, C. Winzen. Finding Optimal Volume Subintervals with k Points and Calculating the Star Discrepancy are NP-Hard Problems, Journal of Complexity, Vol. 25, 115-127, 2009.
M. Gnewuch. Construction of Minimal Bracketing Covers for Rectangles, Electronic Journal of Combinatorics, Vol. 15(1), Research Paper 95, 20 pages, 2008.
B. Doerr, M. Gnewuch, P. Kritzer, F. Pillichshammer. Component-by-component construction of low-discrepancy point sets of small size, Monte Carlo Methods and Applications, Vol. 14, 129-149, 2008.
M. Gnewuch. Bracketing numbers for axis-parallel boxes and applications to geometric discrepancy, Journal of Complexity, Vol. 24, 154-172, 2008.
M. Gnewuch, H. Wozniakowski. Generalized Tractability for Linear Functionals, in: A. Keller, S. Heinrich, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006, 359-381, Springer, Berlin Heidelberg, 2008.
B. Doerr, M. Gnewuch. Construction of low-discrepancy point sets of small size by bracketing covers and dependent randomized rounding, in: A. Keller, S. Heinrich, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006, 299-312, Springer, Berlin Heidelberg, 2008.
M. Gnewuch, R. Lindloh, R. Schneider, A. Srivastav. Cubature formulas for function spaces with moderate smoothness, Journal of Complexity, Vol. 23, 828-850, 2007.
B. Doerr, M. Gnewuch, N. Hebbinghaus, F. Neumann. A Rigorous View On Neutrality, Kay Chen Tan et al. (Eds), Proceedings of the 2007 IEEE Congress on Evolutionary Computation, 2591-2597, Singapore, IEEE Press, Vancouver, BC, Canada, 2007.
M. Gnewuch, H. Wozniakowski. Generalized Tractability for Multivariate Problems, Part I: Linear Tensor Product Problems and Linear Information, Journal of Complexity, Vol. 23, Issue 2, 262-295, 2007.
B. Doerr, M. Gnewuch, N. Hebbinghaus. Discrepancy of Symmetric Products of Hypergraphs, Electronic Journal of Combinatorics, Vol. 13, Research Paper 40, 10 pages, 2006.
M. Gnewuch. Differentiable L^p-functional calculus for certain sums of non-commuting operators, Colloquium Mathematicum, Vol. 105, No. 1, 105-125, 2006.
B. Doerr, M. Gnewuch, A. Srivastav. Bounds and Constructions for the Star-Discrepancy via Delta-covers, Journal of Complexity, Vol. 21, Issue 5, 691-709, 2005, Elsevier.
M. Gnewuch. Bounds for the average L^p-extreme and the L^\infty-extreme discrepancy, Electronic Journal of Combinatorics, Vol. 12, Research Paper 54, 11 pages, 2005.
M. Gnewuch. Spectral multipliers for sub-Laplacians on amenable Lie groups with exponential volume growth, Mathematische Zeitschrift, Vol. 246, No.1-2, 69-83, 2004, Springer-Verlag.

Extended Abstracts and Draft Papers in Proceedings

M. Gnewuch. Weighted L_2 B discrepancy and approximation of integrals over reproducing kernel Hilbert spaces, In: T. Müller-Gronbach, L. Plaskota, J. F. Traub, Dagstuhl Seminar Proceedings, Seminar 09391, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2009. (For a generalized and extended version see the article "Weighted Geometric Discrepancies and Numerical Integration on Reproducing Kernel Hilbert Spaces".)
M. Gnewuch. Discrepancy bounds for mixed sequences, In: T. Müller-Gronbach, L. Plaskota, J. F. Traub, Dagstuhl Seminar Proceedings, Seminar 09391, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2009.
M.Gnewuch. Construction of low-discrepancy point sets of small size, Proc. Appl. Math. Mech. 7, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, 1022605-1022606 (2007). (DOI 10.1002/pamm.200700453)
B. Doerr, M. Gnewuch, N. Hebbinghaus. Discrepancy of Products of Hypergraphs, Discrete Mathematics & Theoretical Computer Science, Proceedings of the European Conference on Combinatorics, Graph Theory and Applications 2005.
M. Gnewuch. Geometric discrepancies and delta-covers, Oberwolfach Reports 1 (2004), 687-690.

Theses

High-Dimensional Problems: Multivariate Linear Tensor Product Problems, Multivariate Numerical Integration, and Geometric Discrepancy, Habilitation thesis, Kiel, June 2009.
Zum differenzierbaren Funktionalkalkül auf Lie-Gruppen mit exponentiellem Volumenwachstum, Dissertation thesis, Kiel, March 2002.
Die Integralgleichungsmethode für elliptische Randwertprobleme, Diploma thesis (enhanced version), Kiel, February 1998.

Older Preprints and Technical Reports

M. Gnewuch. On Selfadjointness and Spectral Multipliers for Sums of Non-Commuting Operators, Erwin Schrödinger International Institute for Mathematical Physics, Vienna 2003, ESI-Preprint No.1401. (A revised and shorter version appeared in Colloquium Mathematicum 2006, see category "Articles".)
M. Gnewuch, S. A. Sauter. Boundary integral equations for second order elliptic boundary value problems, Max Planck Institute for Mathematics in the Sciences, Leipzig 1999, Preprint No.55.

Recent Talks

12.02.13, 5th Workshop on High-Dimensional Approximation (HDA 2013) , Canberra, Australia. New Results on Infinite-Dimensional Integration in the Deterministic and Randomized Setting.
04.10.12, Oberseminar Theoretische Numerik, Friedrich-Schiller-Universität Jena, Jena. Convergence of Net Quadratures in Fractional Haar Wavelet Spaces and Spaces of Fractional Smoothness.
24.09.12, Dagstuhl Seminar 12391: Algorithms and Complexity for Continuous Problems, Dagstuhl. Infinite-Dimensional Integration: Optimal Randomized Multilevel Algorithms in the ANOVA Setting and Related New Results.
28.06.12, 3. International Conference on Uniform Distribution Theory 2012 (UDT 2012), Smolenice (Slovakia). Randomized Algorithms to Approximate Discrepancies and Applications.
13.02.12, 10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2012), Sydney (Australien), Special Session Point Sets and Sequences for Quasi-Monte Carlo. New Multilevel Algorithms Based on Quasi-Monte Carlo Point Sets.
29.08.11, 8th IMACS Seminar on Monte Carlo Methods (MCM 2011), Special Session Stochastic Computation and Complexity of High-Dimensional Problems, Borovets (Bulgaria). A Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting
18.07.11, 7th International Congress on Industrial and Applied Mathematics (ICIAM 2011), Special Session Information-Based Complexity: Avoiding the Curse of Dimensionality, Vancouver (Canada). Infinite-Dimensional Numerical Integration
05.07.11, Foundations of Computational Mathematics (FoCM 2011), Workshop on Information-Based Complexity, Budapest (Hungary). Multilevel Algorithms for Infinite-Dimensional Integration
27.06.11, 4th Workshop on High-Dimensional Approximation (HDA 2011), Bonn (Germany). Infinite-Dimensional Numerical Integration
21.06.11, Workshop on Theoretical Aspects of High-Dimensional Problems and Information-Based Complexity, Hausdorff Research Institute for Mathematics, Bonn (Germany). When are Multivariate and Infinite-Dimensional Integration on Reproducing Kernel Hilbert Spaces Related to Geometric Discrepancy?
22.02.11, University of New South Wales, Computational Mathematics Seminar, Sydney (Australia). Relation between (Weighted) Geometric Discrepancy and (Weighted) Numerical Discrepancy
18.01.11, Antrittsvorlesung, Faculty of Mathematics and Natural Sciences, CAU Kiel (Germany). (Quasi-)Monte-Carlo-Methoden
07.12.10, Johannes Kepler Universität Linz, Institut für Finanzmathematik, Linz (Austria). Relation between Geometric Discrepancy and Numerical Discrepancy in the Weighted and Unweighted $L_2$-Setting
11.10.10, Technische Universität Kaiserslautern, Oberseminar der Arbeitsgruppe Computational Stochastics, Kaiserslautern (Germany). Weighted Geometric Discrepancies and Numerical Integration on Reproducing Kernel Hilbert Spaces
20.08.10, 9th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2010), Warsaw (Poland), Invited Plenary Talk. Entropy, Randomization, Derandomization, and Discrepancy
19.08.10, 9th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2010), Warsaw (Poland), Special Session "Point Sets and Sequences for QMC". Fractional Discrepancy
07.07.10, 2. International Conference on Uniform Distribution Theory 2010 (UDT 2010), Strobl (Austria). Fractional Discrepancy
29.03.10, Columbia University, Seminar on Information-Based Complexity, New York (USA). Infinite Dimensional Integration on Weighted Hilbert Spaces
16.12.09, Habilitation lecture, Faculty of Mathematics and Natural Sciences, CAU Kiel (Germany). Der Preis der Anarchie
09.12.09, Columbia University, Seminar on Information-Based Complexity, New York (USA). Inefficiency of equilibria in non-atomic congestion games
24.09.09, Algorithms and Complexity for Continuous Problems, Dagstuhl (Germany). Discrepancy bounds for mixed sequences
23.04.09, Girl's Day, Faculty of Engineering, CAU Kiel (Germany). Planare Graphen
19.02.09, 3rd Workshop on High-Dimensional Approximation (HDA 2009), Sydney (Australia). Algorithmic Construction of Low-Discrepancy Point Sets via Dependent Randomized Rounding
16.01.09, Kolloquium des Mathematischen Seminars der CAU Kiel, Kiel (Germany). Diskrepanz und Entropie
09.07.08, Eighth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2008), Montreal (Canada). Calculation of the Star Discrepancy and Related Problems
16.06.08, Foundations of Computational Mathematics (FoCM 2008), Hong Kong (China). Generalized Tractability of Linear Tensor Product Problems--The Unrestricted Setting
24.04.08, Girl's Day, Faculty of Engineering, CAU Kiel (Germany). Graphen und Algorithmen
29.11.07, Workshop on Algorithms, Kiel (Germany). Calculation of the Discrepancy of Point Configurations
25.09.07, Columbia University, Seminar on Information-Based Complexity, New York (USA). Construction of Low-Discrepancy Sets
11.09.07, Columbia University, Seminar on Information-Based Complexity, New York (USA). Generalized Tractability for Linear Functionals
01.08.07, First Joint International Meeting between the American Mathematical Society and the Polish Mathematical Society, Warsaw (Poland). Generalized Tractability for Linear Functionals
17.07.07, 6th International Congress on Industrial and Applied Mathematics (iciam 07) , Zurich (Switzerland). Construction of low-discrepancy point sets of small size
18.06.07, Workshop on Discrepancy Theory and Related Areas, Varenna (Italy). Approximation of the Discrepancy of a Given Set
29.03.07, Max-Planck-Institut für Informatik, Saarbruecken (Germany). Construction of low discrepancy sample spaces via dependent randomized rounding
28.09.06, Algorithms and Complexity for Continuous Problems, Dagstuhl (Germany). Generalized Tractability of Linear Tensor Product Problems -The Restricted Setting
18.08.06, 7th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2006), Ulm (Germany). Bracketing covers for d-dimensional boxes and applications to geometric discrepancy
14.08.06, 7th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2006), Ulm (Germany). Generalized tractability for linear tensor product problems
28.03.06, Scuola Normale Superiore di Pisa, Seminari della Classe di Scienze, Pisa (Italy). Differentiable L^p-functional calculus for certain sums of non-commuting operators
15.01.06, Conference on Harmonic Analysis and Related Problems, Zakopane (Poland). Bracketing numbers for axis-parallel boxes and application to the theory of uniform distributions

Mathematical Education

I studied Mathematics at the University of Kiel and got my diploma and doctoral degree there.

My diploma thesis in Numerical Analysis deals with integral equations for second order elliptic boundary value problems. My supervisors were Prof. Dr. Wolfgang Hackbusch and Prof. Dr. Stefan A. Sauter.

I made my doctoral thesis in Harmonic Analysis under the supervision of Prof. Dr. Detlef Müller. The dissertation was about spectral multipliers for differential operators on exponential growth Lie groups.

During my dissertation I stayed 18 months at the University of Genoa, Italy, with the group of Prof. Giancarlo Mauceri.

After staying in northern Italy, I visited Prof. Peter Sjögren at Chalmers University in Gothenburg, Sweden, for three and a half months as a postdoc.

Since October 2002 I am part of the research group in Discrete Optimization here in Kiel. I am interested in Discrepancy Theory, multivariate numerical Integration, and Complexity of high-dimensional continuous problems.

Working in these areas, I spent research periods at the University of Warsaw (March 2005), the Max Planck Institute of Mathematics in the Sciences in Leipzig (April-September 2005), the Friedrich-Schiller-Universität in Jena (May-July 2007), Columbia University in the City of New York (September 2007 and from September 2009 until August 2010), and the University of New South Wales in Sydney (February-March 2009, February-March 2011, and from February 2012 until March 2013).